I periodically collect postings about similar subject matter into a compound posting. With spacecraft from India and Russia reaching the moon why not gather the postings about the moon into a book-length compound posting? There are links to the other compound postings in "Listing Of Compound Postings", December 2022.
TABLE OF CONTENTS
1) Really Understanding The Moon
2) The Earth, The Moon, And The Sun
3) The Rilles On The Moon
4) The Strawberry Moon
5) The Apollo Space Program
6) The Lunar Express
7) Tides And The Distance To The Moon
8) Measuring The Distance To The Moon
1) Really Understanding The Moon
This is something that supports the geological theory that is detailed in the compound posting, "The Story Of Planet Earth", on the geology blog, www.markmeekearth.blogspot.com .
In that theory, where this posting has been added to the "Supporting Documents", the moon and the continents on earth were formed from three "Continental Asteroids" that impacted the earth in succession. This is not a new idea, the moon has long been believed to have formed from the debris of a Mars-sized object, which has been named Theia, that struck the earth, and most of the material from it was hurtled back into earth orbit, where it eventually coalesced by gravity to form the moon.
But my theory takes it further. There were actually three successive impacts, although it could have been that the Mars-sized object had broken apart in orbit into three pieces before impacting the earth. It is highly unlikely that all of the matter from the impacts would have bounced back into space, with none remaining on earth. In my theory, it was the matter from the three impacts that remained on earth which formed the continents. As the theory points out, there are three clear "Original Impact Lines", long and otherwise-unexplained ranges of mountains, that are remnants of these impacts.
This geological theory leaves virtually no major feature of the earth's surface, either on land or the seafloor, unexplained. What happened is that each of the three impacts left a mass on the earth's surface that unbalanced it's rotation. The earth regained it's rotational balance each time by shifting on it's axis so that the center of the new mass on the earth's surface was at one of the poles. In all three impacts, it was the south pole that shifted so that it was at the center of the new mass. That is the reason that the present south pole is in Antarctica.
The spin of the earth causes magma, molten rock from below the surface, to emerge along the earth's equator. But then that must be balanced by longitudinal lines of magma emergence that are perpendicular to the equator. But when the poles shifted to accommodate the new mass of each of the Continental Asteroids, a new set of equatorial and longitudinal lines of magma emergence had to form. But geology changes at a, well, "geological" pace, and the former set of equatorial and longitudinal lines of magma emergence would remain active for a long time.
But what about the moon, after it had formed? What if there had been another impact of a very large asteroid on the already formed moon?
There actually was. One of the largest impact craters in the Solar System is at the moon's south pole. It is known as the Aitken Basin. But let's stop and think. Why would this impact crater be right at the moon's south pole? That would mean that the impact would have had to come at a direction that was perpendicular to the primary orbital plane of the Solar System, and any such impact would have been much more likely to occur in this plane.
The impact greatly changed the surface of the moon, forming a deep and vast depression area. This would have upset the moon's rotational balance. The moon actually does rotate even though it is gravitationally locked by the earth's gravity so that the same side of the moon always faces the earth. We could say that the moon's day is the same length as it's year.
Could it be that when the great impact that formed the Aitken Basin occurred, it was not then at the moon's south pole but the moon shifted it's poles in order to regain rotational balance so that, like the Continental Asteroids on earth, the place that had the change in mass so that the rotational balance was upset is now at the moon's south pole?
The difference between the impact that caused the Aitken Basin and the Continental Asteroids on earth is that the earth's rotational balance was upset three times by the addition of mass on it's surface, while the moon's rotational balance was upset by the loss of mass from it's surface.
The reason for this difference is simply that the earth's surface gravity is six times that of the moon, and the earth held on to mass from each of it's Continental Asteroids, while the moon's much weaker gravity resulted not only the mass of the impact asteroid bouncing back into space, but also mass from it's surface being carved out by the impact and thrown into space. The resulting hollow is the Aitken Basin. If Continental Asteroids can be massive enough to cause the earth to shift on it's axis to regain rotational balance with the addition of the new mass, then it is completely logical that the moon, with a mass only 1 / 81 that of the earth would also undergo such a shift.
Another question is the "seas", or maris, on the side of the moon that faces earth. In ancient times, these were believed to be seas, hence the name. but are actually volcanic lava plains. These seas occur only on the side of the moon that always faces earth, and not on the far side.
The reason for this is obvious. If the moon, with 1 / 81 the mass of the earth, can cause tides in the earth's oceans, then what effect should we suppose that the gravity of the earth, 81 times that of the moon, would have on volcanic lava in times past when the moon was known to have much volcanic activity? The earth's gravity had a tidal effect, pulling the magma to the surface, and forming the lava plains that we call "seas".
But if that is what happened, the tidal effect should be strongest in the moon's equatorial region. But yet these "seas" are concentrated in the northern hemisphere of the moon.
https://en.wikipedia.org/wiki/Moon#/media/File:FullMoon2010.jpg
How can we explain this?
What if my hypothesis here is correct and the moon did shift on it's axis as described. The impact that caused the Aitken Basin would have been most likely to occur on the side of the moon that faces away from earth, because that is the side that faces outward toward space away from the sun from which direction an asteroid would likely come. The moon's south pole would then shift so that the resulting basin was at the south pole. This would then shift the "seas" on the side of the moon that faces earth northward, and that is indeed where they are seen today.
So then if this is what happened, it supports my geological theory because the same process happened on earth with the impact of each of the three Continental Asteroids.
But why is it always the south pole that shifts to the center of the new mass discrepancy, and not the north pole?
The answer to that is simple also. It is actually a reflection of the rotational direction of the large star that preceded the sun before it is known to have exploded in a supernova. The sun and planets were formed by some of the debris of that exploding star which fell back together by gravity. We know that this previous star must have been larger than the sun because only the largest stars explode as a supernova, and the sun is not large enough. This means that some of the mass of that previous star was permanently thrown out into distant space.
The star would have been rotating and the centrifugal force of the star's rotation would have been added to the force of the supernova explosion so that it would be more of the polar mass that would have come together to form the present sun and planets. But, if we form a mental picture of that happening, we then see that the rotational plane of the planets today must be perpendicular to the rotational plane of that previous star,
What that means is that the north and south poles of the earth and moon are roughly aligned with the rotational direction of that previous star that exploded in a supernova. But we cannot tell which direction that star rotated in, or can we?
Information and energy is never lost and the information and rotational energy of that previous star must somehow be traceable in the Solar System that we see today. It is actually seen in why it is always the south pole of the earth and moon that shifts when it is necessary to regain rotational balance. The rotational direction of that star was from what is now north to south.
But if it was north to south on one side of the previous star's rotation then it must have been the opposite, south to north, on the other side. The fact that all three Continental Asteroids on earth and then this impact on the moon all resulted in the south pole being the one that shifted to regain rotational balance shows that an instantaneous factor is at work here. The Mars-sized object, named Theia, that would break into three pieces before each successively struck the earth to form the continents and then the fragments that bounced back into space coalesced by gravity to form the moon shows that it must have entered earth's orbit at a point on the earth's orbit around the sun where the rotational direction of the previous star, that exploded in the supernova, would have been what is now north to south.
One more thing about the moon. As I have written here before, we should really stop referring to the far side of the moon as the "dark side of the moon". That side actually gets more sunlight than the side that always faces earth. The side that faces the earth also faces the sun when it is on the far side of the earth from the sun, at full moon. But the far side of the moon faces the sun when it is closer to the sun than the earth, at new moon, thus we can safely say that the far side of the moon is actually the "bright side of the moon".
2) The Earth, The Moon, And The Sun
It has become clear to me that our concept of the gravitational relationship between the earth, sun and, moon is far from accurate. Conventional wisdom is that the moon orbits the earth while the earth orbits the sun.
But how can the moon possibly orbit the earth? The sun is 400 times as far away from the moon as the earth is but the sun is about 331,950 times the mass of the earth. Since gravitational force is inversely proportional to the square of the distance and the square of 400 is 160,000, the sun exerts 2.07 times the gravitation force on the moon that the earth does.
A smaller body, such as the moon, will logically orbit the larger body that exerts the strongest gravitational force on it. This can only mean that the moon really orbits the sun and not the earth, regardless of how it appears to us. My conclusion is that both the earth and the moon follow the same fundamental orbit around the sun, which I will refer to as the Mean Orbital Path. The moon appears to us to orbit the earth because it interweaves with the earth along the Mean Orbital Path.
If the moon rotated freely, it would seem from there that the earth is orbiting the moon while the moon orbits the sun. Since the same side of the moon always faces the earth because of the earth's tidal force, this is not the case and the earth always remains in the same place in the lunar sky although the earth's phases change in the same way that the moon goes through phases as seen from earth.
Imagine an alternating weave of a thick line and a thin line around a straight line. The straight line represents the mean orbital path, the thick weaving line represents the earth and the thin weaving line represents the moon. The weave of the thin line, the moon follows exactly the same wavelength as the thick line, the earth, but it's weave goes much further from the baseline, the Mean Orbital Path on each cycle.
The earth and moon both weave around the Mean Orbital Path but the mass multiplied by distance from the mean orbital path remains the same. The moon weaves so much further away because it's mass is only 1/81 of the mass of the earth. The moon is 1/4 the earth's diameter and is made of the same type of rock as the earth's mantle but the earth has a heavy iron core that the moon is believed to lack.
The weave of the earth and the moon around the Mean Orbital Path is due to their mutual gravity. It is a dance that has been going on for thousands of millions of years. imagine a donut-shaped (doughnut) concrete platform in space with a hole in the middle of it. Now suppose someone were to throw a ball upward from the platform. The ball would travel upward until the gravity of the platform pulled it back down. But, with no air resistance in space, the momentum of the fall back to the platform would propel the ball an equal distance on the opposite side of the platform as long as it went through the hole. Then it would come to a halt and fall back to the platform again and the cycle would continue indefinitely.
This is what happens in the dance of the earth and the moon as they travel along the Mean Orbital Path around the sun. Both attract each other by gravity from opposite sides of the baseline but then go past the line in opposite directions due to momentum. But then each comes to a halt in their movement away from each other and the Mean Orbital Path and then fall back toward each other again, all the while orbiting the sun.
The earth and moon cross the Mean Orbital Path at the same time but not at the same point. Both earth and moon actually vary in their velocity in orbit around the sun, the moon a lot more than the earth due to it's relatively smaller mass. The moon moves around the sun due to the pull of the sun's gravity on it. But sometimes the moon is between the earth and the sun in it's interweaving with the earth. During this time the earth's gravity is on the opposite side to the sun in that it is pulling on the moon from the opposite direction, this causes the moon to slow down. At other times, the moon is on the other side of the earth from the sun so that the earth's and sun's gravity are both pulling on it from the same direction, this causes the moon to speed up. This means that the moon actually moves more slowly in it's orbit around the sun when it is closer to the sun.
The moon is on the mean orbital baseline, as is the earth, when we see the moon exactly half illuminated by the sun. It is moving more quickly so that it moves ahead of the earth when it's phase is more than half and it is moving more slowly so that it falls behind the earth in the orbit when it's phase is less than half illuminated, such as at new moon. Thus the moon alternates between pulling ahead of and falling behind the earth in the orbit around the sun, while maintaining roughly the same distance from earth. This causes the appearance of it orbiting the earth.
If astronauts had lived on the moon for a period of time, they would have surely noticed this variation in speed every 29 earth days as it orbits the sun. The earth also moves faster when the moon is on the same side of it as the sun and vice versa but this variation has apparently been too slight for us to notice. However, this must be the way it is. The moon cannot possibly behave the same when the relative alignment of the earth and sun change. But since there is no visible change to us, the only possible change must be in velocity that causes us to perceive the moon orbiting the earth.
Once again, that is impossible if the sun exerts more than twice the gravitational force on the moon that the earth does. One full cycle in this dance is 46,394,937 miles (79,229,479 km) along the mean orbital path, or 29 days. So, the weaving of the earth and moon along this line would appear to an outside observer as very flattened versions of sine waves. This seems to have never been noticed before because it causes the earth's distance from the sun to vary by less than the earth's diameter and during the course of a year, the earth's distance from the sun varies by more than three million miles (4,800,000 km) anyway.
The earth's tidal force on the moon caused the lava flows that produced the dark areas that we see on the moon and in doing so redistributed the moon's mass to reach a fine balance and stop the moon from rotating so that the same side of it always faces the earth. You may be wondering how the earth can have such a tidal effect on the moon while the sun apparently does not if the gravitational force of the sun on the moon is more than twice that of the earth.
Let me explain. This tidal effect is the result, not only of gravity but of a difference in gravity. If the force of gravity exerted on the earth's oceans by the sun and moon was exactly the same as the force they exerted on the rock layers under the ocean, there would be no tides. But the surface of the ocean is a few miles closer to the moon than the underlying earth.
This is what causes the tides, not the gravity but the difference in gravity. The tidal force is proportional to the gravitational force from the moon or sun divided by it's distance. The sun exerts 168 times the gravitational force on earth that the moon does but the sun is also 400 times as far away as the moon.
The result is that the tides in the earth's oceans by the moon are more than twice as high as those produced by the sun. This also means that on the moon, the tidal force produced by the earth is about 200 times that produced by the sun, even though the total gravitational force of the sun on the moon is more than twice that of the earth.
Imagine yourself on the moon. What would it be like? How would the sky look different than it does on earth?
It would depend which side of the moon you were on. The same side of the moon always faces earth, so that if you were on the far side of the moon you would never see the earth. From the far side of the moon, it would seem to be rotating to provide night and day, just as earth does. But, instead of 24 hours, a lunar day would last 29 earth days. Half would be dark, and half of that time would be light.
From the far side of the moon, the moon would not seem to rotate around it's center of mass, as the earth does, it would seem to be rotating around a point in space hundreds of thousands of kilometers away, which is where the earth is located. From the near side of the moon, the moon would seem to be rotating around it's center of mass. The earth would seem to rotate 29 times while the moon rotated once.
It would not appear, from the moon, that the moon is revolving around the earth, as it appears to us from earth. It would appear that the moon is revolving around the sun, but with the moon's distance to the sun varying by nearly half a million miles, about 700,000 km, during the course of the month.
This variation in distance would not be apparent with the naked eye, but would be measured if there were astronomers on the moon. The variation in distance from the sun is caused by the gravitational influence of the nearby earth, but it would not appear that the moon is in orbit around the earth.
From the side of the moon facing earth, there would be the same lunar day equal to 29 earth days with half of the time being light and the other half dark. The difference, of course, would be the earth. The earth would not appear to move at all in the sky. No matter where an observer was, on the side of the moon facing earth, the earth would always be in the same place in the sky.
There is a photo taken from the moon by astronauts titled "earthrise", as opposed to sunrise. However, this cannot be technically correct because since the moon does not rotate, relative to the earth, the earth cannot "rise" or "set" in the lunar sky.
The location of the earth in the sky would be determined by the observer's latitude and longitude on the moon. An observer at the moon's north pole would see the earth at the southern horizon, and vice versa. The same for the eastern and western limits of the half of the lunar surface that is visible from earth.
The position of the earth in the lunar sky would be even more valuable for surface navigation than is the North Star (Polaris). A lunar traveler could readily tell both his latitude and longitude by taking a sighting on the position of the earth in the sky. As the traveler headed northward, the earth would appear further south, as the traveller moved westward, the earth would appear further east. Travelers on the far side of the moon would have no such advantage.
The earth would always be visible from the near side of the moon, whether it was day or night there. The earth would appear with about four times the angular diameter that the full moon appears to us on earth. The moon from earth occupies about half an angular degree, the earth from the moon would occupy about two angular degrees.
From the earth, the sun and moon appear as about the same size in the sky because, while the sun is about 400 times the diameter of the moon, it is also about 400 times as far away. But the earth would appear as four times the diameter in the lunar sky, and periodically lunar day would become night as the earth blocked out the sun in what we see as a lunar eclipse, but the moon would experience as we do a solar eclipse.
It would not be entirely dark, but would be reddish because the earth's atmosphere would refract some long-wavelength red light around and onto the moon. We can see this red shade on the moon during a lunar eclipse.
An observer on the near side of the moon would see the earth going through phases similar to the phases of the moon as seen from earth. The rotation of the earth would be easily visible, and thus an earth day could be used on the near side of the moon as a unit of time. The lights of cities could probably be seen as a faint and eerie glow on the earth's night side.
There is a rule that I have noticed concerning the phase relationship between the earth and moon. At any given time, the phase of the moon as seen from the earth, and the phase of the earth as seen from the moon, expressed as a proportion of the full disc, must add up to one full disc.
For example, when we see a full moon an observer on the moon would not see the earth illuminated by the sun at all. In other words, the lunar observer would see a "new" earth. When we cannot see the moon, because the moon is between the earth and the sun, we refer to it as the new moon. At that time, an observer on the near side of the moon would see a full earth. When we see a half moon, and observer on the moon would see a half earth.
An observer on the moon would definitely consider the moon as in orbit around the sun, and not the earth as we see it. The fact is that, from the moon, the gravitational influence of the sun is more than twice that of the earth. I find that just the fact that there are eclipses are proof of this. The plane of the moon's apparent orbit around the earth is tilted about 5 degrees relative to the plane of the earth's orbit around the sun. But yet periodically, the three end up in the same plane or else there would not be eclipses.
If the gravitational influence of the earth on the moon were greater than that of the sun, there would be no reason for the planes of the two to coincide. The earth would be able to hold the moon in an orbit, the plane of which would not at all need to be the same as that of the earth around the sun.
But due to the fact that it is the gravity of the sun which is stronger at the moon, the plane of the apparent path of the moon around the earth still diverges from that of the earth around the sun, but it must change so that while it may be above or below the orbit of the earth around the sun at any given time, it must average out to be the in the same plane as the orbit of the earth around the sun.
This is why there are eclipses, because periodically the plane of the two are the same. But if the plane of the two were always the same, there would be both a lunar and a solar eclipse every month.
3) The Rilles On The Moon
A great mystery is the rilles on the moon. These are the naturally-occuring lines across it's surface, similar to canyons on earth, but the rilles are often very long. The rilles are of two basic types. Some seem to be associated with volcanic magma and seem to have had magma emerge through them. Others are like dry canyons and these are more likely to form straight lines than those associated with magma.
I find that there is a simple example for what formed these rilles.
The first reaction may be that the rilles are cracks in the moon's surface caused by the impact of meteorites. The moon has been bombarded by meteorites for billions of years, which formed the craters. But the pattern of rilles show no relationships with the impact craters. If the impacts caused the rilles then they should emanate from the craters, but they don't.
www.wikipedia.org/wiki/Rille#/media/File%3ARima_Ariadaeus-1.jpg
In contrast the rilles that appear to have had magma emerge through them do appear to have a relationship with the dark-colored maria, or "seas", on the moon that are visible from earth. What I mean by this is that they are more likely to form in the general area of the "seas".
www.wikipedia.org/wiki/Rille#/media/File%3AHadley_Sinuous_Rille.jpg
What is really interesting is the far side of the moon. The moon is tidally locked to the earth so that the same side of the moon always faces the earth. The two sides of the moon are very different. The side facing the earth has the extensive dark-colored "seas", which are virtually absent on the far side of the moon. The far side is more heavily cratered than the near side. This is explained first by the fact that the long-ago lava flows that formed the "seas" erased craters and second, that the far side of the moon is facing the asteroid belt when it is closer to the asteroids than to the earth and the near side is facing the asteroids when the earth is between the two. At this point most of the asteroids that would have hit the near side of the moon hit the earth instead.
But what I find so interesting is that these rilles seem to be missing from the far side of the moon. I can't find any documentation about rilles on the far side but looking closely at imagery of it I couldn't see any, while rilles are very common on the near side of the moon.
A quick review of tidal forces are that tides are not the result of just gravity, but rather a difference in gravity. Gravity operates by the Inverse Square Law, so that it's effect is greater closer to the source. This means that, due to the depth of earth's oceans, the moon's gravitational pull is greater at the surface than at the bottom. This is what causes the earth's tides. The sun also causes tides but since it is four hundred times as distant as the moon it's tidal effect is only about 40% that of the moon, even though the sun is millions of times more massive than the moon. The greater distance causes the proportional difference between gravity on the ocean surface, compared to the depths, to be less.
Similar to the concept of tides is that of the movement of glaciers during the ice ages. When there is a vast sheet of ice, and the earth is spinning, the part of the sheet closer to the equator is moving in the spin faster than the part that is further from the equator, due to the nature of a sphere. This has the effect of pulling the entire sheet of ice toward the equator.
The reason for the volcanic plains that we see on the near side of the moon as "seas" is clear. It is from the tidal forces of the earth's gravity. It pulled magma up on the near side of the moon, but not on the far side, in the same way that the moon causes the tides on earth except that the earth has 81 times the mass of the moon.
Consider that the moon was once much closer to the earth than it is now, believed to be only one-tenth it's present distance. The tidal effect is slowing the earth's rotation, transferring rotational energy into orbital energy for the moon, which causes it to move to a higher orbit. So, using the Inverse Square Law, if the moon was one-tenth it's distance from earth the tidal effect that the earth would have on the moon would be a hundred times as great.
If the moon was one-tenth it's current distance from earth it's diameter would be one-twelfth it's distance from earth. Using the Inverse Square Law, and remembering that the earth has 81 times the mass of the moon, we see that the gravity on the closest side would be 1.19 times as much as on the furthest side. This would put great stress on the moon, and would have the effect of pulling it apart. It would be enough to not only cause magma to emerge, to form the "seas", but also to cause fractures in the surface of the close side. These fractures are what we see today as the rilles. Those with magma beneath had magma emerge through them.
I actually got this idea while reading about Phobos, the largest and closest to the planet of Mars' two moons. There appear to be "fractures" across the surface of Phobos and it is believed that this is the result of tidal forces from Mars' gravity. Why wouldn't the same concept apply to earth's moon, especially since it was once much closer to earth? Another thing is the rings around the large outer planets, particularly Saturn. The rings are always closer to the planet than it's moons and the ring systems are widely believed to have resulted from old moons being torn apart by the planet's tidal forces.
4) The Strawberry Moon
Here is something that I have seen referred to but have never seen explained. Many people admired a recent "Strawberry Moon". It was noted that the moon has reached the lowest point in the sky.
It's all a matter of simple geometry.
The moon revolves around the earth as the earth revolves around the sun. The moon is illuminated by the light of the sun so that the new moon is when the moon is between the earth and the sun and the full moon is when the earth is between the moon and the sun. A half moon is when the moon is alongside the earth during the orbit of both around the sun.
The orbital path of the moon around the earth is elliptical, meaning that it is not perfectly circular. When the moon is thus closer to the earth it naturally appears larger in the sky. If the moon's closest approach to earth happens to coincide with a full moon it results in a brilliant "supermoon".
A solar eclipse is when the moon casts it's shadow on the earth and can happen only at new moon. A lunar eclipse is when the earth casts it's shadow on the moon and can happen only at full moon. The reason there is not both a lunar and a solar eclipse every lunar cycle is that the orbit of the earth around the sun and the orbit of the moon around the earth are not in exactly the same geometric plane, there is a difference of about five degrees between the planes of the two orbits.
The earth is tilted on it's axis 23 1/2 degrees relative to the plane of it's orbit around the sun. This is what causes seasons on earth. When the earth's northern hemisphere is at it's maximum tilt toward the sun it is called the Summer Solstice. The sun is at it's highest in the sky and the days are at their longest. As we might expect it is hotter than at the Winter Solstice, when conditions are opposite.
The band of the earth's surface 23 1/2 degrees north and south of the equator, where the sun is directly overhead at some point during the year, are known as the tropics. The Tropic of Cancer is the northern limit and the Tropic of Capricorn is the southern limit.
But since the earth is tilted on it's axis so that the sun appears higher in the sky during the summer, and lower in the sky during the winter, then what if the moon is visible at night? If the earth is tilted so that the sun appears higher during the day then that must mean that the moon will appear lower in the sky at night during the summer.
That is why it was recently reported that the moon had reached it's lowest point in the sky, in the first half of June. This explains the "Strawberry" Moon. The moon being lower in the sky caused it's light to pass through more of earth's atmosphere before reaching us. The dust particles in the atmosphere tend to scatter the shorter-wavelength blue light more than red, because they are close in scale to the wavelength of blue light.
During a major forest fire the sky sometimes appears temporarily orange or yellow. That is because larger dust and smoke particles are scattering longer wavelengths of light, but these larger particles will settle to earth while the smaller particles that scatter blue light will remain aloft.
This is why the sky is blue and also why the sun appears red at sunset and sunrise, because with more distance through the atmosphere the blue has been scattered out altogether. This is why a blue line can sometimes be seen from space along where night and day meet.
But why should the moon reach it's lowest point in the sky during the first half of June when the Summer Solstice doesn't occur until around June 21? Remember that the orbit of the moon around the earth and the orbit of the earth around the sun are not exactly in the same plane. There is a difference of about five degrees between the two. That is why the day when the sun is highest in the sky and the day when the moon is lowest in the sky do not exactly coincide.
5) The Apollo Space Program
Why don't we have a look back at the Apollo Space Program? This was certainly one of the great events of history, the first time a human had stepped onto a celestial body other than earth. For those readers who weren't around yet it was a fantastic time. I followed the moon landings when I was a boy.
There is an important factor in the success of America's space program that I would like to add, the war that made it possible.
Credit to Wikipedia for dates and fact checking. Dates given for each mission are launch dates, unless otherwise specified.
The Space Age began with the launching of the Soviet Sputnik satellite and then Yuri Gagarin being the first man in space, sent to orbit the earth. Alan Shepard would be the first American in space, in a suborbital flight, and John Glenn would be the first American in orbit. The competition was part of the Cold War scenario.
One thing that I don't think gets enough attention as boosting America's space program is the Korean War of 1950-53. This was the first major war in which jet aircraft were widely used. It wasn't thought of at the time but being a combat jet pilot is an ideal background for an astronaut. The three most famous names from America's space age are probably John Glenn, the first American in orbit, Neil Armstrong, the first man to step onto the moon, and Buzz Aldrin, the second man to step onto the moon. All three had been jet pilots during the Korean War.
Before John F. Kennedy was assassinated he expressed the goal of putting astronauts on the moon by 1970 and bringing them safely back home. There is no doubt that fulfilling Kennedy's vision was a primary reason for the success of the Apollo Space Program.
The heroes of the space program were not all astronauts. James Webb was the administrator of NASA during the Kennedy and Johnson Administrations. His service was considered as so valuable that he got the space telescope, which might be the most important space project of all, named for him. The very expensive space program was not universally popular and it took some convincing to get taxpayers to support it.
The moon is about a quarter the diameter of the earth, about 2,000 miles or 3,220 km. It is made of rock and, since it lacks an iron core, is 1/81 the mass of the earth. The moon's surface gravity is 1/6 that of earth, helping the astronauts to carry heavy loads. The average distance to the moon is 239,000 miles, or 384,500 km.
There is no universally accepted definition of where the atmosphere ends and outer space begins. The atmosphere doesn't end suddenly, it gradually fades out. The so-called "Karmann Line" is the altitude at which an aircraft would theoretically have to fly so fast to maintain lift, due to thinning air at higher altitudes, that it would exceed the necessary orbital velocity for that altitude. But that is just a definition with regard to technology.
The earth has an orbital velocity of about 5 miles, or 8 km, per second and an escape velocity of 7 miles, or 11.3 km, per second. But that applies to ballistic objects, not to a rocket with an engine.
Once a rocket is in outer space it is not necessary to keep the engine running. The rocket will keep moving in the direction it is pointed until it encounters a gravitational field. The engine is only necessary to accelerate, decelerate, or change direction.
For a spacecraft to just take off and reach the moon is actually impossible, due to the weight of the spacecraft and the fuel it would have to carry to escape earth's gravity. But we can get around this by using stages. The Apollo rockets had three stages added, besides the Service Module with the engine that would be used in outer space.
Each stage had it's own engine, fuel tank and oxygen tank. The difference between a jet and a rocket is that the jet takes in air for combustion while the rocket, which will be operating in airless outer space, brings it's own oxygen or oxidizer. The first stage is the largest and most powerful. When it has expended it's fuel it drops away and the second stage ignites.
The spacecraft still has the momentum built up by the first stage, but has shed it's weight. With existing fuels, and their weight to energy ratio, this is the only way to reach orbit. The first two stages were finished in about ten minutes and the third in about thirty minutes. One concern in the Apollo Program was the discarded third stage staying alongside the spacecraft, and potentially colliding with it, since the two had the same momentum.
It looks like the Artemis Program uses two stages, instead of three. America's earlier space programs, Mercury and Gemini, also only used two stages because they were only going to low earth orbit.
Rocket launch facilities are often located on the east coast of a country. This is because the earth rotates eastward and when the rocket takes off it picks up some of the earth's eastward momentum. So if something should go wrong the rocket will crash into the sea, rather than into a populated area. The moon also orbits eastward and orbits the earth in 29 days. 24 hours divided by 29 = 50 minutes, which is why the moon rises 50 minutes later each day. The launch site doesn't have to be on earth's equator but it's generally more efficient the closer to the equator it is, because the earth's spin is greatest at the equator.
A particularly challenging part of the space program was reentry into the earth's atmosphere when the mission was completed. If an unprotected spacecraft entered earth's atmosphere at the speed it was traveling through space it would burn up like a meteor. The capsule that returned to earth had a blunt bottom. This was designed to create a shockwave that carried away much of the energy involved in reentry, so that it wouldn't be manifested as heat. There was also a heat shield that would peel away layer by layer. Finally the spacecraft would splashdown in the ocean and be recovered by a navy ship.
Outer space is a very hostile environment. Small meteors will burn up in earth's atmosphere but above that there is no protection against meteors that might be traveling faster than bullets. The atmosphere also provides some protection from cosmic rays. The astronauts reported seeing flashes, even with their eyes closed, which were caused by cosmic rays. With no air to redistribute heat the side of the spacecraft toward the sun will get extremely hot while the other side gets freezing cold. This can be remedied by having the spacecraft do a gradual "roll".
The earth is a magnet, which is why a magnetic compass works. The magnetic lines of force through space, between the magnetic north and south poles, are known as the Van Allen Belts. These protect the earth from the stream of charged particles from the sun, which cause aurora, but beyond them there is no protection. This is what causes electronics in satellites to gradually break down.
Without this magnetic shield the charged particles could eventually strip away earth's atmosphere. This may be why the moon has no appreciable atmosphere. Lacking an iron core like earth it has practically no magnetic field.
An Apollo spacecraft would have three modules, besides the initial three stages. The Service Module would have the engine and fuel. The Command Module would house the astronauts. The Lunar Module is what would actually land on the moon, while the Command Module would remain in lunar orbit.
The Lunar Module would be discarded once the two astronauts who landed on the moon returned to the Command Module. The Service Module would be discarded before reentry into the atmosphere, and would burn up in the atmosphere. The Command Module, slowed by parachutes before splashdown, would be the only module that returned to earth.
After the Apollo spacecraft had attained earth orbit, called a "parking orbit", checks would be done from Mission Control, on the ground. Since the moon itself is in earth orbit it is possible to go to the moon without leaving earth orbit. If an object in orbit is given a boost in the same direction that it is orbiting it will then have more orbital energy and will climb to a higher orbit. It can be boosted as high as the moon.
It all works by the Inverse Square Law, an object that is given three times the orbital energy will climb to nine times the altitude but will move at only one-third the speed. Satellites are sometimes placed at an orbital altitude of 22,300 miles, or 35,890 km. At this altitude it will orbit earth at the same rate as the earth rotates. This is known as a geostationary orbit because the satellite can be made to stay over the same point on the earth's surface.
The same side of the moon always faces earth. Obviously all landings were done on the side facing earth because radio communication and television broadcast to earth would not be possible from the far side. Since the moon has practically no atmosphere an orbit at much lower altitude than on earth is possible, and the Lunar Module wouldn't have as far to travel.
The phase of the moon was important so the astronauts would be in daylight on the moon, not in the dark. The earth had to be visible from where the astronauts were to make possible radio and television communication with Mission Control.
This means that a lunar mission wouldn't be done at new moon, as seen from earth, because then it would be the far side of the moon that was lighted by the sun. If the mission was done at full moon that would mean communication and television broadcast to the earth would be done at night. Around the half moon phase would seem to be best. The landing site would be chosen and then it would be lit by the sun at half moon phase, either when the moon was waxing or when it was waning.
When the astronauts ascended from the moon back to the Command Module it had to be remembered that the moon is effectively rotating once as it orbits the earth every 29 days. If the Command Module was orbiting the moon in a given time frame, and the astronauts were on the moon for two days, it would have to be remembered that the place on the orbit to meet the Lunar Module would be displaced 2/29 of the moon's circumference at that latitude, backwards or forward depending on whether the Command Module was orbiting in the same direction as the moon orbits the earth.
There was so much that had to be taken into account that "rocket science" became a euphemism for any complicated task that required a lot of intelligence.
The Apollo Space Program was preceded by the Mercury and Gemini Programs. The primary difference between the programs was the number of astronauts on board. The Mercury Program carried one astronaut, Gemini carried two and Apollo carried three. The Mercury and Gemini Programs never went beyond low earth orbit, and only required two stages.
The Mercury Program lasted from 1958 to 1963. After satellites had been put into orbit the next step was to get humans into orbit. The first Americans got into orbit on this program. Seven astronauts were initially chosen and Alan Shepard is generally considered as the first American in space, although it was a suborbital flight. John Glenn was the first American to orbit in this program. During this program NASA took over the space program from the Air Force. Because of the initial seven astronauts each Mercury capsule had a 7 in it's name, such as "Friendship 7". The local channel 7 had a morning children's show called "Rocketship 7".
The Gemini Program lasted from 1961-66. Aside from carrying two astronauts the Gemini flights lasted longer than the Mercury. The NASA Mission Control at Houston was first used. Astronauts did spacewalks, outside the capsule.
The Apollo Missions were numbered. Apollo 1 unfortunately ended in tragedy before it even began. The mission was to be the first step to the moon, a three astronaut flight in low earth orbit. On February 21, 1967, during a launch rehearsal, an electric fire started and the three astronauts suffocated. Today the town of Amherst, NY has streets named for Roger Chaffee, Edward White and, Gus Grissom.
Image from Google Street View.
There had been uncrewed Apollo missions the year before but the 1 designation was used for the deceased astronauts.
Apollo 4, November 9, 1967, was an uncrewed orbital test of the new Saturn V (5) rocket. This rocket had three stages, which would be necessary to get to the moon, as explained above. The earlier Saturn 1B had only two stages.
Apollo 5, January 22, 1968, was another uncrewed orbital test. This time a model of the lunar module, that would actually land on the moon, was attached. You can see how the space program was progressing one step at a time. Each mission was just one step ahead of the last. The Apollo missions were each designated by a letter from A to J. The simplest uncrewed test was an A mission. The final few moon landings were J missions.
Remember that the world was watching, lives were at stake, the Saturn V was a completely new rocket and this was something absolutely unlike anything that had been done before. Three astronauts had already lost their lives. It had to be done carefully and one step at a time.
Apollo 6, April 4, 1968, was another uncrewed orbital test, with all modules attached.
Apollo 7, October 11, 1968, was the first crewed mission since the three astronauts died in Apollo 1. It was a test of everything, with an actual crew, in earth orbit. There was some reported tension between the astronauts and Mission Control, and none of the three astronauts ever flew again. A cardinal rule for an astronaut is not to be difficult to work with. The astronauts had backgrounds as fighter pilots or test pilots, and so are naturally used to working alone and thinking for themselves, as opposed to being "team players".
Apollo 8 was the first mission to the moon, around Christmas time 1968. The three astronauts didn't have a real lunar module, to actually land on the moon, but did ten orbits around the moon. A primary objective of this mission, aside from being the next step, was to help select sites for the landings on the surface that would come. In a broadcast to the world the astronauts read the first ten chapters of the Book of Genesis.
Although Apollo 8 didn't actually land on the moon it is the mission that I remember the best. I had just turned 8 years old and had landed in the United States. My new country was sending astronauts to the moon. In the school library I took out the following children's book and have been interested in science ever since.
Apollo 9, March 3, 1969, was a test with astronauts and a real lunar module, but it didn't leave earth orbit.
Apollo 10, May 18, 1969, was a close rehearsal of the landing that would come on the next mission. The astronauts, from lunar orbit, used the lunar module to approach the surface of the moon just as if they were going to land. They did everything except enter descent mode, that would have taken them down to the surface. They just made sure that everything was in working order, before returning to the Command Module, that was in orbit around the moon, and then back to earth.
They came within 16 km of the moon's surface. In the video you could see the craters close-up. I was near the end of third grade and didn't quite understand why they didn't just land.
There was a story that NASA considered the possibility that the Apollo 10 astronauts might disobey orders in order to be the first on the moon. The astronauts were reportedly told that there wasn't enough fuel in the Lunar Module to get them to the surface of the moon and then back to the Command Module. I suspect that there was enough fuel, just so it wouldn't be a disaster if they did try landing, but they certainly didn't want the astronauts to know that.
The Command Modules are the only part of the Apollo spacecraft that returned to earth, with the astronauts inside. The modules are all in various museums today. The Command Module of Apollo 10 is the only one that was given to another country. I have seen this module in the Science Museum in London.
Finally the day came when humans first walked on the moon. The unforgettable day was July 20, 1969. The mission was Apollo 11. The Lunar Module descent and then ascent stages both worked flawlessly. Neil Armstrong was the first man to step onto the moon, followed by Buzz Aldrin.
I remember a report that there was some tension over who would be on the moon first. But some of the astronauts were still in the military. Neil Armstrong was a civilian and I think it was decided that it would be appropriate to have a civilian step onto the moon first.
The mission went almost perfectly, the American flag that they planted on the moon was too close to the spacecraft and was knocked over when the Lunar Module took off to rejoin the Command Module, which was still in orbit. The Lunar Module was jettisoned after the astronauts were back in the Command Module, and crashed into the moon.
One thing that hadn't been anticipated about the moon is how much it's surface gravity varies from place to place. This caused Apollo 11 to miss it's intended landing site by several km. In 1967 an unmanned spacecraft with a camera, Surveyor 3, had been landed on the moon. In an amazing feat of precision Apollo 12, launched November 12, 1969, landed near Surveyor 3. The astronauts removed it's camera and brought it back to earth.
All had gone well in the space program since the loss of the three astronauts in the Apollo 1 launch rehearsal. That was not to last. Apollo 13, April 11, 1970, was the most tense and dramatic event of the program, except the first moon landing. An oxygen tank exploded on the way to the moon, crippling the spacecraft. The moon landing had to be cancelled.
The astronauts went around the moon to point them back toward earth. The Lunar Module was successfully used as a "life raft" to get the astronauts back home. Fortunately the explosion occurred before they reached the moon so that they hadn't yet discarded the Lunar Module.
The moon has mountains and Apollo 14, explored higher terrain. The astronauts had a "shopping cart" to move the scientific experiments around on the moon's surface. Seeds were brought to germinate in space, growing as the "Moon Trees" back on earth. Alan Shepard, who had been the first American in space in a suborbital flight, finally got to walk on the moon.
If modern computer terminology had been around Apollo 15 onward might have been referred to as "Apollo 2.0". Astronauts began staying longer on the moon and brought a vehicle, the Lunar Rover, to drive around on the moon. Since there is no air on the moon the Lunar Rover had to be electric.
Exactly in the center of the following photo are a large and a small white patch of light. The photo was taken from the Apollo 15 Command Module, in orbit around the moon. The large patch of light is sunlight reflecting off the Lunar Module, down on the moon's surface. The small patch of light looks like sunlight reflecting off the Lunar Rover, parked by the Lunar Module.
Image credit to Wikipedia article "Apollo 15".
Apollo 15 brought the famous televised experiment where a hammer and a feather were dropped from the same height. Because there is no air on the moon both hit the surface at the same moment. A plaque honoring fallen astronauts was placed on the moon. A privately-owned Bulova watch was brought to the moon, which greatly increased it's value.
Trouble came again, with Apollo 16 April 16, 1972. This time it was with the main engine. The decision was made that it was not necessary to cancel the mission, although it was shortened by one day.
Apollo 17, December 7, 1972, would be the last time humans have been on the moon. Apollo 18-20 had been cancelled. There was great interest in the geology of the moon and Harrison Schmitt was a professional geologist. Five mice were brought along, to test their exposure to cosmic rays. Since the earth is rotating, and the moon is moving around earth, there is a "launch window" for the spacecraft to most efficiently reach the moon. This meant Apollo 17 had to be launched at night.
After the trouble with Apollo 16 there was a story that Apollo 17 was pushed back until after Election Day so that it wouldn't risk costing Richard Nixon the presidency if it should end in disaster. I don't know how true the story is.
The Apollo astronauts left scientific equipment on the moon, some of which is still in use. There are sensitive seismometers that can detect the impact of a discarded Lunar Module anywhere on the moon. There is a laser reflector so that the precise distance to the moon can be measured. It is known that the moon is moving away from the earth by a few cm per year because the tides caused by the moon in the earth's oceans are transferring earth's rotational energy to the moon's orbital energy.
The Apollo Space Program was followed by Skylab, and then the Space Shuttle. Skylab was placed in earth orbit and was crewed, at different times, by three astronauts doing various experiments and making observations.
Skylab's orbit eventually deteriorated and it burned up in the atmosphere. Parts of it were found in a remote area of Australia. I saw it go by on one of it's final orbits. It was after dark but the sun was still shining on it so it looked like a bright moving planet.
The Space Shuttle was like a partially reusable space plane. Five were originally built. Like the earlier space programs it couldn't just take off into space, it was attached to a large external fuel tank and two solid fuel booster rockets which got it into orbit. Remember that direct flight into orbit is not possible with the weight of the spacecraft and existing fuels. It accomplished tasks like delivering the Hubble Space Telescope to orbit, and later servicing it.
The Space Shuttle had a crew of seven and there were two fatal mishaps, both of which killed the entire crew, the Challenger in 1986 and the Columbia in 2003. The Challenger was destroyed while taking off and the Columbia while re-entering the atmosphere. I was watching the Challenger launch live on television and wasn't sure why there were multiple lines of smoke all of a sudden.
I wonder if the Space Shuttle being designed for seven astronauts is a reflection of the original seven astronauts and Mercury missions all having a '7" in the name.
I think the greatest benefit by far of the Apollo Program were the technological spinoffs. Ronald Reagan tried to repeat the boost to the economy in the 1980s with the Strategic Defense Initiative.
There were inevitably stories that the moon landings were faked. There are places in Nevada that look like the moon. But for the moon landings to be faked, hundreds upon hundreds of people would have to be in on the secret. There is an old saying that the life expectancy of a secret is inversely proportional to the number of people that are in on it. Theories about the moon landings being faked are the domain of tabloids, not of serious media outlets.
The Apollo Space Program has left a lot for archaeologists of the future. With no water or air on the moon there is no erosion and the astronauts' footprints might last forever, unless struck by a meteor. The Lunar Modules, except for the one used to get the crew of Apollo 13 back to earth, all crashed into the moon after being discarded.
The descent stages of the Lunar Modules remain at the landing sites, along with the Lunar Rovers of the later missions, and whatever else the astronauts left behind. There were a number of Swedish-made Hasselblad cameras left on the moon. Some of the ejected rocket stages, for the trip to the moon, remain in orbit around the sun.
But the 1960s vision of regular space travel with colonies on the moon and other planets never came to be. One reason the Apollo Program was curtailed is that public interest in it was waning, and it was tremendously expensive.
The Space Age ended up giving way to the Computer Age. Anyone could never fly into space but anyone can have a smartphone. We also have to question the wisdom of sending people into space. During the Apollo years computer technology was extremely primitive. Now that has completely changed and we could just send robots, with artificial intelligence, into space. They don't need food, other than power, oxygen, or water. They don't have human emotions and we don't have to worry about getting them back home safely.
Space today is as active as ever but it is mostly about communication satellites in earth orbit and unmanned space probes out into the Solar System.
6) The Lunar Express
There is a posting on the Progress Blog titled "The Westbound Rule". This is an effort to make routine flight more efficient by parceling air corridors to take advantage of the earth's eastward rotation. I explained how it would be best if eastbound flights flew as low as is practical, because the earth's rotation is working with them, while westbound flights should fly as high as possible, to keep a distance from the rotation that is working against them.
Today, I would like to apply a similar concept to space flight between the earth and the moon.
The astronauts in the Apollo missions of around forty years ago obviously wanted to land on the moon where the sun was shining, not in the dark. The daylight on the moon made the mission much easier, particularly the taking of photographs, than it would been in the dark. But it is my observation that this may not be the best in the long run if lunar flight ever becomes routine.
Another factor in the lunar missions involved launches. The take-offs of the rockets during the afternoon was to accommodate the audiences and so that daylight would minimize the chances of errors and complications. But this meant that the spacecraft was launched eastward, along with the direction of the earth's rotation, and thus had to outpace the earth.
While this may have been good for public relations, it certainly was not the most efficient path.
Picture the moon orbiting the earth, as the earth orbits the sun. Of course, this is only an "apparent" orbit, as I described in section 2)"The Earth, The Moon And, The Sun", simply because, at the moon, the gravity of the sun is more than twice as powerful as that of the earth. However, that is not very important for our purposes here.
Let's review the mechanics of the moon, as seen from our perspective on earth.
The moon orbits the earth every 29 days, in the same eastward direction that the earth rotates. This is why the moon rises 50 minutes later each day or night. 24 hours divided by 29 equals about 50 minutes. The same side of the moon always faces earth because the moon's rotation period, or day, is the same as it's orbital period.
The phases of the moon that we see are due to the changing angles between the earth, moon and, sun. Full moon is when the moon is on the opposite side of the sun from the earth, so that those on the night side of the earth see the moon fully illuminated by the sun. Unless, of course, there is a lunar eclipse. This happens when earth, moon and, sun are in the same lateral plane in a straight line so that the earth casts it's shadow on the moon.
New moon is when the moon is between the earth and the sun so that we cannot see the moon at all. A solar eclipse can happen at this point, if all three are in the same plane and in a straight line. Eclipses do not occur every month because there is a difference of about 5 degrees between the moon's path around the earth and the earth's orbit around the sun.
We see a half moon when the moon crosses the earth's path around the sun. A half moon when the moon's phase is waxing, or getting more, between full and new moon, is when the moon crosses the earth's orbit in the direction from which the earth has already passed. A half moon when the phase is waning, or decreasing, is when the moon crosses the earth's path in the direction in which the earth is heading.
At sunset, the direction overhead is the direction from which the earth has come in it's orbit around the sun. At sunrise, the direction overhead is the direction in which the earth is heading. This means that a waxing half moon will be overhead at sunset, and a waning half moon will be overhead at sunrise, taking the observer's latitude into account.
Let's express the path of the moon around the earth, relative to the sun, in degrees and quadrants. Let 0 degrees be the new moon, 90 be waxing half moon, which is also called "first quarter". Let 180 be the full moon and 270 be the waning half moon, also known as "last quarter". This fits in with the posting on the Progress Blog, "New Trigonometric Functions", in which I proposed a function based on 180 degrees, "The Lunar Function", in addition to the standard 90 degree functions.
Here is a link to a diagram of the moon's phases: www.moonconnection.com/moon_phases.phtml
There are three gravitational zones that we will deal with in a trip between the earth and the moon. Simply that where the earth's gravity is the strongest influence on the spacecraft, that of the moon and, that of the sun. At the moon, the sun's gravity is more than twice as powerful as that of the earth so that the majority of the trip will be spent in the sun's gravitational zone.
The concept that I want to discuss today is my vision of optimum points of departure and return on opposite sides of the moon's path around the earth, about two weeks apart. The great advantage of this is that most of the flight will be simply letting the sun's gravity do the work for us. The spacecraft can be made to literally "fall" toward it's destination. First, to the moon, and then the return flight to the earth.
When a spacecraft is on the way to a destination toward the sun, such as Mercury or Venus, the sun's gravity can be put to work. At launch, the spacecraft is essentially a part of the earth orbiting the sun. If we point the engines of the spacecraft in the direction of the earth's orbital path, it will counteract the orbital momentum around the sun that the spacecraft has. This will cause it to lose orbital momentum and literally fall toward the sun, and it's destination.
My thought is that a launch early in the morning, some time after third quarter (waning half moon), would definitely bring about the best flight efficiency. Once the spacecraft left the earth's gravitational zone, the gravity of both the sun and the moon would be working for us, as well as the earth's rotational momentum. Assuming that the flight takes a few days, this would land the spacecraft on the moon with the new moon approaching, in which the side facing the earth is in the dark. Once we are more experienced at lunar landings, this should not be as much of a problem as it would have been in the days of the Apollo landings.
A first quadrant launch, between new moon and first quarter, is also a possibility. But this will make it necessary to speed up the spacecraft, to get ahead of earth in it's orbit around the sun. This would be less efficient than simply losing orbital momentum so that the spacecraft literally falls toward it's target.
I see the return flight back to earth as being best as we approach full moon, after first quarter. the gravity of both the earth and the sun would be working for us. Whereas if we went to the moon near full moon, this most powerful gravitational combination would be working against us. The return trip should be easier, simply because the gravity of the earth is much more powerful than that of the moon.
So, if we approach the moon between last quarter and new moon, and return between first quarter and full moon, all we need to do is to lose orbital momentum by pointing the rocket engines in the direction of the earth's orbit around the sun so that the rocket thrust counteracts this orbital momentum, and we will literally fall along either journey. Gravity will do most of the work for us. We must always consider the tremendous gravity of the sun so that we aim to hit the moon while it is toward the sun, and return to earth when it is toward the sun, relative to the moon.
There is another thing to consider for lunar flights. The Apollo lunar missions from Cape Canaveral in Florida first went into an equatorial orbit around the earth and then, upon arrival, and equatorial orbit around the moon. The landing sites were thus relatively close to the moon's equator.
Another possibility is using polar orbits. This would be more complex, in that we would have to calculate the trajectory in another dimension also, that of north-south. The moon would be approached so that the spacecraft would be to the north or south of the plane of the moon's path around the earth, and it would go into orbit over the moon's north and south poles rather than around it's equator. To accomplish this, we could make use of the 5 degree difference between the planes of the earth's orbit around the sun and the moon's path around the earth.
There are disadvantages to the polar orbit route. There is no rotational momentum to build on during launches, and the mission is simpler if all is kept in the same plane. But a polar approach would make it much easier to land on any specific site, both on the moon and the return to earth, instead of just in the zones around the equators.
7) Tides And The Distance To The Moon
I believe that it was possible to measure the distance to the moon centuries ago, just from what we can see on earth.
The tides in the earth's oceans are caused not just by the gravity of the moon, but by the difference in gravity. The gravitational effect of an object in space decreases with distance, according to the Inverse Square Law.
When the moon is directly overhead it's gravitational force on the surface of the ocean is greater than it's force on the bottom of the ocean. This is simply because, due to the ocean's depth, the bottom of the ocean is further away from the moon. This pulls the water toward the moon, creating the tidal bulge. Since the earth is rotating faster than the moon is revolving around it the tidal bulge effectively moves across the earth.
A tidal bulge forms directly beneath the moon. But there is also a difference in the moon's gravity in the ocean on the opposite side of the earth, at the point furthest away from the moon. This is because the moon's gravity, pulling right through the earth, exerts a greater force on the bottom of the ocean than on the surface, simply because the surface of the ocean is further away from the moon. So a tidal bulge forms on the opposite side of the earth as well.
These tidal bulges, on opposite sides of the world, come at the expense of water in between. Since the earth is rotating this causes two high tides and two low tides every 24 hours and 50 minutes. The 50 minutes is because the moon is revolving eastward around the earth, the same direction that the earth rotates, every 29 days. 24 hours divided by 29 is 50 minutes, meaning that the moon rises 50 minutes later each day.
The earth has a certain diameter. The closer the moon is to the earth the greater will be the earth's diameter, relative to the distance to the moon. This means that the tidal bulge on the opposite side of the earth should be somewhat less than that directly beneath the moon simply because, due to the earth's diameter, it is further away from the moon.
How can we measure the tidal bulge created by the moon's gravity? It is really simple. Since the earth is rotating the tidal bulges, and the low areas between them, wash over land. The difference between the high and low areas of water shows up on shore as the difference between high and low tide. This is known as the tidal range.
Since the opposite side of the earth is further from the moon we would expect the tidal range to be less there than directly beneath the moon. Since we know the diameter of the earth why couldn't we use the difference between high and low tide, when the same coastal point is on diametrically opposite sides of the earth, 12 hours and 25 minutes apart, to measure the distance to the moon? We have to remember that the decrease in gravitational force with distance is not linear, but operates by the Inverse Square Law.
If the distance to the moon is 30 times the diameter of the earth then we should expect the tidal bulge on the opposite side of the earth to be about .936 of that directly beneath the moon. This sounds like a simple and effective way to measure the distance to the moon.
Unfortunately there are a few complications that have to be taken into account. First is that the moon isn't the only factor in producing the tides, there is also the sun. Although the sun is exponentially more massive than the moon it is also 400 times as distant. The end result is that the effect of the sun on the tides is only about 40% that of the moon.
If the sun and moon are lined up relative to earth, at new moon and full moon, the gravity of the sun will reinforce that of the moon, giving a distorted reading. This is known as Spring Tide.
If the sun and moon are perpendicular in the sky, at half moon, the gravity of the two will work against each other, and the tidal range will be less, but this will give us a more accurate reading because it will eliminate the effects of the sun's gravity. This is known as Neap Tide.
If the earth's surface was perfectly smooth and all ocean it would be much easier to use this method. But geology is also a factor in tides, both land masses blocking the movement of the tidal bulge and the shape of the ocean basins. The way to get around this is to take many readings. The readings should show a Bell Curve pattern, with the top of the curve revealing the average distance to the moon, since the moon's orbit is somewhat elliptical so that the distance is not perfectly constant.
8) Measuring The Distance To The Moon
I would like to show how a calculation that I have never seen done before could have been done centuries ago, if we would have realized how information operates in the universe. The distance to the moon could have been calculated, long ago, by knowing just it's orbital period and the rate of free-fall of an object on earth. There must be a direct connection between the two because both are governed by the same gravity and, since gravity is a simple thing and there is no new information added, that connection must also be simple.
The distance to the moon can actually be measured just by things that we can easily measure on earth. We have to know that the earth is spherical and that the moon revolves around the earth, but we do not need to know that the moon's orbital velocity operates by the Inverse Square Law.
We do know that the moon revolves around the earth every 29 days. We can determine this simply by watching the moon go through it's phases. We can also notice that the moon rises 50 minutes later each day, then it did the day before. There is 24 hours in a day, and if we divide that by 50 minutes it tells us that the moon revolves around the earth every 29 days.
We can measure the acceleration due to gravity on earth of a falling object. This acceleration is 32 feet, or 9.75 meters, per second squared. This mean that, starting with a velocity of zero, a dropped object is moving 32 feet per second at the end of the first second, 64 feet per second at the end of the second second, and so on. In the real world this falling velocity does not increase indefinitely, due to air resistance, but we can ignore that for our purposes here.
This means that we can measure the distance that an object falls, in a given period of time, by use of multiples of 16 feet (4.88 m), a unit of measure that I refer to as a "grav", for gravity. I discussed this in my book, "The Patterns Of New Ideas", and also in the posting on this blog, "The Way Things Work". In the first second, the falling object starts at a velocity of zero and the velocity continuously increases to a velocity of 32 feet (9.8 m) per second, at the end of the first second. This means that the average velocity of the object during the first second was 16 feet (4.88 m) per second and, since it fell for one second, that must mean that it fell 16 feet (4.88 m).
This calculation is just easier to do in units of feet and miles, because it gives us round figures that we will not get if we use metric.
At the beginning of the second second of fall, the velocity is 32 feet per second, and is 64 feet per second at the end of the second second. This means that the average velocity during the second second is 48 feet per second, and since the second second is one second, it fell 48 feet.
Notice that 48 feet per second is three times 16 feet per second. This is how falling works, if we ignore air resistance. In the first second, the object falls 16 feet. In the second second, it falls 3 x 16 feet. In the third second, it falls 5 x 16 feet. This means that, by using 16 feet as a unit, we only have to square the number of seconds of fall to see how far an object will fall, ignoring air resistance. In the reverse of this, we can take the square root of a distance, expressed in units of 16 feet, to tell us how many seconds it would take to fall that distance.
The moon is moving at a certain average velocity as it orbits the earth. If we could just determine what that velocity was, we could tell how long it's orbital path was by multiplying it by 29 days. If we knew how long the moon's orbital path was, we could easily determine the distance to the moon by dividing it by 2 pi.
The orbit of the moon around the earth is governed by the same gravity that causes an object to drop on earth. When we drop an object, it's velocity continuously increases. At some point during the object's fall, and we can have a theoretical falling object, it will have a velocity that is identical to the average velocity of the moon in it's orbit. We only have to determine what that point is.
Gravity is a simple thing, there is nothing complicated about it. The movement of the earth in orbit and the fall of an object when dropped is governed by exactly the same gravity from the earth. This can only mean that the relationship that we are looking for must be a simple one.
The velocity of a falling object increases the further it falls. But the velocity of the moon in it's orbit decreases the further it gets from earth. Even if we did not know the Inverse Square Law, it wouldn't make sense that an object in orbit further from earth would move faster than one closer to the earth. We can see this by simply throwing a ball up in the air. It's velocity, whether on the way up or down, is greater the closer it is to the ground.
The velocity of the falling object increases according to the 32 feet, or 9.8 meters, per second, every second, as described above. But the orbital velocity of an object in orbit, such as the moon, decreases in accordance with the Inverse Square Law with increasing distance from earth. If an object is at nine times the distance from earth, it will orbit at 1/3 the velocity and will have three times the orbital energy.
This means that there must be a "crossing point" somewhere, at which the velocity of the falling object equals the velocity of the moon in it's orbit. We are trying to find that point.
The simplest and most logical relationship between these two examples of the same gravity is:
Time / Time = Distance / Distance
If the distance of one increases, the distance of the other must decrease, due to the fact that they have a "crossing point", and the same goes for the times. If the distance of the fall gets longer, the falling object will be moving faster, and if this is applied to the moon it would mean that the moon would have to be closer because the faster it moves in orbit, the closer to the earth it must be. The "crossing point" means that if one time gets longer, the other must get shorter, and the same for distance. Since time and distance are related, although differently for each, this is the only possible relationship.
The only one of the four variables that we know so far is that the moon's orbit is 29 days. Since we are expressing the velocity of the falling objects in seconds, let's convert the moon's orbit into seconds 29 days = 2,505,600 seconds.
Let's express the above equation as A,B,C, D. A and B are the two time measurements, the time of free-fall of the object and the time of the moon's orbital period. C and D are the two distance measurements.
A = time of fall on earth to reach velocity equal to the moon's orbital velocity.
B = the moon's orbital period of 2,505,600 seconds.
C = the distance that the object on earth must fall to reach the velocity equal to the moon's orbital velocity.
D = the distance of the moon's orbital path.
Now, let's start by picking a number of seconds for the object to fall on earth. How about trying 20 seconds of fall, and see where it gets us?
If an object theoretically falls for 20 seconds, it will fall 20 squared x 16 feet = 400 x 16 feet = 6400 feet. This would bring the velocity of the object to 640 feet per second (32 feet per second x 20).
So, if this might be correct, it would mean 20 / 2,505,600 = 6400 / D. With D being the distance around the moon's orbital path, in feet. This would give us 80,179,200 feet as the moon's orbital path.
But this would not work because it would give us the velocity of the moon in it's orbit as only 32 feet per second, which falls far short of the falling object's velocity of 640 feet per second after falling for 20 seconds. But we can see how we can calculate the moon's velocity in orbit if we can get those two numbers to match.
Let's try 100 seconds of free fall for the falling object. 100 squared x 16 feet = 160,000 feet. This would bring the velocity of the falling object to 3200 feet per second (32 feet per second x 100).
So, if this might be correct, it would mean 100 / 2,505,600 = 160,000 / D. With D being the distance around the moon's orbital path, in feet. This would give us 40,008,960,000 feet as the moon's orbital path.
But this would not work either because it would give us the velocity of the moon in it's orbit as 16,000 feet per second, which is far higher than 3200 feet per second of free-fall velocity. Thus, 100 seconds is too high.
Our first guess, 20 seconds of free fall, was too low and our second guess, 100 seconds of free fall, was too high. But this gives us something to go on as we see that our first guess was too low by a factor of 20 (640 / 32), and our second guess was too high by a factor of 5 (16,000 / 3200). This gives us a clue that the answer that we are looking for, the number of seconds of free fall on earth that it takes to equal the moon's orbital velocity, is much closer to 100 seconds than to 20 seconds.
In fact, the number must be four times (20 / 5) closer to 100 seconds than to 20 seconds. The difference between 20 and 100 divided by 5 gives us 16. 100 - 16 = 84. Let's try 84 seconds of free fall on earth.
An object that has been in theoretical free-fall for 84 seconds will have a velocity of 84 x 32 = 2688 feet per second. During those 84 seconds it would fall 112,896 feet (84 squared x 16 feet, as described above).
We know that the moon has the orbital period of 2,505,600 seconds. If the moon were indeed moving at 2688 feet per second, this would mean that the length of it's orbital path was 6,735,052,800 feet.
Calculating the moon's orbital velocity with 84 seconds of free-fall of the object on earth gives us 84 / 2,505,600 = 112,896 / D, with D being the distance around the moon's orbital path in feet. This gives us an orbital path of 3,367,526,400 feet.
This falls short of 6,735,052,800, but notice that 3,367,526,400 is exactly half of our target figure.
We have arrived at our answer but have to consider that the moon's orbit goes all around the earth, while our falling object is only affected by the gravity from one direction of earth. This is why the calculation gives us the length of half the total orbital path of the moon, rather than the complete orbital path.
Dividing this by pi (3.14), which is the relationship between the circumference of a circle and it's diameter, or the relationship of half the circumference to the radius that we are dealing with here, we get a distance to the moon of 1,072,460,637 feet. Dividing this by 5,280 feet in a mile, we get 203,117 miles as the distance to the moon.
This answer is not exactly correct, we know today that the average distance to the moon is about 239,000 miles. But the answer by this method here is within about 16% of it. The reason that our answer is short is that we, on the surface of the earth, are some distance from the center of gravity of the earth. The moon is affected by this center of gravity but our falling object would take less time to fall a distance if we were closer to the center of gravity.
This would decrease the value of A relative to C, in the equation above, and thus make the moon's orbital path longer and the moon further away. It is the same reason that you would weigh less at the top of a mountain then at sea level.
But I think you can see how this concept of how information flows through the universe could have been used, centuries ago, to have effectively measured the distance to the moon. Gravity is simple so the relationship that would enable us to measure the distance to the moon must be simple. The falling of an object on earth, and the revolution of the moon around the earth are both governed by the same gravity, and there is no added information from anywhere. If the scale of the distance to the moon could have been measured so long ago, it would have revolutionized the understanding of the scales of the universe, at a much earlier time.
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