Eclipses And Associated Science

Many people are awaiting the upcoming solar eclipse. This would be a good time to review what eclipses are all about as an event like an eclipse can be the beginning of an interest in science.

The principle behind eclipses is simple. The moon orbits the earth as the earth orbits the sun. When the moon is on the far side of the earth from the sun the earth may cast it's shadow on the moon, this is known as a lunar eclipse. When the moon is between the earth and the sun the moon may cast it's shadow on the earth, this is known as a solar eclipse. 

It is just by sheer chance that the moon and the sun appear as just about exactly the same size in the sky, about half an angular degree. This is why the moon can cover the sun during a solar eclipse. The diameter of the sun is about four hundred times that of the moon but it is about four hundred times as far away as the moon.

Both the earth and the moon get their light from the sun. Since we can only see the half of the moon that is lit by the sun the moon appears to go through phases as it orbits the earth. The following diagram shows how the phases of the moon operate. You can see why a solar eclipse can only occur at new moon and a solar eclipse at full moon. All diagrams in this posting are drawn for clarity and are not to scale.

When the phases of the moon are proceeding from new moon to full moon the first half moon is referred to as the "first quarter", because the phase cycle is one quarter complete. The second half moon is referred to as the "third quarter" because, at that point, the cycle is three quarters complete. Leading up to full moon, when the phase is increasing every day, the phase is referred to as "waxing". After full moon, when the phase is decreasing every day, the moon is referred to as "waning".

The moon goes through it's phase cycle every 29 days. The earth rotates every 24 hours. 24 hours divided by 29 equals 50 minutes. The moon orbits the earth in the same direction that the earth rotates, which is eastward. This is why the moon rises 50 minutes later each day.

The earth orbits the sun in the same direction as the earth rotates and the moon orbits the earth, which is eastward. The direction overhead at sunrise is the direction that the earth is moving through space as it orbits the sun.

The moon is higher in the sky during the winter, and lower in the summer. If the orbit of the moon around the earth and the orbit of the earth around the sun are in close to the same geometric plane, and the sun is higher in the sky during the summer and lower in the winter, then the moon, which is more visible when opposite the sun, must be the opposite.

The reason that there isn't both a lunar and a solar eclipse every month is that the orbit of the moon around the earth and the orbit of the earth around the sun are not in exactly the same geometric plane. There is a difference of about five degrees between the planes of the two orbits. If the two orbits were in the same plane there would be both a lunar and a solar eclipse every month. The plane of the moon's orbit actually undergoes a precession cycle that takes 18.6 years.

The earth also goes through phases, as seen from the moon. One day I looked at the moon and realized that the phase of the moon, as seen from the earth, and the phase of the earth, as seen from the moon, must always add up to a full circle.

A solar eclipse can be seen as total or partial. Since the sun is larger than the moon the zone of total solar eclipse forms a cone in space. This zone is known as the umbra. The zone of partial solar eclipse is known as the penumbra. The following diagram shows the umbra and the penumbra. We could say that a solar eclipse is going on continuously, since there is always a zone where the sun's light is blocked by the moon, we see the eclipse when the earth passes through this zone.

The solid lines are the umbra lines and the broken lines are the penumbra lines. A total solar eclipse is seen within the umbra and a partial eclipse in the penumbra. Since the sun and moon are about the same angular diameter in the sky, the umbra only just reaches earth and the total eclipse is visible in only a limited area.

The diameter of the moon is about a quarter that of the earth. This means the earth has 64 times the volume of the moon. But the earth is more dense than the moon so that the earth has 81 times the mass of the moon. The reason is that the moon is made of rock but the earth has a heavy iron core that the moon lacks. The moon thus has almost no magnetic field.

According to my calculations, when you look at a full moon you see an area about the size of Russia. When you look at a half moon you see an area about the size of the U.S., or China, or Canada.

While the principle behind eclipses is simple, it does get a little bit more complicated than this. For one thing neither the orbit of the moon around the earth nor the orbit of the earth around the sun are perfectly circular. Sometimes the moon is further from earth relative to earth's distance from the sun. When the moon is closer to earth it appears larger in the sky and covers the sun during a total solar eclipse. When the moon is further away from earth, relative to the distance to the sun, it may not completely cover the sun during a solar eclipse. 

In January the earth is closest to the sun and in July it is furthest away. When the sun is closer, and thus appears larger in the sky, it is less likely that the moon can completely cover it. What that means is that the zone of total solar eclipse, the umbra, does not reach the earth.

The orbits of the moon around the earth and the earth around the sun are in the form of ellipses, rather than perfect circles. The orbiting object moves faster when it is closer so that a line between the two objects moves over equal areas of space in equal periods of time. But this means that the average distance from the moon to the earth or the earth to the sun is a matter of definition. We might take the furthest distance in the orbit and the closest distance and simply average them together. But the orbiting object moves faster when it is closer. That means the orbiting object spends less time closer and more time further during the course of it's orbit. So if we took a distance measurement every day during the course of the orbit, and averaged them together, we would get a further distance than the simple average of the closest and furthest distance. 

The fact that the orbiting object moves faster in it's orbit when it is closer results in what I refer to as the "Solstice Gap". By the rules of celestial mechanics it would seem that the solstices should align with the aphelion and perihelion of the earth's orbit around the sun, when the earth is furthest and closest to the sun, since the earth's northern hemisphere is heavier than the southern hemisphere. But there is actually a gap of two weeks. The northern winter solstice is around December 21 while the earth is closest to the sun on January 4. The northern summer solstice is around June 21 while the earth is furthest from the sun on July 4. This two week gap is because the change in length of day and night is constant but the velocity in orbit is not. The earth moves faster in it's orbit when it is closer to the sun.

Related to eclipses are tides. Gravity operates by the Inverse Square Law, diminishing with distance from the source. This means that, when the moon is overhead, the oceans are deep enough that the moon's gravitational force on the surface of the ocean is significantly greater than on the bottom of the ocean. This causes a tidal "bulge" in the water as the earth rotates. There is also a tidal bulge on the opposite side of the earth as the moon pulls the earth away from the water. This causes two high and two low tides each day. Obviously a body of water must be deep enough to manifest tides, which is why there is no visible tides in the Great Lakes.

The sun also exerts tidal force. But since the sun is so much further away than the moon it's tidal force is only about forty percent that of the moon, despite it's great mass. Remember that tidal force is not just gravity but a difference in gravity. The further away a source of gravity is, relative to the diameter of the earth, the weaker it's tidal force must be even if it's gravitational force is very strong. Tides are strongest, Spring Tides, at new or full moon when the moon and sun are pulling together. Tides are weakest, Neap Tides, at half moon when the sun and moon are pulling perpendicular to each other.

The moon was once much closer to the earth. What happens is that the moving tidal bulge that is induced by the moon's gravity as the earth rotates also affects the moon. It transfers energy from the earth's rotation to the moon's orbit. Over a long period of time the moon has been boosted into a higher orbit at the expense of slowing the earth's rotation. When the moon was close to the earth it's tidal effect must have been much greater, especially since the earth was rotating faster. If the moon has tidal effects on the ocean it should also have an effect on magma within the earth and I believe this was a major factor in early volcanism.

The same side of the moon always faces earth. This is because the moon is tidally locked by the earth's gravity. On the side of the moon facing earth the earth would always appear in the same place in the sky, meaning that it would be useful for navigation. If the moon's gravity causes the tides on earth then what about the effect of earth's gravity on the moon, since the earth is 81 times the mass of the moon? This is what caused the dark "seas" that we see on the moon, which are actually lava plains. There is no such "seas" on the far side of the moon.

The far side of the moon is often referred to as "the dark side of the moon". This is incorrect. It actually gets more sunlight than the side of the moon that faces us. Both sides of the moon spend an equal amount of time facing the sun as the moon orbits the earth. But the far side of the moon faces the sun around new moon, when the moon is closer to the sun than the earth. The side of the moon that faces us faces the sun around full moon, when the moon is further from the sun than the earth. That is why I say that the far side of the moon gets more sunlight than the side that faces us.

We say that the moon orbits the earth while the earth orbits the sun, and that is a convenient way of looking at it. But some simple calculations show that, from the moon, the gravity of the sun is more than twice as strong as that of the earth. This means that the earth and moon are more like co-planets whose orbits interweave while they both orbit the sun. The moon moves much more than the earth simply because the earth's mass is 81 times greater. 

The moon seems to orbit the earth because it is moving around the sun slower than the earth at new moon, because the gravitational pulls of the sun and earth are on opposite sides and opposing each other, and faster than the earth at full moon, because the earth and sun are pulling together. What this interweaving means is that the earth is a little bit further from the sun than it would be otherwise at new moon and a little bit closer to the sun at full moon.

In the following diagram, with the bottom toward the sun, the blue line represents the orbit of the earth and the red line represents the moon. Each "F" represents a full moon and each "N" a new moon. The weave in the earth's orbit is so much less than that of the moon because it's mass is 81 times that of the moon. We perceive this interweaving as the moon orbiting the earth. The line of the center of mass of the earth and moon remains constant.

A lunar eclipse, when the earth casts it's shadow on the moon, is much more easily visible than a solar eclipse. The moon often appears red during a lunar eclipse. That is because the earth's atmosphere refracts sunlight that would otherwise be completely blocked. Both air and water refract short wavelength blue light more than long wavelength red light. The earth's atmosphere refracts the blue and other colors away altogether so that it is only red light that continues on, in a relatively straight line, to the moon. 

Water absorbs light, starting with the longest wavelength red, so that only blue light survives long enough to be refracted back to the surface. This is why deep water appears blue. In underwater photos you may notice that nothing red is ever seen below about 9 meters (30 feet) depth.

At Niagara Falls the water sometimes appears green because the current keeps rock on the river bottom clear of sediment so that it reflects some light back to the surface. The green light has not yet been absorbed and is reflected back to the surface whereas, given it's refractive index, it would otherwise be absorbed before having the chance to be refracted back to the surface and only blue light would get back to the surface. 

There is a compound posting, "The Moon", August 2023.