In sending observational spacecraft into space Lagrangian Points are becoming ever more important. Whenever a smaller object is in orbit around a larger object, such as the earth around the sun, five Lagrangian Points are created. These points are usually defined as the locations where there is a balance between the gravity of the earth and that of the sun. The points are labeled L1 to L5.
The James Webb Space Telescope is positioned at L2 and India's spacecraft to observe the sun is on the way to L1. L2 is defined as the point in space beyond the earth, in a line with the sun, where the earth and sun's gravity balances. L1 is the point of balance in the direction of the sun.
Defining Lagrangian Points as the point where the gravity of the earth and sun balances is a way to give an idea of the concept but is actually not accurate. The earth's Lagrangian Points are well beyond the orbit of the moon. But the point where the gravity of the earth and sun are equal is closer to the earth than the moon.
We know that gravitational force is proportional to mass and diminishes with distance according to the Inverse Square Law. From the moon the sun is 400 times as distant as the earth. So if the earth and sun had the same mass the gravitational force of the earth on the moon would be 160,000, which is 400 squared, times as great as that of the sun.
But the mass of the sun is 330,000 times that of the earth. This means that, from the moon, the gravitational force of the sun is more than twice that of the earth. The point where the gravity of the earth and is equal must thus be between the earth and the moon, while L1 and L2 are defined as being well beyond the orbit of the moon.
What a Lagrangian Point actually can be defined as is the point on a line that includes both the earth and the sun where the gravity of the earth adds to or subtracts from the gravity of the sun so that the orbital period of an object at that point around the sun is the same as the earth, even though the object is closer or further from the sun than the earth.
When a planet or an object orbits the sun, the closer it is to the sun the faster it moves in it's orbit. This is because the gravity of the sun is stronger in close. An object at L2 would normally move more slowly than the earth through it's orbit, because it is further from the sun, and an object at L1 would normally move faster through it's orbit because it is closer to the sun.
Lagrangian Points are created because the earth has gravitational force also. It is nowhere as near as great as the sun but it is enough to make a difference.
An object at L1 is closer to the earth than the sun but the earth is in the opposite direction than the sun. This causes the earth's gravity to effectively subtract from the sun's gravity so that the object moves more slowly in it's orbit around the sun than it otherwise would. In fact it moves at just the right speed so that it's year is exactly the same as the earth's, and so it stays at a stationary point relative to the earth. It's orbital velocity is actually slower than earth's because the circumference of it's orbit is less.
In a similar way an object at L2 is further from the sun than earth so it would ordinarily move around the sun more slowly than the earth. But the earth's gravity adds to that of the sun so that it's year is exactly the same as that of the earth. It stays in a stationary point relative to earth. It's orbital velocity is actually faster than that of the earth because it's orbital circumference is longer.
That is the actual definition of Lagrangian Points.
Related to this idea is what we saw in the compound posting "The Moon", August 2023, section 2) THE EARTH, THE MOON AND, THE SUN. The moon is technically not in orbit around the earth. It is in orbit around the sun, as is the earth, because the force of the sun's gravity on the moon is more than twice that of the earth's gravity. What is happening is that the moon moves slower when it is between the earth and the sun, at new moon, and faster when it is opposite the earth from the sun, at full moon. This causes it to fall behind, and then pull ahead, of the earth so that it effectively orbits the earth.
Another thing that is related to this is geostationary orbits. A satellite will orbit earth more slowly the higher altitude it is. Meanwhile the earth is rotating. This means that, if a satellite is placed at a certain altitude, it will orbit the earth just as fast as the earth rotates so that it appears to stay directly overhead. This is known as a "geostationary" orbit and is at 22,300 miles.
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