[BattyMilk]

Apologies in advance for the (hopefully not) stupid questions from a layperson...

How constant is the L2 point for the relay satellite's orbit? If I understand correctly, this is the "balance" point between the earth and sun's gravity. Does the moon's gravity affect this? If so the L2 point will shift as the moon moves towards and away from this point?

As the moon orbits the earth, presumably the relay satellite would stay put and not follow the moon in its orbit. This would mean that communication from the lander and rover to the satellite is only possible when the moon is in a particular position (between the earth and the sun), correct?

[fspeech]

The balance is between Moon and Earth gravity. However it is more subtle than that at L2 as both gravitational forces are in the same direction so they don't apparently cancel. The way to see it is to realize that L2 is relatively stationary to the Moon but not the Earth. As the L2 point is farther away than the Moon but has the same angular velocity as the Moon, Earth gravity alone is not able to keep any object at the L2 in synchrony with the Moon. One may want to recall that Earth gravity is just right for the Moon in its orbit so any satellite further away will have a longer orbital period than the Moon. The Moon gravity therefore supplies the additional force needed to keep an object at L2 orbiting the Earth in synchrony with the Moon. This balance (Earth gravity + Moon gravity = centrifugal force) determines the location of L2.

[BattyMilk]

Thank you for the good explanation!! Cheers!

[0nce]

Lagrange points are found near any couple of large bodies. They are points where a smaller object will maintain its position relative to the large orbiting bodies.

The Chinese relay satellite is orbiting the L2 point of the Earth-Moon system. That is beyond the Moon on a line which goes from Earth to Moon. Hence, this L2 point orbits the Earth like the Moon does, and the whole system orbits the Sun as well.

Now if the spacecraft would be exactly at that point, the Moon would be blocking communications between the probe and Earth antennas. So instead, it follows a halo orbit which is quite stable around that point, but goes over the Moon horizon so that there is always a direct line of sight between Earth and the spacecraft.

Not a stupid question at all !

[Symmetry]

I just wanted to add that L2 (and L1 and L3) are unstable in that if a satellite is a bit further than the exact point it will tend to get ever further with time and a satellite that's closer will tend to get even closer. But the closer you are to the exact L2 point the smaller these tendencies are and the amount of fuel needed to remain on station is minimal, a satellite will just eventually run out some day and fall out.

The L4 and L5 Lagrange points are the stable ones. Something that finds its way there is going to stick around indefinitely. That's why many planets have asteroids in the L4 and L5 they make with the Sun. These are called Trojan asteroids and the names of the Jupiter-Sun Trojans are taken from the Trojan war.

[hanoz]

So how can this craft orbit a point that is not a gravity well but a gravity hill, so to speak?

[Symmetry]

It's a gravity saddle! From Earth's perspective it's a hill in the r direction but a well in the phi/theta directions. To orbit at a location always visible from Earth it needs to move in the phi/theta directions but moving the the r direction doesn't help, so it doesn't.

[Latteland]

And you clearly know this but i had to refresh my own knowledge of spherical coordinates - https://en.wikipedia.org/wiki/Spherical_coordinate_system

[BattyMilk]

Thank you for taking the time to explain. Very helpful :)

[mkl]

The L2 point that the satellite is orbiting is a Lagrange point [1], a place where the gravity (edit: and centrifugal forces) of the Earth and the moon balance. L2 follows the moon as the moon orbits, because the moon is what makes it exist.

[1] https://en.wikipedia.org/wiki/Lagrangian_point

[juloo]

It's the L2 point in the earth-moon system, it is different from the earth-sun L2 point. And yes, the satellite follow the moon in its orbit, the point in the L2 point.