# Could a radio telescope orbit Earth-Moon L2 so that it is in the Moon's radio shadow?

Chang'e 4, a Lunar orbiter and lander on the far side of the Moon, will put a relay satellite in a halo orbit around EML2 that also will do some low frequency radio astronomy. Since the Chang'e 4 satellite will also be a relay satellite, it obviously will have Earth in lone of sight at least part time. More generally, could any potential telescope around EML2 use a halo orbit that takes advantage of the Moon shadowing radio disturbances from Earth, as if it were on the surface on the far side of the Moon?

It's a reasonably easy calculation how far from L2 you can go and still be in radio shadow. Roughly, if you move x km from L2 (in a non-radial direction) you can see Earth's limb if $7*(1700-x) > 6000$ which gives something like $x < 800$. This is unfortunately not far enough to reach any of the stable Halo orbits (which are probably not that stable for the Moon anyway, due to perturbation from the Sun), so you would need to use a small amount of fuel actively station-keeping. On the other hand, a radio astronomy satellite probably has a rather accurate idea of its position, as a pre-requisite for doing its job, so it could stay very precisely on L2, using very little fuel.