A person in an artificial satellite of the earth feels weightlessness. But a person on the moon has weight even though moon is also a satellite. Why?
In principle, it could be solved just by solving Newton equation for the case of potential being a sum of two gravitational potentials. Not sure it is a graduate-level question though.
Voting to close. 500+ rep users please vote on the closevote in the link if you (dis)agree.
Although not graduate level I find this question interesting and I learned something I did not know. I won't vote to close although strictly speaking, indeed, not graduate level.
@conformal_gk: Closed questions can still be viewed by clicking on the 'Closed Question' category on the side bar (towards the button). They can also be found by search on title key words. They are just no longer on the main menu.