The little prince has really come
to like this little body that's orbiting him.
He knows at what distance it orbits
and knows how fast it goes.
And I think the little prince fell in love
with that little body.
And now he wants to see it all the time
as it goes around the asteroid.
But the little prince just wants to keep sitting there.
He doesn't want to move.
So how fast does the asteroid need
to rotate so that the little prince will always see the body
as it rotates around him?
Well, for that, we need to simply consider
that the period of the little body going around the asteroid
needs to be the same as the asteroid rotation period.
So we're going to call that Ta for asteroid.
And well, if we want to know at what distance that works out,
then we're going to use Kepler's laws here again.
And we're going to have that the radius
between the body and the asteroid
will be Gm1 over 4 pi squared.
And now we have Ta squared in here and the third of that.
So all of these wonderful quantities
make the little prince really happy.