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The little prince
has really come

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to like this little body
that's orbiting him.

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He knows at what
distance it orbits

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and knows how fast it goes.

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And I think the little
prince fell in love

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with that little body.

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And now he wants to
see it all the time

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as it goes around the asteroid.

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But the little prince just
wants to keep sitting there.

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He doesn't want to move.

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So how fast does
the asteroid need

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to rotate so that the little
prince will always see the body

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as it rotates around him?

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Well, for that, we
need to simply consider

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that the period of the little
body going around the asteroid

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needs to be the same as the
asteroid rotation period.

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So we're going to call
that Ta for asteroid.

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And well, if we want to know at
what distance that works out,

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then we're going to use
Kepler's laws here again.

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And we're going to
have that the radius

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between the body
and the asteroid

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will be Gm1 over 4 pi squared.

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And now we have Ta squared in
here and the third of that.

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So all of these
wonderful quantities

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make the little
prince really happy.