The "escape velocity" of a spaceship is the speed needed for the spaceship to
go from the surface of a planet into orbit.

The reason the moon does not fall into the Earth is that

Kepler's third law says
that planets orbiting the sun do so with an orbital period (the planet's "year")
equal to T = sqrt(K*r^3), where K is equal to 2.97E-19 s^2/m^3. Can this same
equation, with this same K, be used to describe the moon orbiting the Earth?

Ralph noticed the negative sign
in the general equation for gravitation potential energy, *PE *= -*GMm*/*r*,
and he read the book's statement (8th edition, chapter summary) that "this expression
reduces to *PE *= *mgh *close to the surface of Earth". He is very
confused, because one equation has a negative sign and the other one doesn't!
How can they be equivalent? What can you tell Ralph to help him out?