Warm-Up Exercise for lecture 14

Due 8:00 am, Thurs, Oct 16

Physics 105, Fall 2008

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
the gravitational pull of the Earth on the moon is weak
the moon has a sufficiently large orbital speed
the gravitational pull of the sun keeps the moon up
the moon has less mass than Earth
none of the above

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?