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?
(combining two students' explanations) Gravitational potential energy assumes that energy is 0 at an infinite distance from earth, or when height is infinity. When you are close to the earth, the surface of the earth usually represents PE=0. When you use conservation of energy, you must subtract the initial potential energy from the final potential energy. By subtracting these quantities, you will always end up with a positive change in potential energy for an object that moves away from the earth.
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