Which of the following is
not one of Kepler’s laws?
☑ Planets all move in the same plane
☐ Planets move in elliptical orbits
☐ Equal areas swept out in equal time: faster closer to sun
☐ The period of orbit increases as r increases
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
The "escape velocity" of a planet is the speed needed for a rocket to
go from the surface of the planet into orbit.
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 possibly be equivalent? What can you tell Ralph to help him out?
The general equation for gravitational potential energy assumes that energy is 0 at an infinite distance from earth, or when height is infinity. The surface of the earth is “below” that, so must have less potential energy. Therefore, the general equation for PE must be negative at the surface of the earth. However, in conservation of energy problems, we are always looking at *differences* in energy (there is PE on both sides of the equation). The PE change will still be positive for an object that moves away from the surface earth, so the two equations can co-exist.
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