Question

1. If our sun shrank in size to become a black hole, using the gravitational force equation, explain why the Earth's orbit would not be affected.
2. Strictly speaking, you weigh a tiny bit less when you are in the lobby of a massive skyscraper than you do at home. Why is this so?
3. Ultimately, the universe may expand without limit, or it may coast to a stop, or it may turn around and collapse to a "big crunch." What is the single most important quantity that will determine which of these fates is in store for the universe?
4. Which requires more fuel - a rocket going from the Earth to the moon or a rocket coming from the moon to the Earth?
I know more fuel is required to go from the earth to the moon but why?

Answer 1

1. The "gravitational force equation" depends only upon the mass of the central body and the distance from it. The size of the body makes no difference.

2. There is a lot of mass above you pulling you away fromthe center of the Earth.

3. The rate of expansion of the universe (Hubble constant) and the density are equally important. See http://en.wikipedia.org/wiki/Critical_density
The apparent acceleration of the rate of expansion is not understood, not are the roles of dark energy and dark matter. We really cannot make predictions at this time.
4. Getting to the moon requires much more energy for two reasons:
(a) Going there, you need to take extra supplies necesary for life support and getting back again.
(b) The atmosphere of the Earth provides most of the deceleration necessary to land on earth safely, with heat shields, parachutes or lifting-body airplane shapes like Space Shuttle.