High School Physics/Gravitation

Orbit
Why do satellites follow a path around the earth when they are broadcasting MTV. Think about it this way, if they were going a bit slower, they would fall, and if they were going a bit faster, they would fly away.

The distance a satellite is orbiting at will be determined in much the same way as how far Shakira's hair will be from her head when she tosses it. The faster, the farther.

Newton made this observation in regards to the fact that the moon rotates around the earth as determined by the law of gravitation:

$$F=G\frac{m_1m_2}{r^2}$$

$$G$$ = gravitation constant. $$m_1$$ = mass of first object. $$m_2$$ = mass of second object. $$r$$ = Radius from center of $$m_1$$ to center of $$m_2$$.

R is what we are concerned with here. The equation requires that the farther away from the gravitational force the satellite is, the slower it needs to go to stay in orbit.

Leaning Tower of Pisa Experiment
It is said that Galileo dropped two bowling bowls of different masses from the tower of pisa, but this is debated with many believing it only occurred as a thought experiment. The natural inclination is to believe that the heavier object would fall faster without air resistance, but this is not true, as it has been shown they both fall at the same time. The force equation above proves that the force is greater on the larger object all other things being equal ($$m_1$$ or $$m_2$$ is what we are concerned with here...they are interchangeable). We know that it requires stronger muscles to hold up a person than a feather. So why doesn't the object that is heavier fall faster? One word. Inertia. You may have noticed that it is easier to throw a baseball than a bowling ball. The same applies to the Earth. You may be under the impression that the same rules that apply to you do not apply to the earth, but they do. The earth has to pull twice as hard on an object with twice the mass in order to produce the same acceleration as it would something with half that mass, so the fact that the force is twice as large is cancelled by the inertia being twice as great as well. This is of course ignoring air resistance. It takes a lot more energy to throw a whiffle ball a given distance than it does a baseball because of this. Without air resistance (in a vacuum), a normal whiffle ball is easier to throw a given distance than a baseball as hard as that is to believe.