2. The earth is curved, and an object has to be moving at a very fast rate in order to drop that distance and not actually fall into the planet - they say that the measurement for the curve of earth is that for every 8000km, the horizon drops about 5 meters, so the object is actually orbiting the earth instead of "dropping".
3. Inside the atmosphere, an object would have to maintain constant motion itself (like using energy like a jet engine or something similar) than just using gravity and the curve of earth to stay in orbit. The orbital path would eventually "decay" because the ratio of dropping to speed would change in short periods of time, and would slow down enough not to maintain the orbit. (Newton's 1st law - the object would have stayed in motion unless earth's gravity hadn't have interefered too much to inhibit the orbit.) The slowing is caused by the friction of the atmosphere.
4. Gravity is constant, and there is no friction in outer space. The gravity continuously pulls the satellite to the center of mass, but inertia keeps it moving around. This is only true in circular orbits. In elliptical orbits, the speed of the satellite changes depending on the speed initially and its relative position to the center of mass.
5. Kepler: Using Kepler's second law of planetary motion, the area covered by the arc of motion and the lines connecting the two bodies are equal to all other areas covered in the same amount of time. Using this, one must determine that the speed of the orbit changes in order to maintain the same amount of area covered in the same amount of time. Since this applies to ellipses, the satellite isn't the same distance away from the center of mass the entire orbit, like in a circle, so the speed HAS to change in order to keep Kepler's second law.
Newton: Using the law of inertia, one can explain why the speed of an elliptical orbit changes. Since the center of mass and the satellite are not the same distance from each other throughout the orbit, the centrifugal/centripetal forces will react with each other in a different way. The farther away the satellite is from the center of the centripetal force, the less that force affects the satellite's orbit. The close the satellite is, the greater the effect of the force, and the greater the speed of the satellite is. When the satellite is closest to the center of mass, it moves the fastest.
These are true in all elliptical cases... however, the speed of a circular orbit never changes.
Using the equation, one can see that the greater the distance between the center of mass and the satellite, the less the velocity (or speed). Therefore, the smaller the distance, the greater the velocity.
Some really helpful sites that may be useful for other students as well:
6. When the satellite slows, it is merely using less energy to move than if it were closer to the center of mass. When it is closer, the satellite gains energy from moving (kinetic), then turns into potential energy as it slows down. The potential is then used to get back closer to the center of mass. The total amount of energy, whether it is kinetic or potential, never changes though.
7. The "escape speed" is the amount of velocity required to free an object from the surface gravity of the launching site. In earth's case, 11km/sec is required to get away from earth and not get pulled back because of gravity. The distance, the mass of both bodies, and the amount of friction in the atmosphere all affect the success.
8. The escape velocity for earth is 11km/sec at LEAST. It is not the same for all planets because they all have different amounts of gravity. The moon requires a lesser amount of speed to defy its gravity than the earth.
Escape velocity of the moon: 2.4 km/sec
Escape velocity of Jupiter: 59 km/sec
(both calculated on paper)
9. The surface gravity for all planets are different. Their masses are all different, so the gravity is different. It is calculated using the gravity constant x the mass of the object all divided by the radius of the object squared.
10. Moon: 1.627m/s^2, yes, I calculated 1.63m/s^2.
Jupiter: 24.79m/s^2, calculated 24.8m/s^2.
I used the masses/radii/gravity constant found on Google.
11. For a satellite's orbit to decay, there must be friction occurring that slows the satellite down enough to the point where it cannot orbit anymore and instead falls into the gravitational pull of the center of mass.