ORBITAL MOTION

Newton first proposed that gravity is the force which holds planets in their orbits about the Sun. (Newton is the one who postulated the existence of universal gravitation between massive bodies.) Gravity is a central force, which means that it is directed toward the mass

( for center-of-mass, watch from 2:32)

The explicit expression for gravity is

Gravity = - GMm/R²

Here, M is the mass of one object, m is the mass of the other object and R is how far apart are the two masses. The minus sign means that the gravitational force is attractive, it always tries to pull the two masses together. The quantity G is known as the gravitational constant and must be measured.
Gravity behaves sensibly.

The attraction is stronger if the product of the masses, M times m, is made larger and/or also if the masses are moved closer together.

The attraction is weaker if the product of the masses, M times m, is made smaller and/or if the masses are moved farther apart.

Let's perform a couple of experiments:

I hold two unequal masses at arms length. Gravity pulls both downward. Which mass feels the greater force? I can measure this by asking the equivalent question of which weighs more?
If I release the masses, which one will reach the ground first?
Are the results of these experiment as expected?
Let's use our new found understanding to talk about orbital motion. Let's try another experiment.
Previously, when I dropped objects (see (a)), gravity pulled them to the ground. The rate at which they fell turned out to not depend upon their masses.

Suppose I roll an object, giving it some horizontal motion (see (b) and (c)), now what happens?

Well, gravity pulls the object down but , did the horizontal motion affect the rate at which the object fell?

Does gravity affect the horizontal motion?

The Earth exerts a downward force on the ball which accelerates the ball toward the ground at a rate of 9.8 (meters per second) per second. This rate of increase of this rate at which the ball falls is independent of the mass of the ball and how hard I throw the ball outward. This implies that the distance the ball travels from my feet depends upon how hard I throw the ball horizontally and that how long it takes to reach the ground is independent of how hard I throw the ball out horizontally. If I am 4.9 meters tall, the ball will take 1 second to reach the ground, regardless of how hard I throw it horizontally (unless I am Superman).
To see how orbital motion works, we must take account of the fact that the surface of the Earth is not flat, it is curved. (The Earth is spherical in shape.)

The surface of the Earth falls away from the ball while the ball falls toward the center of the Earth. If you throw the ball out just right, the ball and the surface of the Earth fall together and allow the ball to go into orbit. For a circular orbit around the Earth, a speed of
orbital speed = [GM_earth/R_earth] ^1/2 = 28,500 km/hr is required.
An interactive orbit simulator that can be used to illustrate some thing about orbits: PHET orbit simulator