Gravitation and Mechanics
Newton's Principles of Mechanics
Sir Isaac Newton realized that the force that makes apples fall to the ground is the same force that makes the planets "fall" around the sun.
He established that a force of attraction toward the sun becomes weaker in proportion to the square of the distance from the sun.
Newton postulated that the shape of an orbit should be an ellipse. Circular orbits are merely a special case of an ellipse where the foci are coincident.
Newton's Laws of Motion
There are three ways to modify the momentum of a body. The mass can be changed, the velocity can be changed (acceleration), or both.
Force (F) equals change in velocity (acceleration, A) times mass (M):
F = MA
Acceleration may be produced by applying a force to a mass (such as a spacecraft). If applied in the same direction as an object's velocity, the object's velocity increases in relation to an unaccelerated observer. If acceleration is produced by applying a force in the opposite direction from the object's original velocity, it will slow down relative to an unaccelerated observer. If the acceleration is produced by a force at some other angle to the velocity, the object will be deflected. These cases are illustrated below.