Basic Orbital Mechanics

ORBITAL MECHANICS is the study of the forces that cause stars, planets, satellites, spacecraft, and other things to move in space. It is also the study of the mathematics that describes the way those things move. The forces cause the movement.

GRAVITY was explained by Isaac Newton with a formula that says two masses M1 and M2 are attracted to each other by a Gravitational Force. The Gravitational Force, F1, is calculated by the equation below:

• F1 = G x M1/R x M2 / R

• Where R is the distance between the center of M1 and the center of M2 and G is the Constant of Gravitation.

• If you use metric units, M! and M2 are kilograms, R is meters, G is

CENTRIPETAL FORCE, F2, is the force that pulls on a string if you tie a rock on the end of a string and twirl the string with the rock on the end around your body. The Centripetal Force is the force that pulls on the string. A similar thing happens when a planet orbits around the sun or when our moon orbits around the Earth or when the space shuttle orbits around the Earth. The smaller object revolve around the bigger objects. The string is like gravity.

• F2 = M! x V x V / R

• Where V is the velocity (speed) of the rock or satellite

• If you use metric units, V is meters per second

ORBITS: A less massive object M1 can orbit around a more massive object M2 if the Centripetal Force of the orbiting object is the same as the Gravitational Force between the two object. If you look at F1 and F2 above, then there is an orbit if F1 = F2. Another form of this equation is

• G x M1/R x M2 / R = M1 x V x V / R

Or the speed of the satellite, M1, must be V = SQRT (G x M2 / R)