>>>LEO satellites orbit closer to the earth, so to keep from being pulled out of orbit, they are made smaller.<<<
Not true.
When an object is in orbit around the earth, two forces are balanced - the force experienced by an object traveling in a circular path and the force of gravity.
The force experienced by an object traveling in a circular path is given by the equation F = m*v^2/r and points away from the earth.
The gravitational force is given by F = G*M*m/r^2 and points toward the earth.
In these equations,
G = universal gravitational constant
M = Mass of the Earth
m = mass of the object
r = distance from the center of the Earth
v = velocity of the object
When an object is in orbit, the two forces are balanced, such that the object neither falls to the earth nor escapes its gravity. Therefore,
G*M*m/r^2 = m*v^2/r
The first thing that is apparent is that m, the mass of the object, appears on both sides of the equation in the numerator, and therefore is eliminated. The final equation governing the motion of the object in orbit is:
v = SQRT (G*M/r)
For a given object orbiting the earth, the only variables are the object's velocity and its distance away from the earth (because universal Gravitational constant and the Earth's mass are constant). The object's mass has nothing to do with it.
Low earth orbit satellites, because their r is smaller, have to have a greater v. But their mass is not restricted by their low orbit.
Edit - one more note:
It takes energy (fuel) to reach orbital velocity, but once the object reaches orbital velocity, no fuel is needed to keep the object in orbit, assuming the effect of air resistance is negligible. Air resitance plays a greater role nearer to the Earth of course, and I don't know if LEO's are low enough for this to be a factor. |
