Stable Orbits Around the Earth

I know that man-made objects in orbit around the earth eventually re-enter the atmosphere. I also know that geostationary satellites, many thousands of miles from the earth, will stay up almost indefinitely. The moon, I understand, is slowing in its orbit and gradually moving further from the earth. My question: How far away from the earth would a typical man-made satellite have to be in order to remain in earth orbit permanently? In other words, is there such a thing as an orbit that will not decay?
- Clif Brown (age 63)
Evanston, IL, USA

Hi Clif,

Satellite orbits around the earth are basically stable except for perturbative effects.  For example if there is a cloud of dust or other junk that an orbiting satellite can run into and lose kinetic energy then that orbit will decay and eventually crash into the earth.   In the case of the moon, indeed it is moving further from the earth and slowing down.  This is due to the earth-moon tidal effect.  What happens is that the period of the lunar month and the period of the earth's rotation will eventually coincide and become tidally locked together at about 47 of our current days. 
Don't hold your breath. It won't happen for another several billion days.   After that the orbit is stable. 

See:    for some examples.

LeeH

 

p.s. Those tidal effects depend strongly on the mass of the satellite, so they become very weak for a typical man-made satellite. The tidal effects that give that systematic effect on the Moon are caused by the distortion that the Moon's tides make on the Earth. A man-made satellite induces almost no distrotion of the Earth.

Still, your idea that there should in principle be a point where the forces causing a satellite to speed up and come down and those causing the opposite effects should cancel sounds right. Whether that would in an ideal case give a stable orbit depends on which of those two effects falls off more rapidly with distance. I think that for a simple model of the atmosphere, its effects fall off more rapidly, which would mean that even at the balanced point the orbit wouldn't quite be stable. /mw

(published on 01/05/2014)