Image credit: NASA, of the ISS in orbit around Earth.

Why are Earth-orbiting satellites fundamentally unstable?

Without a boost, they’ll all come crashing down.

“I’m here for several reason, Mr. Pepin, first of all for aid. When something tragic happens in our skies, we do our utmost to extend sympathy. But sympathy without action,that’s an empty emotion. Mainly I’m here for the purposes of reentry.”
“I don’t understand.”
“Adjustment,” Harold said, “to earth. I’m here to make sure you didn’t leave your whole life in the sky.” -Adam Ross

It might seem like making a satellite orbit the Earth is the simplest, most natural thing in the world. After all, the Moon has been doing it without fail for over four billion years, and there’s no trickery or chicanery to its motion. Yet if we left the Earth-orbiting satellites we’ve put up in space alone for just a few years or decades, they’d re-enter the atmosphere, either burning up or crashing through to the ground and ocean, as so many satellites and spacecraft have famously (or infamously) done before.

Image credit: NASA, of the atmospheric re-entry of the ATV-1 satellite.

Moreover, if we look at the natural satellites of all the other planets, they’re all considerably farther away than the human-made satellites that orbit the Earth…