eli5: I’ve heard orbit described as continuously falling past or missing the Earth, how then do objects in geosynchronous orbit above a single point not fall out of the sky?

Question

eli5: I’ve heard orbit described as continuously falling past or missing the Earth, how then do objects in geosynchronous orbit above a single point not fall out of the sky?

In: 2204

Answer 1

A sustainable orbit (one that doesn’t collide with the planet) around a planet is almost completely independent of the concept of geosynchronous (specifically geostationary) orbiting.

What I mean by that is, a random planet could have very different rates of spin. Some planets could have no spin. Others can be rotating around at thousands of miles per hour. Outside of some tiny influences from things like General Relativity (that we can ignore), this spinning of the planet has no influence on the sustainable orbits around the planet.

So for a planet with no spin, there is no geostationary orbit that doesn’t cause the satellite (or whatever object) to fall into the planet. The planet doesn’t rotate and so the object can’t move in its orbit if it wants to stay geosynchronous. The only way to do this is to fall straight down into the planet and that’s not a sustainable orbit.

If the planet is spinning, then there is a chance at a geostationary orbit existing. That possibility will depend on the gravitational force of the planet and the speed of its surface. If the surface is too slow it won’t meet the escape velocity needed to overcome the gravitational pull of the planet. And so the orbit will end up intersecting the planet.

If the speed is high enough, then there will be some altitude away from the surface that a satellite can sit that will be a sustainable orbit and allow the surface and the satellite to have the same orbital period.

The [formula](https://en.wikipedia.org/wiki/Geosynchronous_orbit?wprov=sfla1) that relates all these is:

r = [ (G * M * T^2) / (4 * π^2) ]^(1/3)

Where T is the period (length of the day), r is the orbits radius, and G is the gravitational constant and M is the mass of the planet. Taking a step back from this complication, you can see that, at a high level r is positively correlated with T. So if T is 0, then r must also be 0. Which is the behavior we expected.