Why Does a Slowed Down Satellite Spiral Inwards? - Gary

[garytse86]

If a satellite in orbit has been slowed down, why does it spiral inwards?

The explanation I have been given is that the gravitational force on the satellite is constant but the centripetal acceleration has reduced and therefore there is some spare gravitational force to pull the satellite inwards.

Are there any alternative explanations? The "spare" force doesn't convince me though.

Thanks.

Gary

 

[selfAdjoint]

The satellite doesn't spiral inwards until it enters the atmosphere which retards it. Initially when it slows down it just enters a lower orbit.

 

[BobG]

That's a pretty good explanation.

Your satellite in orbit has two types of energy: kinetic (based on its mass and speed) and potential (based on how far from Earth it is).

In a stable orbit, the total energy (KE + PE) stays constant (so a satellite is faster at perigee when it's close to the Earth and slow at apogee when it's far from Earth). While a few will give me problems over this, you could visually grasp the idea of how much total energy was in the orbit by looking how at much area lies within the orbit (some will correctly point out that the area is more directly related to the angular momentum).

If you take some kinetic energy out of the orbit with some external force (due to atmospheric drag, for instance), the total energy of the orbit decreases. The area enclosed by the orbit will aso decrease. The decrease in the total energy is the key parameter.

The atmosphere doesn't cut off suddenly. It tapers off, so there is still at least 'some' atmosphere even up to around 600 miles (and even further, but eventually it's so sparse you can ignore it). The result is that satellites in low orbits, such as the ISS, experience some atmospheric drag.

The Earth's gravitational attraction isn't constant, either. It's inversely proportional to the distance between the satellite and the center of the Earth. A lower altitude results in a stronger pull from the Earth.

Any decrease in the mean altitude means the satellite will wind up closer to the Earth, in denser atmosphere, hence an increase in atmospheric drag and the force of gravity and a very slow spiraling into the atmosphere. Unless, of course, you compensate by adding some kinetic energy by speeding the satellite up.

 

[krab]

The explanation I have been given is that the gravitational force on the satellite is constant but the centripetal acceleration has reduced and therefore there is some spare gravitational force to pull the satellite inwards.

Nothing wrong with that explanation. If you want a more visual picture, think of the following.

Say the orbit is circular to start with. Now say the satellite is slowed very slightly. The new orbit is an ellipse, with the location where the slowing was experienced as the far point. 90 degrees of orbit later it is at the near point. Imagine that at this point it receives another decrement in velocity. The new orbit can be circular again, but its radius is now the near-point distance. And so on. I think you can see that if the slowing down is continuous, the orbit will continually decrease in size.

 

[remcook]

The explanation I have been given is that the gravitational force on the satellite is constant but the centripetal acceleration has reduced and therefore there is some spare gravitational force to pull the satellite inwards.

This is only valid at the time when the sudden (discontinuous) velocity change takes place. Gravitational force is not constant for an elliptical orbit of course.