# Earth's rotation and geosynchronous satellites

1. Aug 16, 2010

### BenC

I am told that the earth's rotation is inconstant and unpredictable.

If that's the case, then how do geosynchronous satellites, such as weather satellites, stay so well aligned?

Thanks

2. Aug 16, 2010

### AJ Bentley

That's a gross exaggeration.
The rotation has small perturbations - about 1 millisecond maximum on the length of a day caused by such things as the weight distribution of the ice caps and small movements of the mantle.

3. Aug 16, 2010

### BenC

Would the movement be so slight as to mean that no re-alignment would be necessary?

4. Aug 16, 2010

### Staff: Mentor

Through what angle does the earth rotate in one millisecond? That gives you a ballpark estimate of the "pointing error" introduced by these rotational speed fluctuations.

5. Aug 16, 2010

### ErikD

There are 86,400,000 milliseconds in a day. A satellite in geostationary orbit travels a distance of around http://en.wikipedia.org/wiki/Geostationary_orbit" [Broken] per day.

So per day it's orbit could be off by 265,000 / 86,400,000 = 0,0031 km.

The nice thing is that the changes in the length of a day are both ways. Some days the earth will take a bit longer to make a full rotation and some days it will do it faster.

So I'm guessing overall it doesn't matter much.

Last edited by a moderator: May 4, 2017
6. Aug 16, 2010

### sophiecentaur

Geostationary Satellites need propellant to keep them on station. If you don't control their position their mutual gravitational attraction will pull them out of their planned positions. One of the things that limits the life of a broadcast satellite is the station keeping fuel runs out.
One of the factors governing how many geosynchronous orbital positions they can fit around the equator is this mutual attraction and the effects of Sun's and Moon's gravity. Another factor is the size of receiving dishes and the resulting beam-widths of the receivers - interference is a serious consideration when planning coverage with a limited number of available broadcast channels.

7. Aug 16, 2010

### D H

Staff Emeritus
The first and last sentences are correct. The middle one is not. The gravitational attraction between two satellites in orbit is many, many orders of magnitude smaller than perturbations that result from gravitation due to the Earth's non-spherical shape, the Moon, and the Sun and from solar radiation pressure.

8. Aug 17, 2010

### BenC

Thanks for the analysis.
You appear to suggest that the to and fro minuscule nature of the perturbations will cancel out making rotation uniform and constant for purposes of satellite synch.

1. Is there any evidence that the claimed perturbations occur at all?
2. If so, would a time lapse from a weather satellite not register the movements?

9. Aug 17, 2010

### pallidin

"Perturbations" are a fact of reality as nothing is perfect. There are many gravitational influences on an object in space.

But what does this have to do with satellite imaging? Those perturbations are so small as to be of no consequence to weather imaging, or much any satellite function.

10. Aug 17, 2010

### BenC

Just looking for evidence, if it exists. How do we know about these movements apart from theoretically?

11. Aug 17, 2010

### ErikD

It's done using http://en.wikipedia.org/wiki/Quasar" [Broken]. You can take two of them and measure the distance at some point in the earths rotation. Now you wait until you get to that exact point in the earths rotation again and you check how long it took.

Watch this video for a better explanation: http://www.youtube.com/watch?v=KHR1XuIzvts"

Last edited by a moderator: May 4, 2017
12. Aug 17, 2010

### mugaliens

Absolutely, and is the principle reason station-keeping fuel is required. In the "old days," this would usually involve some sort of chemical propellant, or for simplicity's sake, an H2O2 catalytic reaction.

I'm not sure what you mean. Usually the orbits are simply monitorerd over time, and as the satellite slowly drifts off station due to the variety of factors, those factors are logged, along with the satellite's movements. We've become very adept at correllating the factors and predicting just what sort of nudge is required to return it to an orbit that will require negligible adjustments.

We can even predict the effects of the solar cycles, magnetic field reversals, and several other solar factors. What we can't predict well, if at all, is whether or a solar flare will fire this way vs that way, and that throws much of the error into the mix, not just the immediate effect of the flare on the satellite, but of the ancillary effects of the flare on our atmosphere, magnetic field, weather, and more, all of which play a role with respect to the effects of the various factors on satellite orbits.

In summary, we guess. It's a good game, and provided the sun remains predictible, we guess pretty darn good. But the sun is predictible only within certain limits, and the error of those limits of predictibility are proportional to the amount of extra fuel we must load for maneuvering purposes.

13. Aug 17, 2010

### BenC

Right, so you are saying a satellite may drift offcourse for various reasons, such as solar flares, perturbations and whatnot. When it does, we can re-align it either based on predictive models or otherwise after the fact, using its on board fuel in both instances.

I have had the pleasure of watching some time lapse weather satellite footage, and there's zero visible lateral movement over 1 month. Should I be surprised at this?