Geostationary satellites

[Kushal]

Homework Statement

Explain why a geostationary satellite must be placed vertically above the equator.

Homework Equations

i know a GS has a period of 24 h,... and that it remains at a specific position with respect to a point on earth.

The Attempt at a Solution

i googled a bit and i saw that if the satellite is not above the equator, it will bob up and down. but WHY is this?

thnks

 

[Borek]

Imagine the circular orbit. Where is its center? It lies on the plane - imagine how this plane is positioned when compared with equatorial plane.

 

[Kushal]

the centre of the orbit is at the centre of earth. the plane of the circular orbit if the satellite is above the equator is the same as the equatorial plane.

but if the satellite is not above the equator, the plane of the orbit will be at an angle with the equatorial plane. then there will also be a vertical component.

is it right?

 

[dynamicsolo]

Since the problem is calling 'vertical' what is actually 'radial', let's not call the oscillation of the satellite about the Equator 'vertical'; 'latitudinal' or 'North-South' might be better.

The point is that the plane of the orbit must pass through the center of the Earth, so if that plane is inclined to the Equatorial plane, the satellite will spend half its orbit north of the Equatorial plane and half of it to the south of that plane. So your last statement is basically correct.

 

[Kushal]

thnks borek and dynamicsolo. i understood the problem.

what if the plane is parallel to the equatorial plane, but it is above(or below) it, i.e. it does not pass through the centre?

the satellite will have to oppose the vertically downward force (when above the equatorial plane) in order to remain in that position.

right?

 

[dynamicsolo]

There would be a component of gravitational force perpendicular to that plane, since gravity is a radial (or 'central') force. Yes, to remain in an orbital plane parallel to the Equatorial plane, the satellite would have to carry some form of propulsion to provide a continual force opposing that gravitational component. (Such a technique was proposed back in the '80s for extending the range of possible orbits for geosynchronous satellites, making more 'orbital slots' available for the growing number of such spacecraft . Improvements in the capacity of the communications technology aboard these satellites, though, have forestalled the need for such expensive alternatives.)