physics question

Question

The Earth rotates on its axis once every 24 hours. Satellites that complete one orbit around the earth in 24 hours basically stay in the same spot above Earth. This is called a geosynchronous orbit. 

If the satellite decreased its orbit (35855910.176167 m above the Earth) decreased by a factor of 1/2, then by what factor would the orbital velocity change?

Answer 1

I think the key "trap" here is that the altitude of the satellite (above the surface of the Earth) is different from the radius of the orbit (centered on the center of the Earth).

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\

Earth \

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x---------|-------------------------s

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/

/

/

The question seems to imply that the quantity being halved is the altitude (above the surface of the Earth) rather than the full radius of the orbit.

The orbital velocity (as I'm guessing has been covered in your class) can be expressed in terms of the radius of the orbit and G and M the standard gravitational parameters (this is assuming the satellite's mass is negligible compared to the mass of the Earth): v ~ sqrt(GM / r) (where 'sqrt' is square root).

I hope this gets you closer to answering the question :-)