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## Homework Statement

[PLAIN][PLAIN]http://i77.photobucket.com/albums/j64/mrbebu/Physics_orbit_problem.jpg [Broken]

## Homework Equations

[tex]\frac{GMm}{R^{2}}[/tex]

v = [tex]\sqrt{\frac{GM}{R}}[/tex]

v = wR

## The Attempt at a Solution

Am I correct in my methods and thinking?

R_g = Geosynchrous orbit from earth's center = 4.22 x 10[tex]^{7}[/tex]m

R_e = Radius of earth = 6.37 x 10[tex]^{6}[/tex]

velocity of geosynchrous orbits (same for both satelites) --->

v = [tex]\sqrt{\frac{GM}{R_g}}[/tex] = 3072 m/s

Then I decided to find the angular velocity to relate it with angular displacement--->

w = [tex]\frac{v}{R_g}[/tex] = 7.28 x 10[tex]^{-5}[/tex] rad/s

so 10 orbits in a geosynchrous orbit is 240 hours = 864000 seconds

The satellite that needs to catch up needs to complete 10.5 orbits in the same time.

10.5 orbits = 21[tex]\pi[/tex] radians ---> [tex]\bar{w}[/tex] = [tex]\frac{d\theta}{dt}[/tex] = 7.64 x 10[tex]^{-5}[/tex] rad/s

Ratio of the w's =

[tex]\frac{7.28 x 10^{-5}}{7.64 x 10^{-5}}[/tex] = 0.95

since w is inversely proportional to the radius, the satellite that needs to catch up will need to have a radius 0.95 times a geosynchrous one which --->

0.95 x 4.22 x 10[tex]^{7}[/tex] = 4.01 x 10[tex]^{7}[/tex] m from earth's center

But, i have a feeling that this is an incorrect assumption.

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