# Mars rotates on its axis once every 24.8 hours.?

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Mars rotates on its axis once every 24.8 hours.

a. What is the speed of a geosynchronous satellite orbiting Mars?

b. What is the altitude of a geosynchronous satellite orbiting Mars?

I have already found the answer to (b), I got 1.72 x 10^7 m.

But I can’t seem to get the answer to (a). Any help would be greatly appreciated. I am looking to find be shown how the problem is done and what the answer is. Thanks

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• Satellite motion, circular

V = √(GM/R)

T = 2π√[R³/GM]

T is period of satellite in sec

V = velocity in m/s

G = 6.673e-11 Nm²/kg²

M is mass of central body in kg

R is radius of orbit in m

mars

Mass 6.4185×10^23 kg

radius 3,396.2 km = 3.396 e6 m

T = 2π√[R³/GM]

T = 24.8 hours (earth hours I assume)

T = 89280 seconds

2π√[R³/GM] = 89280

R³/GM = 2.019e8

R³ = (2.019e8)(6.673e-11)(6.4185e23)

R = ∛((2.019e8)(6.673e-11)(6.4185e23)) = 2.053e7 m

that is above the center of mars, you want altitude

h = 2.053e7 – 3.396e6 = 1.713e7 m

V = √(GM/R) = √((6.673e-11)(6.4185e23) / (2.053e7)) = 1444 m/s 