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
1 Answer
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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
