The Mars Reconnaissance Orbiter circles the red planet with a 116 min period. Th

Question

The Mars Reconnaissance Orbiter circles the red planet with a 116 min period. The mass of Mars is 6.42×1023kg, the radius is 3.38×106m.

Part A

What's the spacecraft's altitude?

So far I have gotten the following answers which have all been incorrect.....

3.2106m

ANSWER 2:

3.39106m

ANSWER 3:

1.81010m

ANSWER 4:

3.7106m

ANSWER 5:

3.2105m

The Mars Reconnaissance Orbiter circles the red planet with a 116 min period. The mass of Mars is 6.42×1023kg, the radius is 3.38×106m.

Part A

What's the spacecraft's altitude?

So far I have gotten the following answers which have all been incorrect.....

H =

3.2106m

ANSWER 2:

H =

3.39106m

ANSWER 3:

H =

1.81010m

ANSWER 4:

H =

3.7106m

ANSWER 5:

H =

3.2105m

Explanation / Answer

for circular orbit,

G M m / r^2 = m v^2 / r

G M = v^2 r

6.67 x 10^-11 x 6.42 x 10^23 = v^2 r

v^2 r = 4.282 x 10^13

and time period . T = 2pir / v

v = 2 pi r / T = (2 x pi x r ) / (116 x 60 sec)

v = 9.0276r x 10^-4

(9.0276r x 10^-4)^2 r =4.282 x 10^13

r = 3745431.01 m

h= r - R = 3745431.01 - 3.38x10^6 = 365431 m Or 3.65 x 10^5 m

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