Is the Time of Orbit for a Satellite Above Mars Really 800 Million Years?

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The discussion centers on calculating the orbital period of a satellite around Mars, using the equation R^3/T^2 = 1x10^13 m^3 s^(-2). Initially, an incorrect calculation suggested an orbital time of 800 million years, which raised confusion about the acceleration involved. After reevaluating the math, the correct orbital period was determined to be approximately 2529.8 seconds, indicating a much faster orbit. Participants acknowledged the error in the initial calculations and clarified the correct approach. The conversation highlights the importance of accurate mathematical application in orbital mechanics.
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Homework Statement


We have been asked to work out the approximate time of orbit, T, of a satellite orbiting above the centre of Mars, radius 4000km.

Homework Equations


We have been given the equation:

R^3/T^2 =1x〖10〗^13 m^3 s^(-2)

The Attempt at a Solution


When using the equation:

T=√((4x〖10〗^6 )^3/〖1x10〗^13 )

I get an answer of 2.53 x 10^16 seconds and I don't understand how something that seems to be accelerating so fast turns out to be taking 800 million years to orbit mars. Is my math just totally wrong?

EDIT: That maths was wrong I'm pretty sure, I now have an answer of 2529.8 seconds which is pretty fast for an orbit of Mars but 1x10^13 m^3 s^-2 is a hell of an acceleration.
 
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Hi Xanthippus! :smile:
Xanthippus said:
EDIT: That maths was wrong I'm pretty sure, I now have an answer of 2529.8 seconds …

I think you're √10 out :wink:
 
I don't see where...

T=√((〖4x10〗^6 )^3/〖1x10〗^13 )

T=√(〖64x10〗^18/〖1x10〗^13 )

T=√(〖64x10〗^5 )

T=2529.8s
 
oops!

sorry, you're right! :redface:
 

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