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

[Xanthippus]

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.

 

[tiny-tim]

Hi Xanthippus!

EDIT: That maths was wrong I'm pretty sure, I now have an answer of 2529.8 seconds …

I think you're √10 out

 

[Xanthippus]

I don't see where...

T=√((〖4x10〗^6 )^3/〖1x10〗^13 )

T=√(〖64x10〗^18/〖1x10〗^13 )

T=√(〖64x10〗^5 )

T=2529.8s

 

[tiny-tim]

oops!

sorry, you're right!