Finding radius of satellite in orbit given mass and rotational period

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SUMMARY

The discussion focuses on calculating the radius of a satellite in geosynchronous orbit around Planet X, which has a mass of 5.90 x 1024 kg and a rotational period of 26.4 hours. The correct formula used is T2/r3 = 4π2/GM, leading to the rearranged equation r = (GMT2 / 4π2)1/3. After substituting the gravitational constant G = 6.67 x 10-11 m3kg-1s-2, the mass M, and the period T converted to seconds (95040 s), the calculated radius is 2.06 x 108 m or 2.06 x 105 km. The user expressed confusion over discrepancies in the calculations, indicating potential arithmetic errors.

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Homework Statement



Suppose that Captain Omega of the Imperial Space Patrol wishes to place a spy satellite in geosynchronous orbit above the mysterious Planet X, which has a mass of 5.90 x1024 kg, and a rotational period of 26.4 hours.

(a) What should be the radius of the satellite's orbit?
(b) What would be the orbital speed of the satellite?

Homework Equations


The Attempt at a Solution



I used the law of periods : T2/r3 = 4∏2/GM

So I rearranged that to get:

r = (GMT2 / 4∏2) 1/3

I plugged in:
G = 6.67 e -11
M = 5.9 e 24 kg
T = 95040s

I ended up with 2.06e8 m = 2.06e5 km

But that answer isn't right and I don't understand what I'm doing wrong.
 
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I plug in your numbers to your formula and I get a different answer. You must have forgot a step in your arithmetic.
 
Thank you! I'm not sure what I was doing wrong..mistake while entering in the calculator I guess!
 

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