Kepler's Third Law satellite problem

AI Thread Summary
To determine the altitude of a synchronous orbit over Pluto, the equation r = [(G*M*T^2)/4pi^2]^(1/3) is used, with G as the gravitational constant, M as Pluto's mass, and T as the orbital period. After calculating the radius, which results in approximately 1.89e^7 m, the radius of Pluto (1,153,000 m) is subtracted to find the altitude, yielding 1.77e^4 km. Despite this calculation, the answer is marked incorrect in the system, prompting a request for assistance in identifying potential errors in the approach. Other participants confirm the calculations align with their own, suggesting the issue may lie elsewhere. Further clarification or verification of the input values may be necessary to resolve the discrepancy.
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Homework Statement



An orbiting satellite stays over a certain spot on the equator of (rotating) Pluto. What is the altitude (in km) of the orbit (called a "synchronous orbit")?


Homework Equations


r = [(G*M*T^2)/4pi^2]^(1/3)
h= r-radius of pluto


The Attempt at a Solution


I have plugged in the numbers (6.67e^-11) for G, (1.31e^22 kg) for M, and (551852 s) for T. I get (1.89e^7 m) for the radius. Then I subtract 1,153,000 meters from my answer to account for the radius of Pluto. My final answer in meters is (1.77e^7 m). My final answer in km is (1.77e^4 km). However, when I input this, the system shows this is wrong. I've tried several variations of the answer, but nothing works. Does anyone know if I've overlooked something in the equation? Thanks.
 
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Seems right.
 
I get the same answer.
 

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