Need help with keplers 3rd law of periods problem

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SUMMARY

The discussion focuses on solving a problem related to Kepler's Third Law of Periods, specifically for a satellite orbiting a planet. The satellite has a mass of 20 kg, an orbital period of 2.6 hours, and a radius of 9.4E6 m. The gravitational acceleration on the planet's surface is given as 8.6 m/s². The key equations used are T² = (4π²/GM)r³ for orbital period and a = GM/r² for gravitational acceleration. The user encountered difficulties in calculating the planet's radius, indicating a misunderstanding of the variables in the equations.

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[SOLVED] need help with keplers 3rd law of periods problem

Homework Statement


A 20 kg satellite has a circular orbit with a period of 2.6 h and a radius of 9.4E6 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 8.6 m/s2, what is the radius of the planet?



Homework Equations


T^2=((4pi^2)/(GM))r^3

a gravity=(GM)/r^2


The Attempt at a Solution



I used the law of periods to find the mass and then used the second equation to find the radius of the planet but I got a really small number
 
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Can you show your calculations in more detail? Note that r in your first equation is not the same as r in the second (in case you forgot that).
 

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