Will someone check my application of kepler's laws?

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The discussion focuses on verifying calculations related to Kepler's laws. The first calculation involves determining the length of the Earth's orbit's major axis using its orbital period of approximately 365.25 days, the mass of the sun, and the gravitational constant. The second calculation addresses the altitude required for a satellite to maintain a fixed position over a specific location on the equator, utilizing the Earth's mass and radius. Errors identified include incorrect unit conversion for the first problem and minor arithmetic mistakes in the second. Overall, the thread emphasizes the importance of accuracy in applying Kepler's laws and gravitational principles.
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1. The period of the Earth's orbit is approximately 365.25 days. Use this fact and Kepler's Third Law to find the length of the major (not semi-major) axis of the Earth's orbit. You will need the mass of the sun, M = 1.99x10^30 kg, and the gravitational constant, G = 6.67x10^-11 Nm^2/kg^2.


2. It's possible to place a satellite into orbit about the Earth so that it remains fixed above a given location on the equator. Compute the altitude that is needed for such a satellite. The Earth's mass is 5.98x10^24 kg; its radius is 6.37x10^6 m.

Sorry, I couldn't figure out how to get the equations from microsoft equation editor into the question, so you'll have to open the attachment (you may have to save it, I apologize). I've got full solutions worked out, so all I need is for someone to double check me.
Thanks in advance!
 

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First one you have the wrong answer. You forgot to convert days to seconds. Also your maths in the various stages is a little off. I'll let you see if you can spot what it is.

Second one is slightly off as well. I think that's just arithmetic.
 
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