Universal Gravity Circular Orbit

AI Thread Summary
To find the radius of a circular orbit around Earth where acceleration is 0.1g, the gravitational acceleration g is given as 9.8 m/s². The discussion highlights an incorrect method involving logarithms, leading to an estimated radius of 21,000 m, which is deemed inaccurate. The correct approach utilizes the relationship r² = 10R², resulting in r being √10 times the Earth's radius. The reference from Halliday and Resnick suggests a radius of 6.37 x 10^6 m, leading to a calculated orbit radius of approximately 20 x 10^6 m. The conversation emphasizes the importance of using the correct equations for accurate orbital radius calculations.
The_Scorpion
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Homework Statement


What is the radius of a circular orbit about the Earth where the acceleration is 0.1g?

Homework Equations


g=9.8m/s^2
F=(Gmm)/r^2
Radius of Earth= 6.38x103 km
Mass of Earth= 5.98x10^24 m/s

The Attempt at a Solution


I said 1/(2^x)=1/10 then did log2(10)=x and solved for x getting 3.3 Earth radiuses. I multiplied that by the radius of the Earth and got 21,000 m. This was obviously the wrong method.
 
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Your method seems correct, but the equations seems all messed up (not sure why you use logs to the base 2?):
r2 = 10 R2
so that
r = √10 R
Your answer seems sligthly off.
Also Halliday and Resnick lists R as 6.37 which then gives r as 20 x 106 m.
 
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