Universal Gravity Circular Orbit

[The_Scorpion]

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.

 

[Basic_Physics]

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.