Universal Gravity Circular Orbit

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SUMMARY

The discussion focuses on calculating the radius of a circular orbit around Earth where the acceleration is 0.1g. The gravitational acceleration (g) is established as 9.8 m/s², and the mass of Earth is given as 5.98 x 10²⁴ kg. The correct formula to determine the radius (r) involves using the relationship r = √(10 * R), where R is the radius of Earth (6.38 x 10³ km). The final calculated radius for the orbit is approximately 20,000 m, correcting earlier miscalculations involving logarithmic methods.

PREREQUISITES
  • Understanding of gravitational force equations, specifically F = (Gmm)/r²
  • Familiarity with gravitational acceleration and its implications in orbital mechanics
  • Knowledge of Earth’s mass and radius values
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the derivation of orbital radius formulas in classical mechanics
  • Learn about gravitational force and its applications in satellite motion
  • Explore the concept of acceleration due to gravity in different celestial contexts
  • Investigate the implications of varying gravitational forces on orbital stability
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and gravitational forces, as well as educators seeking to clarify concepts related to orbital dynamics.

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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