Universal Gravity Circular Orbit

In summary, to find the radius of a circular orbit around Earth with an acceleration of 0.1g, one can use the equation r = √10 R, where R is the radius of Earth. This results in a radius of approximately 20 x 106 m, according to Halliday and Resnick's value of R as 6.37.
  • #1
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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  • #2
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.
 

Related to Universal Gravity Circular Orbit

What is Universal Gravity Circular Orbit?

Universal Gravity Circular Orbit is a fundamental concept in physics that explains how objects in the universe move in circular orbits around each other due to the force of gravity.

Who discovered the concept of Universal Gravity Circular Orbit?

The concept of Universal Gravity Circular Orbit was first introduced by Sir Isaac Newton in his famous book "Principia Mathematica" in 1687.

How does Universal Gravity Circular Orbit affect the motion of planets?

Universal Gravity Circular Orbit explains that the gravitational force between the sun and the planets keeps them in a circular orbit around each other, causing them to revolve around the sun in a specific path.

What is the formula for calculating the force of gravity in a Universal Gravity Circular Orbit?

The formula for calculating the force of gravity in a Universal Gravity Circular Orbit is F = G * (m1 * m2)/d^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

Can Universal Gravity Circular Orbit be applied to objects on Earth?

Yes, Universal Gravity Circular Orbit can be applied to objects on Earth, as the force of gravity affects all objects in the universe, regardless of their size or location.

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