Understanding the Force of Gravity, Step-by-Step

AI Thread Summary
An astronaut weighing 900 N on Earth's surface experiences a gravitational force of 225 N at an altitude equal to Earth's radius. The calculation involves using the formula F = Gm1m2/r^2, where the distance from the center of the Earth doubles when in a satellite. This leads to the force being divided by four, resulting in 225 N. A common mistake is neglecting the Earth's radius in the calculations. Understanding the impact of distance on gravitational force is crucial for accurate results.
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Homework Statement



An astronaut weighs 900 N when measured on the surface of Earth. How large would the force of gravity be if he were in an Earth Satellite at an altitude equal to Earth's radius?

The correct answer is 225 N. However, I need to know the exact steps taken to get the answer. I already tried many methods and I would appreciate somebody explaining it to me.

Homework Equations



I used F=Gm1m2/r^2

and w=mg

The Attempt at a Solution



I plugged everything into above equation and got wrong answer. Correct answer is 225N which I cannot figure out.
 
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F = 900N = Gm1m2/r^2 when r is equal to Earth's radius

On a satellite at an altitude equal to Earth's radius, the distance between the astronaut and the centre of the Earth is doubled, so...

Answer = Gm1m2/(2r)^2 = (Gm1m2/r^2)/4 = 900/4 = 225 NewtonsNot taking the radius of the Earth into account with the calculations is a common mistake.
 
thanks, yeah i missed out on the radius of earth
 

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