Understanding the Force of Gravity, Step-by-Step

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SUMMARY

The discussion focuses on calculating the force of gravity experienced by an astronaut in an Earth satellite at an altitude equal to Earth's radius. The astronaut's weight on Earth is 900 N, and the correct gravitational force in the satellite is determined to be 225 N. The calculation utilizes the formula F=Gm1m2/r^2, with the key insight that the distance from the center of the Earth doubles when in the satellite, leading to the conclusion that the gravitational force is one-fourth of the weight on the surface of the Earth.

PREREQUISITES
  • Understanding of gravitational force equations, specifically F=Gm1m2/r^2
  • Knowledge of weight calculation using w=mg
  • Familiarity with the concept of gravitational force variation with distance
  • Basic understanding of Earth's radius and its significance in gravitational calculations
NEXT STEPS
  • Study the implications of gravitational force changes at varying altitudes
  • Learn about the Universal Law of Gravitation and its applications
  • Explore the concept of weightlessness in orbiting satellites
  • Investigate the effects of altitude on gravitational acceleration
USEFUL FOR

Students studying physics, educators teaching gravitational concepts, and anyone interested in the mechanics of weight and gravity in different environments.

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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.
 
Physics news on Phys.org
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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