How Does Height Above Earth Affect Satellite Weight?

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SUMMARY

The weight of a satellite decreases as its altitude increases due to the diminishing gravitational force. At a height of 12.8 * 10^6 m above Earth's surface, the gravitational acceleration (g) is not constant at 9.81 m/s². Instead, it should be recalculated using the formula F = GMm/d², where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and d is the distance from the center of the Earth to the satellite. This approach provides a more accurate weight calculation for satellites at significant altitudes.

PREREQUISITES
  • Understanding of gravitational force and its dependence on distance
  • Familiarity with the formula F = GMm/d²
  • Basic knowledge of physics concepts such as mass and weight
  • Ability to perform calculations involving large distances and constants
NEXT STEPS
  • Research the gravitational constant (G) and its significance in satellite calculations
  • Learn how to derive gravitational acceleration at various altitudes
  • Explore the implications of altitude on satellite operations and stability
  • Study the effects of orbital mechanics on satellite weight and performance
USEFUL FOR

Students studying physics, aerospace engineers, satellite operators, and anyone interested in the effects of altitude on gravitational forces.

Arooj
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Homework Statement


What is the weight of a 200 kg satellite 12.8 * 10^6 m above the surface of the Earth.


Homework Equations


F = mg


The Attempt at a Solution


F=200 (9.81)
F = 1962 N

I thought this was a basic weight problem, but I was confused on whether the height above the Earth affects the weight.
 
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The gravitational force gets weaker as you go further out from the center of the Earth. The g = 9.81 value will not be accurate. You could use the basic gravitational force formula F = GMm/d² (M=mass of Earth, m = mass of satellite, d = distance from center of Earth to center of satellite) or you could use the F = mg with g = GM/d².
 

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