How Far Above Earth is the Satellite?

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SUMMARY

The discussion centers on calculating the altitude of a satellite above Earth's surface, given Earth's radius of 6.86 million meters and gravitational acceleration of 3.2 m/s². The gravitational force equation, GMm/R², is correctly identified, but the user initially misinterprets the radius R as the distance from the center of the Earth rather than the altitude above the surface. The correct approach requires subtracting Earth's radius from the calculated distance to find the satellite's height above the surface.

PREREQUISITES
  • Understanding of gravitational force equations (GMm/R²)
  • Knowledge of Earth's radius (6.86 million meters)
  • Basic algebra for solving equations
  • Familiarity with gravitational acceleration concepts
NEXT STEPS
  • Review gravitational force calculations in physics
  • Learn about the implications of gravitational acceleration at different altitudes
  • Study the relationship between mass, radius, and gravitational force
  • Explore satellite dynamics and orbital mechanics
USEFUL FOR

Students studying physics, particularly those focusing on gravitational forces and satellite motion, as well as educators seeking to clarify concepts related to gravitational acceleration and distance calculations.

Rbethell16
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1. Homework Statement
The radius of the Earth is 6.86 e6 m and the mass of the Earth is 5.98 e24kg. There is a satellite floating in space at a point where the Earth's gravitational acceleration is 3.2 m/s^2.

How far above the Earths surface is the Satellite?
2. Homework Equations
GMm/R^2 = F


3. The Attempt at a Solution
So I did 3.2 = GM/R^2...R = 1164480.51. But that isn't right - could someone please guide me as to how I should go about setting up the equation
 
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That is the correct equation. Why do you think your answer is wrong?
 
I didn't check the calculation, but let's assume you did it correctly and R is indeed 1164480.

Then whát distance exactly is 1164480 (and in what units? Always state your units!).
Is that the distance you were asked to find?
 

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