Centripetal Acceleration of object orbiting earth

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SUMMARY

The centripetal acceleration of an object orbiting Earth at a radius of 6.38x106 m is derived from the gravitational force equation, where acceleration equals GM/r2. The discussion clarifies that centripetal acceleration is indeed equal to GM/r2 when the object is in a stable orbit. Discrepancies in calculations arise when different methods are applied, but the fundamental relationship holds true under the conditions specified.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Familiarity with centripetal force and acceleration concepts
  • Basic knowledge of circular motion dynamics
  • Ability to manipulate equations involving gravitational constants
NEXT STEPS
  • Study the derivation of centripetal acceleration using GM/r2
  • Explore the implications of varying orbital radii on centripetal acceleration
  • Learn about the differences between gravitational force and centripetal force
  • Investigate real-world applications of centripetal acceleration in satellite motion
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Physics students, educators, and anyone interested in understanding orbital mechanics and gravitational forces.

Fusilli_Jerry89
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Homework Statement


An object orbits the Earth at a constant speed in a circle of radius 6.38x10^6m, very close to but not touching the Earth's surface. What is its centripetal acceleraion?


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The Attempt at a Solution


Quick question, when would GM/r^2 equal to the centripetal acceleration, and when wouldn't it? I thought it always did but some calculations don't have the same numbers if you do it both ways. For this question would it be?
 
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Well, force is GMm/r^2 (Newton et al) and acceleration is force/m (Newton et al). So acceleration=GM/r^2. If you have evidence otherwise, cough it up.
 

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