Kepler's Third Law: Homewor Help

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SUMMARY

The discussion focuses on calculating the period of revolution for a spy satellite located one Earth radius above the Earth's surface using Kepler's Third Law. The derived answer is 1.5 x 104 seconds. Participants emphasize the use of Kepler's constant, k = T2/R3, and suggest employing Newton's law of gravitation to relate gravitational force to centripetal force for accurate calculations.

PREREQUISITES
  • Understanding of Kepler's Third Law
  • Familiarity with Newton's law of gravitation
  • Basic knowledge of centripetal force
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Research the derivation of Kepler's laws in celestial mechanics
  • Study the application of Newton's law of gravitation in orbital mechanics
  • Learn about centripetal acceleration and its relation to gravitational force
  • Explore the concept of gravitational constants and their significance in calculations
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Students studying physics, particularly those focusing on orbital mechanics and gravitational forces, as well as educators seeking to enhance their understanding of Kepler's laws and their applications.

No2
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Homework Statement



A spy satellite is located one Earth radius above the surface of the Earth. What is its period of revolution?

ans. 1.5 x 10^4 s

Homework Equations



I'm trying to use the kepler's constant: k = T^2/R^3

The Attempt at a Solution

 
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Kepler's law can be derived by equating the force of attraction with centripetal force

i.e. GMm/r2=mω2r

or GM/r3=(2π/T)2

So what would be your constant or proportionality 'k' if you rearrange to get T2/r3?
 
Welcome to PF!

Hi No2! Welcome to PF! :smile:

(try using the X2 icon just above the Reply box :wink:)
No2 said:
I'm trying to use the kepler's constant: k = T^2/R^3

Unless you're using the Moon, what T are you going to compare with? :confused:

Use the ordinary Newton's law of gravitation to find the force of gravity as a multiple of g (that's our g, not G ! :wink:), and https://www.physicsforums.com/library.php?do=view_item&itemid=27" :smile:
 
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