Calculating Orbital Velocity and Period Using Kepler's Laws

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SUMMARY

This discussion focuses on calculating the orbital velocity and period of a ship in orbit 155 miles above Earth using Kepler's Laws. The velocity was determined to be approximately 7757.8 m/s using the equation v=(G*(m/r))^0.5. The orbital period was initially miscalculated but was corrected to approximately 5358 seconds using the formula T² = 4π²R³/(GM), confirming the time to be around 1 hour and 30 minutes is inaccurate.

PREREQUISITES
  • Understanding of Kepler's Laws of planetary motion
  • Familiarity with gravitational equations, specifically Fc = Fg
  • Knowledge of the constants G (gravitational constant) and M (mass of Earth)
  • Ability to perform unit conversions between miles and meters
NEXT STEPS
  • Study the derivation of Kepler's Laws for deeper insights
  • Learn about gravitational constant G and its applications in orbital mechanics
  • Explore advanced orbital dynamics simulations using software like MATLAB or Python
  • Investigate the effects of altitude on orbital velocity and period
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in orbital mechanics and satellite dynamics will benefit from this discussion.

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Homework Statement


A ship is in orbit 155 mi. above the earth, (a) what is its velocity? (b) How long will it take the ship to orbit the earth?



Homework Equations


v=(G*(m/r)).5, (2*PI*r)/T=v


The Attempt at a Solution


I added 155 mi to 3963 mi and got 4118 mi and that is about 6627359 m, which is how high the ship is from the center of the earth. I plugged that into the first equation I gave, and got a velocity of about 7757.8 m/s, which seems pretty logical to me. However, I'm not sure about the time. I solve for T in the second equation (ex. (2*PI*6627359)/7757.8) and get about 5367.6 seconds, about 1 hour and 30 minutes, and that seems way to short. Any ideas on where to point me?
Thanks in advanced :)
 
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I found the period directly.
Fc = Fg
4π²mR/T² = GMm/R²
T² = 4π²R³/(GM)
Using R = 6619448 m I got T = 5358 s.
It is a reasonable time.
 

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