Particle in uniform circular motion

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SUMMARY

The discussion focuses on calculating the speed and orbital period of a satellite orbiting 600 km above the Earth's surface, where the gravitational acceleration is 8.21 m/s² and the Earth's radius is 6400 km. The satellite's angular velocity (w) was calculated as 0.0346 rad/s, leading to an orbital period (T) of approximately 0.76 seconds, which is incorrect. The correct orbital period should be around 7000 seconds, indicating a significant error in the calculations, likely due to unit mismanagement.

PREREQUISITES
  • Understanding of circular motion equations, specifically v = (2πr)/T
  • Knowledge of angular velocity and its relationship to period (w = 2π/T)
  • Familiarity with gravitational acceleration and its impact on orbital mechanics
  • Ability to perform unit conversions and dimensional analysis in physics calculations
NEXT STEPS
  • Review the derivation of orbital speed formulas in circular motion
  • Learn about gravitational forces and their effects on satellite motion
  • Study the concept of centripetal acceleration in the context of orbital mechanics
  • Explore the use of dimensional analysis to verify calculations in physics
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Students studying physics, particularly those focused on mechanics and orbital dynamics, as well as educators seeking to clarify concepts related to satellite motion and gravitational effects.

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Homework Statement



A satellite is orbiting 600km above the Earths surface. The free fall speed is 8.21 m/s^2. The radius of Earth is 6400km.

What is the satellites speed, and the time interval for one orbit around Earth.

Homework Equations



v = ((2)(PI)(r))/T
ac = rw^2
w = (2)(PI) / T

The Attempt at a Solution



8.21 = 7000w^2
w = .0346

.0346 = (2(PI)) / T
T = .76

(2)(PI)(7000) / .76 = 57871.44

I am unsure of what to do or where I went wrong.
 
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You should always use units in your calculations. In this case, units would have shown you where the error is.
(The result should be somewhere around 2 hours or ~7000 seconds, probably a bit less)
 

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