Calculating energy of a geosynchronous satellite

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SUMMARY

The discussion focuses on calculating the total energy (E) of a geosynchronous satellite with a mass of 1500 kg orbiting Earth at a height of 325 km and an orbital speed of 5000 m/s. The participant correctly identifies the formulas for kinetic energy (KE = 1/2 mV^2) and gravitational potential energy (PE = mgH), but misapplies the gravitational force calculation by using an incorrect height for a geosynchronous orbit. The correct orbital height for geosynchronous satellites is approximately 35,786 km, not 325 km, which would result in the satellite falling back to Earth.

PREREQUISITES
  • Understanding of gravitational force and orbital mechanics
  • Familiarity with the equations for kinetic and potential energy
  • Knowledge of the universal law of gravitation (Fg = Gm1m2/d^2)
  • Basic principles of satellite motion and geosynchronous orbits
NEXT STEPS
  • Research the correct altitude for geosynchronous satellites (approximately 35,786 km)
  • Learn about the implications of orbital speed on satellite stability
  • Study the derivation and application of gravitational potential energy in orbital mechanics
  • Explore the differences between geostationary and geosynchronous satellites
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Students studying physics, aerospace engineers, and anyone interested in satellite dynamics and orbital mechanics.

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Homework Statement



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hey i was just wondering if i was on the right track here, the question is calculate the total energy(E) of a geosynchronous satelite (that orbits around a fixed spot) with a mass of 1500kg orbiting Earth at a height of 325km with an orbital speed of 5000 m/s,

Homework Equations



ok i was taught that Total E = Kinetic E + Potential E, and also that Kinetic E= 1/2mV^2 and Potential E= mgH

The Attempt at a Solution


ok i took into account that gravity would not be 9.8 so
i calculated what it would be Using Fg=Gm1m2/d^2 and i came up with 1.32x10^4,also note that to calculate distace i added 325km to the radius of the earth, then i plugged
in 1/2(1500)(5000)^2 + 1.32x10^4(1500)325000 = Total E, does this seem correct? thanks
 
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Remember energy is force * distance and so gravitatonal potential energy = GMm/r
 
There is a problem with the question. Geosynchronous satellites do not orbit at 325 Km height. And a satellite at 325km with an orbital speed of 5000m/s will fall back to earth.
 

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