Satellite pedigree/apogee ratio. 2 values given both __Earth radii

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SUMMARY

The discussion centers on calculating the gravitational potential energy ratio of a satellite in a noncircular orbit around Earth, specifically focusing on its apogee and perigee distances. The apogee is 3.6 Earth radii, while the perigee is 2.7 Earth radii. The gravitational potential energy (U) is defined as zero at infinite separation, and the formula U = (G m1 m2) / r is referenced, although the masses are unknown. The initial attempts to calculate the ratio using direct division of the distances were incorrect, highlighting the need for a proper application of gravitational potential energy principles.

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  • Understanding of gravitational potential energy (U = (G m1 m2) / r)
  • Knowledge of orbital mechanics, specifically apogee and perigee
  • Familiarity with the concept of Earth radii as a unit of measurement
  • Basic algebra skills for manipulating equations
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  • Study the derivation of gravitational potential energy in orbital mechanics
  • Learn about the conservation of energy in satellite orbits
  • Explore the effects of varying mass on gravitational potential energy calculations
  • Investigate the significance of apogee and perigee in satellite trajectory analysis
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Students and professionals in astrophysics, aerospace engineering, and physics who are interested in satellite dynamics and gravitational calculations.

bharminder
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A satellite is placed in a noncircular orbit about the Earth. The farthest point of its orbit (apogee) is 3.6 Earth radii from the center of the Earth, while its nearest point (perigee) is 2.7 Earth radii from the Earth's center. If we define the gravitational potential energy U to be zero for an infinite separation of Earth and satellite, find the ratio

Upedigree
Uapogee
.


I tried 3.6 Earth radii / 2.7 Earth radii and put 1.3 as the ratio. Then i tried the other way around with 2.7 / 3.6. I looked in my textbook and there is no explanation for this type of problem. I know the equation for gravitational potential energy ( U = (G m1 m2) / r

but I don't have either mass.


Bobby
 
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Try write up the division anyway using the unknown masses and see what happens.

And please make your spell checker stop replacing perigee with pedigree :)
 
The other way round

but this is not even a level question
 

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