Satellite orbiting Earth problem involving weight?

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SUMMARY

The discussion revolves around calculating the altitude at which a satellite would experience half of its weight due to gravitational forces. Using the gravitational force equation F=Gm1m2/r^2, participants are tasked with determining the distance from Earth's surface where this occurs and the corresponding orbital velocity required to maintain the satellite's orbit. The gravitational constant G is specified as 6.673 x 10^-11. Additionally, participants are encouraged to consider the implications of measuring weight in a satellite environment.

PREREQUISITES
  • Understanding of gravitational force equations, specifically F=Gm1m2/r^2
  • Familiarity with gravitational potential energy, PE=-GMEm/r
  • Basic knowledge of orbital mechanics and satellite motion
  • Ability to perform calculations involving mass and weight
NEXT STEPS
  • Calculate the altitude where weight is halved using F=Gm1m2/r^2
  • Determine the orbital velocity required for a satellite at that altitude
  • Explore the effects of microgravity on weight measurement in a satellite
  • Study the implications of gravitational potential energy in satellite dynamics
USEFUL FOR

Students in physics, aerospace engineers, and anyone interested in satellite dynamics and gravitational effects on weight measurement.

kalisious
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Homework Statement


Imagine you are sent in a satellite.
a) How far above the surface of the Earth would you lose 1/2 of your weight?
b) To maintain the satellite orbiting around the Earth at that distance, what will be the velocity of the satellite?
c) Imagine you have taken a weighing machine with you. If you try to measure your weight what will it be? (Satellite is still orbiting Earth as in b)


Homework Equations


F=Gm1m2/r^2
PE=-GMEm/r

G=6.673*10^-11


The Attempt at a Solution


No idea.
 
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F=Gm1m2/r^2 is the weight. Weight is a force in units of Newtons.
I suggest you put in some reasonable number for your mass and figure out your weight at the surface of the Earth. Then see if you can find the radius that results in half that weight.
 

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