Distance from Satellite to Earth Question

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SUMMARY

The discussion focuses on calculating the distance from a satellite in circular orbit to the center of the Earth, given its orbital speed of 7.15 x 103 m/s. The key equations used are the gravitational force equation (FG = GMm / r2) and the centripetal force equation (Fc = mv2 / r). The final answer for the distance from the Earth's center is determined to be 1.22 times the Earth's radius (rearth = 6.38 x 106 m), which translates to a radius of approximately 5.58 x 1010 m.

PREREQUISITES
  • Understanding of gravitational force and centripetal force equations
  • Familiarity with the universal gravitational constant (G = 6.67 x 10-11 Nm2/kg2)
  • Knowledge of Earth's mass (Mearth = 5.98 x 1024 kg)
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the derivation of orbital mechanics equations, specifically v2 = GM/r
  • Learn about the implications of satellite altitude on orbital speed
  • Explore the concept of gravitational potential energy in satellite motion
  • Investigate the effects of varying satellite mass on orbital calculations
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Students studying physics, particularly those focusing on mechanics and orbital dynamics, as well as educators looking for practical examples of gravitational calculations.

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Homework Statement


A satellite in a circular orbit around Earth has a speed of 7.15x103 m/s. Determine, in terms of Earth's radius (radius of earth= 6.38 x106m):

a) the distance the satellite is from Earth's centre
b) the altitiude of the satellite


Homework Equations


FG = GMm / r2
Fc = mv2 / r
G = 6.67 x 10-11


The Attempt at a Solution


I'm seriously unsure on how to even start on this one, because I'm not sure what they mean by 'in terms of Earth's radius.' The answer key says 1.22 rearth for a. Do you have to do this through proportionality and ratios?

In terms of writing down the given/known:
v = 7.15 x 103 m/s
rearth = 6.38 x 106 m
Mearth = 5.98 x 1024 kg
G = 6.67 x 10-11 Nm2/kg2

I can't figure out the force of gravity because I don't have the mass of the satellite, so that cancels out finding Fc as well since I need the mass for that too.

Any help on how to start this would be appreciated, thank you.
 
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You won't need the mass of the satellite.

Fc = mv2/r = Fg = GMm/r2

v2 = GM/r
 
LowlyPion said:
You won't need the mass of the satellite.

Fc = mv2/r = Fg = GMm/r2

v2 = GM/r

Oh, I see. But I'm still confused by "in terms of Earth's radius," what exactly do they mean by that?
By the way, I used v2 = GM /r to find that r = 5.58 x 1010 Would that be the radius from the Earth's centre to the satellite?
Thanks for your help
 
In terms of Earth's radius means how many multiples of the Earth's radius is the satellite orbiting at.
 
Kurdt said:
In terms of Earth's radius means how many multiples of the Earth's radius is the satellite orbiting at.

Ah, I got it now. Thanks for the help Kurdt and LowlyPion.
 

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