Finding the orbital height of a satellite

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Homework Help Overview

The discussion revolves around finding the orbital height of a satellite given a specific gravitational force of 5.7 m/s². The original poster is using the equation g = Gm/(r+h)², where G is the gravitational constant, m is the mass of the Earth, r is the radius of the Earth, and h is the orbital height from the Earth.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the gravitational equation and the implications of rearranging it to isolate h. There is uncertainty about how to handle the term (r+h) within the equation, particularly when trying to solve for h.

Discussion Status

Some participants have provided algebraic manipulation suggestions, while others express confusion regarding the steps needed to isolate h. The discussion reflects a mix of attempts to clarify the mathematical approach and explore the implications of the given parameters.

Contextual Notes

Participants note the challenge posed by the requirement to find h when it is part of a squared term in the equation. There is an acknowledgment of known constants (G, M, R) but a lack of consensus on the next steps to resolve the equation effectively.

centripitacal
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Homework Statement


I have to find the orbital height of a satellite with a specific g force (ie. the acceleration due to gravity). g=5.7(ms)2


Homework Equations



So far I have been using the equation g=Gm/(r+h)2 to find the acceleration due to gravity, where G= gravitational constant, m=mass of the Earth ,r=radius of the Earth and h= the orbital height from the Earth

except now I am given a specific g force and have been asked to find the height.


The Attempt at a Solution

 
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centripitacal said:

Homework Equations



So far I have been using the equation g=Gm/(r+h)2 to find the acceleration due to gravity, where G= gravitational constant, m=mass of the Earth ,r=radius of the Earth and h= the orbital height from the Earth

except now I am given a specific g force and have been asked to find the height.


The Attempt at a Solution


Not sure what is puzzling you.

g=GM/(r+h)2 and they give you g=5.7 m/s2

∴5.7=GM/(R+h)2

G,M and R are all known, cross multiply and then do some algebra to get 'h'.
 
Cheers,
bit slow on the uptake today, but that was all I wanted to know.
 
Back again, moving the equation around dosn't help because the h is inside the brackets, along with the Earth's radius (r+h). What am I missing?
 
centripitacal said:
Back again, moving the equation around dosn't help because the h is inside the brackets, along with the Earth's radius (r+h). What am I missing?

When you reach (R+h)2=A, take the square root of both sides.
 

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