How Far is the Satellite from Earth's Surface?

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Homework Help Overview

The problem involves determining the altitude of a satellite above the Earth's surface based on gravitational acceleration. The context includes the radius and mass of the Earth, along with the gravitational force equation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to find gravitational force and its relation to centripetal force. There are questions about which mass to use in the calculations and confusion regarding the mass of the satellite.

Discussion Status

Some participants have offered guidance on equating gravitational force with centripetal force, while others express confusion about the variables involved. There is an acknowledgment that the mass of the satellite is not necessary for the calculations, leading to further exploration of the relationship between gravitational acceleration and radius.

Contextual Notes

Participants are navigating assumptions about the problem setup and the relevance of certain variables, such as the mass of the satellite, in the context of gravitational equations.

Rbethell16
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Homework Statement


The radius of the Earth is 6.86 e6 m and the mass of the Earth is 5.98 e24kg. There is a satellite floating in space at a point where the Earth's gravitational acceleration is 3.2 m/s^2.

How far above the Earth's surface is the satellite?


Homework Equations


Fg = Gmm/r^2


The Attempt at a Solution


I know I need to find Fg - at least I think. But I don't know how to start...
 
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Rbethell16 said:

Homework Equations


Fg = Gmm/r^2

The Attempt at a Solution


I know I need to find Fg - at least I think. But I don't know how to start...
The gravitational force of attraction provides the centripetal force. So you need to equate Fg and Fcentripetal (which you can just write as ma for this case).
 
rock.freak667 said:
The gravitational force of attraction provides the centripetal force. So you need to equate Fg and Fcentripetal (which you can just write as ma for this case).

ma - ok, I have the acceleration, but I get confused as to which "m" i am using. My problem is the intuition with formulas
 
Wow I reread the problem and I am extra confused. How do I figure out the mass of the shuttle?
 
Rbethell16 said:
Wow I reread the problem and I am extra confused. How do I figure out the mass of the shuttle?

You don't need it! if you have

ma= GMm/r2

an 'm' (the mass of the shuttle) cancels out :wink:
 
Ahhh so 3.2 = G(5.98e24)/R^2. Then solve for R?
 
Rbethell16 said:
Ahhh so 3.2 = G(5.98e24)/R^2. Then solve for R?

Yes, but be aware of what that R is.
 

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