Planetary motion and a space station

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Homework Help Overview

The discussion revolves around a problem in gravitational physics, specifically concerning the forces acting on a space station located between the Earth and the moon. The original poster is trying to determine the distances from the space station to both the Earth and the moon, given that the gravitational forces from both bodies are equal.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the problem, questioning the definitions of variables used for distances. There are attempts to clarify the relationships between the distances and the gravitational forces involved.

Discussion Status

Some participants have provided insights into the reasoning behind the calculations, while others are seeking clarification on specific steps. There is an ongoing exploration of the problem, with no explicit consensus reached yet.

Contextual Notes

Participants note potential confusion regarding the definitions of distances in relation to the centers of the Earth and moon, as well as the implications of using these distances in calculations.

serunder

Homework Statement


A space station is in orbit between the Earth and the moon. The force due to gravity on the space station from the moon is the same as the force due to gravity from the Earth. (FGmoon = FGearth). How far away from the Earth is the space station? How far from the moon is the space station?

Homework Equations

+ attempt at a solution[/B]

a8kkYXK.png


I keep getting 0.213 for r(earth) and I have no idea how to solve for the variable, can someone please help me?
 
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serunder said:

Homework Statement


A space station is in orbit between the Earth and the moon. The force due to gravity on the space station from the moon is the same as the force due to gravity from the Earth. (FGmoon = FGearth). How far away from the Earth is the space station? How far from the moon is the space station?

Homework Equations

+ attempt at a solution[/B]

View attachment 206637

I keep getting 0.213 for r(earth) and I have no idea how to solve for the variable, can someone please help me?
It (nearly) all made sense until the final step. You had 3.844.108m-rmoon=9.02 rmoon. How did you proceed from there?

The other small mistake is that in your "given" you defined rmoon and rearth as the radii of those two bodies, but thereafter used them as the respective distances from their centres to the space station.
 
haruspex said:
It (nearly) all made sense until the final step. You had 3.844.108m-rmoon=9.02 rmoon. How did you proceed from there?

The other small mistake is that in your "given" you defined rmoon and rearth as the radii of those two bodies, but thereafter used them as the respective distances from their centres to the space station.
I figured it out now I think since like you said, it didn't make sense when I tried to use them as their distance, so what I ended up doing was this:

VOFJuHd.png

sorry for the crappy formatting but does this seem to be correct?
 
serunder said:
I figured it out now I think since like you said, it didn't make sense when I tried to use them as their distance, so what I ended up doing was this:

View attachment 206640
sorry for the crappy formatting but does this seem to be correct?
Yes.
 

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