Planetary motion and a space station

In summary, a space station is in orbit between the Earth and the moon with the force of gravity from both bodies being equal. The distance from the Earth to the space station is 0.213 times the radius of the Earth, and the distance from the moon to the space station is 0.922 times the radius of the moon. The final step in solving for the variable involved subtracting the radius of the moon from the total distance and then dividing by 10.02. There was also a small mistake in using the radii of the bodies as their respective distances to the space station, but this was corrected in the final solution.
  • #1
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

Related to Planetary motion and a space station

1. What causes planetary motion?

Planetary motion is caused by the gravitational pull of the sun and other celestial bodies. This gravitational force keeps the planets in orbit around the sun and also affects their speed and direction of motion.

2. How does a space station stay in orbit?

A space station stays in orbit due to the balance between its forward motion and the force of gravity pulling it towards the Earth. This is known as an orbiting object's centripetal force and it keeps the space station in a stable circular or elliptical path around the Earth.

3. Can a space station's orbit change?

Yes, a space station's orbit can change due to various factors such as atmospheric drag, solar radiation, and gravitational pulls from other objects. In order to maintain a stable orbit, the space station may need to use thrusters to make adjustments.

4. How do scientists calculate the trajectory of a space station?

Scientists use mathematical equations and data from various sources, such as the station's speed and position, to calculate its trajectory. They also take into account factors such as the Earth's gravity and atmospheric conditions.

5. What challenges do astronauts face in a space station in terms of planetary motion?

Astronauts in a space station may experience microgravity, which can affect their bodies and make it difficult to move around without proper training. They may also have to adjust to the constant motion of the station as it orbits the Earth, and the changing views of the planets and stars outside the windows.

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