Geosynchronous Orbit Satellite Altitude Calculated from Moon

  • Thread starter KillerZ
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In summary, the goal is to place a satellite in orbit around the moon that remains in a fixed position above the lunar surface. Using the equation T^{2} = \left(\frac{4\pi^{2}}{GM}\right)r^{3}, the satellite's altitude can be calculated to be 7.30x10^{6}m from the moon. This calculation is based on the satellite being in synchronous orbit with the moon and does not involve the Earth or the Moon's mass. Alternatively, the satellite could be placed at any of the Earth-Moon Lagrange points.
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KillerZ
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Homework Statement



NASA would like to place a satellite in orbit around the moon such that the satellite always remains in the same position over the lunar surface. What is the satellite's altitude?

Homework Equations



[tex]T^{2} = \left(\frac{4\pi^{2}}{GM}\right)r^{3}[/tex]

The Attempt at a Solution



I think I have this right:

[tex]r_{geo} = R_{e} + h_{geo} = \left[\left(\frac{GM}{4\pi^{2}}\right)T^{2}\right]^{1/3}[/tex]

[tex]r_{geo} = R_{e} + h_{geo} = \left[\left(\frac{(6.67x10^{-11})(5.98x10^{24})}{4\pi^{2}}\right)(2358720)^{2}\right]^{1/3}[/tex]

[tex]= 383065776.5m[/tex]

[tex]h_{geo} = r_{geo} - R_{e} = 383065776.5m - 6.67x10^{6}m[/tex]

[tex]= 376695776.5m[/tex] from earth.

[tex]=>3.84x10^{8}m - 376695776.5m[/tex]

[tex]= 7304223.492m[/tex]

[tex]= 7.30x10^{6}m[/tex] from moon

I calculated it from the Earth then subtracted that from the distance between the Earth and the moon to get the distance from moon. I used the Earth because the moon is in synchronous orbit with the Earth and for T I used the moons period around the Earth to keep the satellite with it.
 
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  • #2
You want the satellite to be in orbit around the Moon. I don't understand why you're involving the Earth. I don't see the Moon's mass used anywhere.
 
  • #3
You would want your satellite at any of the Earth-Moon Lagrange points.
 

1. What is a geosynchronous orbit?

A geosynchronous orbit refers to a circular orbit around the Earth that has the same orbital period as the Earth's rotation. This means that the satellite stays in a fixed position relative to a specific location on Earth, making it appear to be stationary from the ground.

2. How is the altitude of a geosynchronous orbit satellite calculated from the moon?

The altitude of a geosynchronous orbit satellite can be calculated by using the distance from the Earth to the Moon, which is approximately 384,400 kilometers. This distance is then divided by the ratio of the Earth's and Moon's masses to determine the altitude at which the satellite needs to orbit in order to maintain a geosynchronous position.

3. Why is the moon used to calculate the altitude of a geosynchronous orbit satellite?

The moon is used because it is a large celestial body with a known distance from the Earth. This distance can be used in calculations to determine the altitude at which a satellite needs to orbit in order to maintain a geosynchronous position.

4. What is the importance of calculating the altitude of a geosynchronous orbit satellite from the moon?

Calculating the altitude of a geosynchronous orbit satellite from the moon is important because it helps scientists and engineers accurately place satellites in orbit for communication, weather monitoring, and other purposes. It also ensures that the satellite will maintain a stable position relative to a specific location on Earth.

5. Are there any other factors that affect the altitude of a geosynchronous orbit satellite?

Yes, there are other factors that can affect the altitude of a geosynchronous orbit satellite, such as the gravitational pull of other celestial bodies, atmospheric drag, and the satellite's own propulsion system. These factors must be taken into consideration when calculating the altitude of a geosynchronous orbit satellite.

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