How High Is a Geostationary Satellite Above Earth?

In summary, the height of a geostationary satellite from the Earth's center can be calculated using the formula r^3/T^2 = GM/4pi^2, where T is the period of the satellite around Earth. This period is equal to 86400 seconds for a geostationary satellite, which means it takes 24 hours to complete one orbit. Using this period and the given values for GM and pi, the height of the satellite is calculated to be approximately 2.16*10^9 meters. This type of satellite has a synchronous orbit, meaning it appears stationary when viewed from Earth. For more information on this topic and a step-by-step explanation of the calculations, refer to the blog post provided
  • #1
crosbykins
53
0

Homework Statement



What is the height of a geostationary satellite measured from the Earth's centre?

Homework Equations



r^3/T^2 = GM/4pi^2

T of Earth = 3.16 * 10^7 s

The Attempt at a Solution



GM/4p2 = r3/T2
3root[T2 * GM/4p2 ] = r
3root[(3.16*107 s)2 * ((6.67*10^ -11N * m2 /kg2 )(5.98*1024 kg)/4p2 )] = r
2.16*109m = r
Therefore the height of the satellite from the Earth’s center is 2.16*109m.
 
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  • #2
Why are you using a year as the period of the satellite?
 
  • #3
gneill said:
Why are you using a year as the period of the satellite?

because in my textbook it gives 3.16*10^7 s as the period of revolution of orbit for earth, so since the satellite is geocentric its period is the same
 
  • #4
A geostationary satellite has an orbit that keeps pace with the rotation of the Earth -- a daily rotation -- so that it remains over the same geographical location.
 
  • #5
gneill said:
A geostationary satellite has an orbit that keeps pace with the rotation of the Earth -- a daily rotation -- so that it remains over the same geographical location.

ok well then i don't mean geocentric i just mean that it has the same orbit period as the Earth
 
  • #6
Dude, your calculations are fine you are using the wrong period T.
Geostationary orbit means when you look up from Earth it appears the satellite isn't moving.
For this to be the case, the satellite must revolve around Earth at the same period as Earth rotates about it's axis.
This period is 24 hours x 60 minutes x 60 seconds = 86400 seconds.
T = 86400 seconds.
 
  • #7
Jonnyb42 said:
Dude, your calculations are fine you are using the wrong period T.
Geostationary orbit means when you look up from Earth it appears the satellite isn't moving.
For this to be the case, the satellite must revolve around Earth at the same period as Earth rotates about it's axis.
This period is 24 hours x 60 minutes x 60 seconds = 86400 seconds.
T = 86400 seconds.

the question calls it a synchronous satellite...is this the same thing
 
  • #8
I think you'd be better putting such a satellite at one of the http://en.wikipedia.org/wiki/Lagrangian_point" .
 
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  • #9
Hi there,

For a full explanation of how to calculate the height of a geostationary satellite, check out a blog post I wrote on this very subject:

http://davechessgames.blogspot.com/2011/01/maths-problems-5-geostationary.html

This uses the formulae and the constants you've been given - it also calculates the distance from the centre of the Earth to the satellite, and also from the Earth's surface to the satellite.

Any problems, leave me a comment on the blog!

Cheers

Dave
 

1. What is a geostationary orbit?

A geostationary orbit is a specific type of orbit around the Earth where a satellite appears to remain stationary in the sky when viewed from a specific location on the ground. This is achieved by placing the satellite at an altitude of around 35,786 kilometers above the Earth's equator and having its orbital speed match the Earth's rotational speed.

2. Why are geostationary orbits important?

Geostationary orbits are important because they allow satellites to provide continuous coverage and communication to a specific location on the ground. This is particularly useful for satellite navigation, weather forecasting, and telecommunication services.

3. How do satellites maintain a geostationary orbit?

Satellites in geostationary orbit use small thrusters to adjust their speed and direction to counteract any external forces, such as gravity and solar pressure, that may cause them to drift away from their designated position.

4. What are some disadvantages of geostationary orbits?

One disadvantage of geostationary orbits is that they are limited to the Earth's equatorial region, making them less useful for polar regions. Additionally, the high altitude of these orbits can result in a longer communication delay, which may not be suitable for certain real-time applications.

5. How long can a satellite remain in a geostationary orbit?

The lifespan of a satellite in geostationary orbit depends on various factors, such as its design, fuel, and external forces. However, most satellites in geostationary orbit have a lifespan of around 15 years before they need to be replaced or repositioned.

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