Finding Speed of Satellite in Geosynchronous Orbit

  • Thread starter Lance WIlliam
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In summary, the conversation is about finding the speed of a satellite in geosynchronous orbit. The formula T^2=4(pi)^2(r)^3/GM is used, where T is the time in 24 hours or 86400 seconds. The value of r is found using the equation r=(GM_earth_T/4(pi)^2)1/3 and then used as the distance in the formula V=D/T. The units should be consistent in meters, kilograms, and seconds. It is suggested to check the units by substituting the values. There is also a suggestion to use angular velocity to solve for the speed.
  • #1
Lance WIlliam
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Homework Statement


Find the speed of a satellite in geosynchronous orbit?

in finding the speed for geosnychronous orbit the Time is 1 day, or 24hours , 86400 seconds.
I tried using
T^2=4(pi)^2(r)^3/GM is the eqn.
I manipluated it into:

r=(GM_earth_T/4(pi)^2)1/3

Once I found r I used it as Distance and then used:
V=D/T
...

i think my units are wrong. When using the eqn. does ur distance come out in meters or Kilometers?
 
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  • #2
It would help if one would right out the values for G, M, T.

They should all be consistent in m, kg, s (meter, kilogram, second).
 
  • #3
But is my process right?
Once I find 'r" do I use v=d/t to find the speed?
 
  • #4
I disagree with you expression for the radius, In my opinion you are missing a set of brackets or have made a mistake in your powers. Then as Astronuc said, to check the units simply substitute in their values to check the units cancel down.

Have you considered using angular velocity to solve for the speed?
 

1. What is a geosynchronous orbit?

A geosynchronous orbit is a type of orbit in which a satellite orbits the Earth at the same rate as the Earth's rotation, allowing it to remain in a fixed position relative to a specific point on Earth's surface.

2. How is the speed of a satellite in geosynchronous orbit calculated?

The speed of a satellite in geosynchronous orbit is calculated using the formula v = √(GM/R), where v is the orbital speed, G is the gravitational constant, M is the mass of the Earth, and R is the distance from the satellite to the center of the Earth.

3. Can a satellite be in geosynchronous orbit at any altitude?

No, a satellite can only be in geosynchronous orbit at an altitude of approximately 35,786 kilometers (22,236 miles) above the Earth's equator. This altitude is known as the geostationary orbit.

4. How long does it take for a satellite in geosynchronous orbit to complete one orbit?

A satellite in geosynchronous orbit takes approximately 24 hours to complete one orbit, which is the same amount of time it takes for the Earth to make one full rotation.

5. What are some applications of satellites in geosynchronous orbit?

Satellites in geosynchronous orbit are commonly used for telecommunications, weather monitoring, and navigation systems such as GPS. They are also used for television broadcasting and monitoring of natural disasters.

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