Finding the orbital height of a satellite

In summary, to find the orbital height of a satellite with a specific g force, you can use the equation g=Gm/(r+h)2 and solve for h by first substituting in the known values for G, m, and r and then rearranging the equation to isolate h. Once you have (r+h)2=A, take the square root of both sides to find the orbital height.
  • #1
centripitacal
8
0

Homework Statement


I have to find the orbital height of a satellite with a specific g force (ie. the acceleration due to gravity). g=5.7(ms)2


Homework Equations



So far I have been using the equation g=Gm/(r+h)2 to find the acceleration due to gravity, where G= gravitational constant, m=mass of the Earth ,r=radius of the Earth and h= the orbital height from the Earth

except now I am given a specific g force and have been asked to find the height.


The Attempt at a Solution

 
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  • #2
centripitacal said:

Homework Equations



So far I have been using the equation g=Gm/(r+h)2 to find the acceleration due to gravity, where G= gravitational constant, m=mass of the Earth ,r=radius of the Earth and h= the orbital height from the Earth

except now I am given a specific g force and have been asked to find the height.


The Attempt at a Solution


Not sure what is puzzling you.

g=GM/(r+h)2 and they give you g=5.7 m/s2

∴5.7=GM/(R+h)2

G,M and R are all known, cross multiply and then do some algebra to get 'h'.
 
  • #3
Cheers,
bit slow on the uptake today, but that was all I wanted to know.
 
  • #4
Back again, moving the equation around dosn't help because the h is inside the brackets, along with the Earth's radius (r+h). What am I missing?
 
  • #5
centripitacal said:
Back again, moving the equation around dosn't help because the h is inside the brackets, along with the Earth's radius (r+h). What am I missing?

When you reach (R+h)2=A, take the square root of both sides.
 

Related to Finding the orbital height of a satellite

1. How is the orbital height of a satellite determined?

The orbital height of a satellite is determined by a combination of factors including the satellite's mass, the speed at which it is traveling, and the gravitational pull of the planet it is orbiting. These factors are used in mathematical equations to calculate the ideal height for the satellite's orbit.

2. What is the purpose of finding the orbital height of a satellite?

Finding the orbital height of a satellite is important for ensuring that it remains in a stable orbit and is able to fulfill its intended purpose. It also helps to prevent collisions with other objects in space and allows for efficient communication and data transmission between the satellite and ground stations.

3. How does the orbital height affect the satellite's speed?

The orbital height of a satellite directly affects its speed. The higher the orbital height, the slower the satellite's speed will be. This is because the gravitational pull decreases as the distance from the planet increases, causing the satellite to require less speed to maintain its orbit.

4. Can the orbital height of a satellite be changed?

Yes, the orbital height of a satellite can be changed through the use of thrusters or gravitational maneuvers. However, this requires careful planning and precise calculations to ensure that the satellite remains in a stable orbit and does not collide with other objects.

5. How is the orbital height of a satellite measured?

The orbital height of a satellite is typically measured using a combination of radar and GPS technology. Radar can track the satellite's position and distance from the ground, while GPS can provide precise location data. This information is used to calculate the satellite's orbital height.

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