Centripetal acceleration of an orbit to the earth help

In summary, the module of a geostationary satellite's centripetal acceleration can be calculated using the equation ac = (4∏2r) / T2, where r is the distance from the center of the Earth, not the altitude. To find the distance from the center of the Earth for a geostationary satellite, you would add the radius of the Earth (6371 km) to the altitude of the satellite.
  • #1
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Homework Statement



A geostationary satellite goes around the Earth in 24hr. Thus, it appears motionless in the sky and is a valuable component for telecommunications, including digital television. If such a satellite is in orbit around the Earth at an altitude of 35 800 km above the Earth's surface, what is the module of its centripetal acceleration?

Homework Equations


I believe I should use
ac = (4∏2r) / T2

Converted:
T= 24 hr = 86400s
r = 35800 km = 35 800 000 m = 3.58 x 107 m

The Attempt at a Solution


I plugged in the values:
ac = (4∏235 800 000) / 864002
ac = 0,189

The answer SHOULD be 0.223 m/s2

Help!
 
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  • #2
I have highlighted your error:

MissJewels said:
If such a satellite is in orbit around the Earth at an altitude of 35 800 km above the Earth's surface ...

r = 35800 km

Do you see the problem?
 
  • #3
D H said:
I have highlighted your error:



Do you see the problem?

ahaha... isn't altitude the radius?
 
  • #4
No. Altitude is the distance between the satellite and the closest point on the surface of the Earth. Radius is the distance to the center of the Earth.
 
  • #5
D H said:
No. Altitude is the distance between the satellite and the closest point on the surface of the Earth. Radius is the distance to the center of the Earth.

OOOOH so i add the radius with the altitude, and THATS the r value i use! Right?
THANKS
 
  • #6
Nvm, I got it, thanks again !
 
  • #7
Very good, and you're welcome.
 
  • #8
how do you calculate the distance from the center of the Earth for a geosynchronous satellite orbit?
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that keeps an object moving in a circular path. It is always directed towards the center of the circle.

2. How is centripetal acceleration related to orbits around the Earth?

Centripetal acceleration is crucial for objects to maintain their orbits around the Earth. It is responsible for keeping satellites and other objects in a circular path around the Earth.

3. How is centripetal acceleration calculated?

Centripetal acceleration is calculated using the formula a = v^2/r, where a is the acceleration, v is the velocity, and r is the radius of the circular path.

4. How does centripetal acceleration differ from tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path, while tangential acceleration is the acceleration along the tangent of the circular path. They are perpendicular to each other.

5. What factors affect the centripetal acceleration of an orbit around the Earth?

The centripetal acceleration of an orbit around the Earth is affected by the object's mass, the radius of the orbit, and the gravitational force between the object and the Earth.

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