Centripetal acceleration of an orbit to the earth... help!

MissJewels

1. The problem statement, all variables and given/known data

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?

2. Relevant equations
I believe I should use
a_c = (4∏²r) / T²

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

3. The attempt at a solution
I plugged in the values:
a_c = (4∏²35 800 000) / 86400²
a_c = 0,189

The answer SHOULD be 0.223 m/s²

Help!

D H

I have highlighted your error:

Do you see the problem?

MissJewels

ahaha... isnt altitude the radius?

D H

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.

MissJewels

OOOOH so i add the radius with the altitude, and THATS the r value i use! Right?
THANKS

MissJewels

Nvm, I got it, thanks again !

D H

Very good, and you're welcome.

mnicorici

how do you calculate the distance from the center of the Earth for a geosynchronous satellite orbit?