Question on uniform circular motion

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SUMMARY

An Earth satellite orbits at a height of 589 km above the Earth's surface with a period of 96.26 minutes. To calculate the satellite's speed and centripetal acceleration, the equations T = (2πr)/v and a = v²/r are utilized. The user converted the period to 5775.6 seconds and the altitude to 589,000 meters but encountered errors in their calculations, suspecting an incorrect interpretation of the radius (r). The radius should be the sum of Earth's radius (approximately 6,371 km) and the altitude of 589 km.

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An Earth satellite moves in a circular orbit 589 km above Earth's surface with a period of 96.26 min. What are (a) the speed and (b) the magnitude of the centripetal acceleration of the satellite?

I know I need the equations for 1) period and 2) centripetal acceleration and 3) r.

1) T= (2pi x r)/v (seconds)
2) a= v^2/r (m/s^2)
3) 589 km

I converted T=92.26 min into seconds and got 5775.6s and converted 589km to meters. I then plugged these numbers into equation 1 to solve for velocity (v= (2pi x r)/T). I used this velocity as well as 589,000m for r to find acceleration using equation 2.

The answers I calculated for both velocity and acceleration are wrong, and I think my problem lies in my value for r.

Did I interpret this incorrectly? Any input on what r should be (or if I made another mistake) is greatly appreciated! Thank you!
 
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