How Do You Calculate the Speed and Centripetal Acceleration of a Satellite?

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To calculate the speed and centripetal acceleration of a satellite orbiting 597 km above Earth's surface with a period of 96.42 minutes, the radius of the orbit must include Earth's radius, totaling approximately 6,371 km. The speed is determined using the formula v = (2 * π * r) / T, resulting in a calculated speed of 648.39 m/s. The centripetal acceleration is found using a = v^2 / r, yielding a value of 0.704 m/s², which was noted as incorrect. Clarification is sought on the distinction between speed and magnitude. Accurate calculations require careful consideration of the total radius of the orbit.
Coldchillin
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"An Earth satellite moves in a circular orbit 597 km above Earth's surface with a period of 96.42 min. What are (a) the speed and (b) the magnitude of the centripetal acceleration of the satellite?"


Ok, so first I converted everything to standard units. I made a circle diagram with radius 597,000m and it's period is 5785.2 seconds. So to find the acceleration I had to find the velocity, which I had as v=(2*(Pi)*(597,000))/5785.2s and got v=648.39 m/s. Then to find the acceleration I used a=(648.39)^2/597,000 and got a=.704 m/s^2, which apparently is wrong. Can someone help me out? Also, what is the difference between the speed and magnitude? Thank you!
 
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Since the satellite is orbiting above the Earth the radius of its orbit must include the radius of the earth!
 
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