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

[Coldchillin]

"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!

 

[andrevdh]

Since the satellite is orbiting above the Earth the radius of its orbit must include the radius of the earth!

 

[m2003]

Hello, thank you for reaching out for help with your calculation. It seems like you have the right approach, but there may be a small error in your calculations. First, let's address the difference between speed and magnitude. Speed is the rate at which an object is moving, while magnitude is the size or amount of a quantity. In this case, the speed refers to the velocity of the satellite, while the magnitude of the centripetal acceleration refers to the size of the acceleration vector.

Now, let's take a look at your calculations. The formula you used to find the velocity (v=(2*(Pi)*(597,000))/5785.2s) is correct, but your unit conversion may have been off. The period should be converted to seconds, so it should be 96.42 min * 60 s/min = 5785.2 s. This may have caused a slight discrepancy in your final answer.

For the acceleration, you are correct in using the formula a=(v^2)/r, but you should use the velocity you calculated earlier (648.39 m/s) instead of squaring it again. This will give you a centripetal acceleration of 0.11 m/s^2, which is a more reasonable answer for the magnitude of the acceleration.

I hope this helps clarify your calculations. Remember to always double check your unit conversions and use the correct formulas for the given situation. Good luck with your studies!