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

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SUMMARY

The discussion focuses on calculating the speed and centripetal acceleration of an Earth satellite orbiting at 597 km above the surface with a period of 96.42 minutes. The user converted the satellite's altitude to a radius of 597,000 meters and the orbital period to 5785.2 seconds. The calculated speed was determined using the formula v = (2 * π * 597,000) / 5785.2, resulting in a speed of 648.39 m/s. However, the user encountered an error in calculating the centripetal acceleration, which was computed as a = (648.39)^2 / 597,000, yielding a value of 0.704 m/s², which was later identified as incorrect due to not accounting for the Earth's radius in the total orbital radius.

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  • Understanding of circular motion and orbital mechanics
  • Familiarity with the formulas for speed and centripetal acceleration
  • Basic knowledge of unit conversions, particularly for time and distance
  • Proficiency in using mathematical constants such as π
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  • Review the concept of gravitational force and its effect on satellite motion
  • Learn how to calculate the total radius of an orbit by including the Earth's radius
  • Explore the implications of orbital period on satellite speed and acceleration
  • Investigate common errors in calculating centripetal acceleration in orbital mechanics
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Students studying physics, aerospace engineers, and anyone interested in understanding satellite dynamics and orbital calculations.

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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