What is the speed of the satellite?

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SUMMARY

The speed of a satellite in a circular orbit 605 km above Earth's surface, with a period of 96.6 minutes, can be calculated using the formula T = (2πr)/v. The total radius of the orbit is approximately 6,976,000 meters, which includes the Earth's radius of about 6,371 km plus the altitude of the satellite. The correct calculation requires converting the period from minutes to seconds, resulting in a speed of approximately 4,537.42 m/s.

PREREQUISITES
  • Understanding of circular motion and gravitational forces
  • Familiarity with the formula for orbital speed
  • Ability to convert units, specifically time from minutes to seconds
  • Knowledge of Earth's radius (approximately 6,371 km)
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  • Learn about gravitational force and its effect on satellite motion
  • Study the derivation of orbital speed formulas
  • Explore the concept of orbital periods and their calculations
  • Investigate the effects of altitude on satellite speed and orbital mechanics
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Students studying physics, particularly those focusing on mechanics and orbital dynamics, as well as educators seeking to clarify satellite motion concepts.

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Homework Statement



An Earth satellite moves in a circular orbit 605 km above the Earth's surface. The period of the motion is 96.6 min.

What is the speed of the satellite?

Homework Equations





The Attempt at a Solution



First, I know that it is orbiting 605 km above Earth's surface. So, that number plus the radius of Earth gives a total for the radius of the motion. That comes out to be about 6976000 meters.

Then, I used the equation:

T = (2pir)/(v)

96.6 = (2pi(6967000)) / (v)

v = 453742.24

But it's marking it as incorrect. Any ideas?
 
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Shoot me in the face for not converting units.
 
if 2pie radius/period=speed then add radius of Earth in meters to 605E3meters plug that in for r, change the 96.6minutes to seconds plug that in for T and you should get the right answer.
 

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