A question on centripetal acceleration

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SUMMARY

The discussion focuses on calculating the time it takes for a satellite in near-Earth orbit to complete one full revolution around the Earth. The centripetal acceleration required for this orbit is defined by the formula a = v²/r, where 'r' is the Earth's radius (approximately 6400 km). Participants emphasize that the gravitational force acting on the satellite is equivalent to its weight (mg), which can be used to derive the necessary velocity for maintaining orbit. The centripetal force acting on the satellite is crucial for determining this velocity.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula (a = v²/r)
  • Basic knowledge of gravitational force (mg) and its application in orbital mechanics
  • Familiarity with the concept of circular motion in physics
  • Knowledge of Earth's radius (approximately 6400 km)
NEXT STEPS
  • Calculate the velocity of a satellite in near-Earth orbit using the centripetal force equation
  • Explore the relationship between gravitational force and centripetal acceleration in orbital mechanics
  • Research the orbital period of satellites and how it relates to their altitude
  • Learn about the effects of varying altitudes on satellite velocity and orbital dynamics
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Estimate the time it takes a satellite in “near-earth” orbit to go once around the earth. To do this, assume that it is close enough to the earth’s surface that the gravitational force acting on it is about equal to its weight on earth, mg. Proceed as follows:

a. Find the centripetal acceleration the satellite must experience in its circular orbit.

a=v^2/r
Since we're talking about the earth, I'm assuming that we use the Earth's radius, 6400km. However, I have no idea where to get the velocity of this satellite from.
 
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What is the centripetal force acting on the satellite? Can you use this to find the velocity of the satellite?
 

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