# Centripetal Acceleration and Satellite Question

• chihockey7
In summary, the astronaut orbiting the Earth in Figure P4.30 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 600 km above the Earth's surface, where the free-fall acceleration is 8.21 m/s2. The radius of the Earth is 6400 km.
chihockey7
1. The astronaut orbiting the Earth in Figure P4.30 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 600 km above the Earth's surface, where the free-fall acceleration is 8.21 m/s2. The radius of the Earth is 6400 km.
a) Determine the speed of the satellite. m/s
b) Determine the time required to complete one orbit around the Earth. min

2. Homework Equations [/b]
distance*speed= time

3. The Attempt at a Solution [/b]
To solve for the speed I used 8.21 as the centripetal acceleration and made that equal to v squared/7000 and then solved for v.

8.21=v squared/7000
v= 239 m/s

I then took 14000*3.14 for the circumference of the orbit and multiplied that by 239 m/s for the total time to orbit and divided that by 60 to put the answer in minutes. I got 2919.94 minutes.

However, both answers are wrong. Can I not use the free fall acceleration for centripetal acceleration?

Welcome to PF,

chihockey7 said:
I then took 14000*3.14 for the circumference of the orbit and multiplied that by 239 m/s for the total time to orbit

Are you trying to claim that distance*speed = time? You might want to rethink that one...

chihockey7 said:
However, both answers are wrong. Can I not use the free fall acceleration for centripetal acceleration?

Yes, you can, and you should, because gravity is what is providing the centripetal force that keeps the satellite moving in a circle. You might have a computation error. Can you post your calculations for part a?

for part a I used the equation centripetal acceleration= v^2/ radius

8.21= v^2/(6400+600)
57470=v^2
v= 239.73

what is wrong with this calculation?

Concerning finding the time. I completely forgot that t=distance/speed.

I just realized my problem. I did not do the simple unit conversions from km to m. Everything worked out fine. Thanks for all of your help!

## What is centripetal acceleration?

Centripetal acceleration is the acceleration directed towards the center of a circular path. It is always perpendicular to the velocity of the object and is necessary to keep the object moving in a circular motion.

## How is centripetal acceleration related to centripetal force?

Centripetal acceleration is directly proportional to the centripetal force acting on an object. This means that as the force increases, so does the acceleration. The formula for centripetal acceleration is a = v²/r, where v is the velocity and r is the radius of the circular path.

## What is the difference between centripetal acceleration and tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path, while tangential acceleration is the acceleration along the tangent of the circular path. Tangential acceleration is responsible for changes in the speed of an object, while centripetal acceleration is responsible for changes in the direction of the velocity.

## How is centripetal acceleration involved in satellite motion?

In satellite motion, the centripetal acceleration is provided by the gravitational force between the satellite and the object it is orbiting. This keeps the satellite in a circular orbit around the object, with the centripetal acceleration constantly changing the direction of the satellite's velocity to keep it in a circular path.

## What factors affect the magnitude of centripetal acceleration in a satellite orbit?

The magnitude of centripetal acceleration in a satellite orbit is affected by the mass of the object the satellite is orbiting, the distance between the satellite and the object, and the speed of the satellite. As the mass of the object or the distance between the satellite and the object increases, the centripetal acceleration decreases. As the speed of the satellite increases, the centripetal acceleration also increases.

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