# Centripetal Acceleration of Satellite

• Physics53
In summary, the conversation was about a person seeking help with a physics question regarding the centripetal acceleration of a satellite in orbit around the Earth. They had attempted to solve the problem using the formula for centripetal acceleration, but ended up calculating the tangential velocity instead. The expert clarified that the units were different and pointed out that the velocity found was tangent to the satellite's path, whereas the acceleration points inward, hence it being referred to as centripetal acceleration. The person then asked if they should use the formula for gravity to calculate the centripetal acceleration.

## Homework Statement

Hi, I am stuck on this question:
A satellite of mass 1200 kg is in orbit around the Earth at a distance of 22000 km from the centre of the Earth.
Calculate the magnitude of the centripetal acceleration of the satellite at this distance.

## The Attempt at a Solution

I did:
mv^2/r= GMm/r^2
so v= square root of GM/r
v= square root of 6.67 x10^-11 x 6.0 x 10^24/ 22000 x 10^3
this gave me=
4.266x 10^-3 m/s but the answer at the back is 0.83 m/s^2, can someone please explain to where i went wrong.

Thanks[/B]

vela said:
Hi, I've reread it many time, but i still feel confused

What's it asking you to find? What did you actually calculate?

vela said:
What's it asking you to find? What did you actually calculate?
Oh I see what you mean, are you implying that I solved centripetal velocity instead of centripetal acceleration?

Essentially. You solved for what's sometimes called the tangential velocity, not centripetal velocity.

vela said:
Essentially. You solved for what's sometimes called the tangential velocity, not centripetal velocity.
So does this mean I consider gravity of Earth as my centripetal velocity and therefore:
g= GM/r^2, but i still have a query, if you could kindly clear this up for me, why can't we use the centripetal formula in this question.

The work you did was correct, but you didn't actually solve for the quantity you were asked for. (The fact that the units were different is a big clue.)

I was just pointing out the phrase "centripetal velocity" doesn't really make sense. The velocity you found is tangent to the satellite's path; it doesn't point inward. The acceleration, however, does, so that's why it's referred to as centripetal acceleration.

## 1. What is centripetal acceleration and how does it relate to satellites?

Centripetal acceleration is the acceleration that an object experiences when it moves in a circular path. In the case of satellites, this acceleration is due to the gravitational force of the planet they are orbiting. This force causes the satellite to continuously change direction, resulting in a circular orbit.

## 2. How is centripetal acceleration of a satellite calculated?

The centripetal acceleration of a satellite can be calculated using the formula a = v^2/r, where a is the acceleration, v is the orbital velocity, and r is the distance from the satellite to the center of the planet. This formula can also be written as a = 4π^2r/T^2, where T is the orbital period of the satellite.

## 3. What factors affect the centripetal acceleration of a satellite?

The centripetal acceleration of a satellite is affected by the mass of the satellite, the mass of the planet it is orbiting, and the distance between the satellite and the planet. A higher mass of the satellite or planet will result in a higher acceleration, while a greater distance will result in a lower acceleration.

## 4. How does the centripetal acceleration of a satellite impact its orbit?

The centripetal acceleration of a satellite determines the shape and stability of its orbit. If the acceleration is too low, the satellite will not have enough speed to maintain its orbit and will eventually fall back to the planet's surface. If the acceleration is too high, the satellite will escape the planet's gravitational pull and enter a new orbit or fly off into space.

## 5. How does the centripetal acceleration of a satellite affect its velocity?

The centripetal acceleration of a satellite is directly related to its orbital velocity. As the acceleration increases, the satellite's velocity will also increase. This means that a satellite in a lower orbit will have a higher velocity than one in a higher orbit, as it experiences a greater centripetal acceleration from the planet's gravitational force.