Centripetal Acceleration Part II

In summary, the speed of a satellite in a stable circular orbit is 7723.55 m/s, with a radius of 6689 km. In order to find the time required to complete one orbit, the equation v=2pir/T is used, resulting in a time of approximately 1.51155 hours.
  • #1
BitterSuites
38
0
[SOLVED] Centripetal Acceleration Part II

Homework Statement



(From previous question) In order for a satellite to move in a stable circular orbit of radius 6689 km at a constant speed, its centripetal acceleration must be inversely proportional to the square of the radius of the orbit.

What is the speed of the satellite? The G is 6.67259e-11 and the mass of the Earth is 5.98e24kg.

The answer to this was 7723.55 m/s.

Part II:

Find the time required to complete one orbit. Answer in units of h.

Homework Equations



The book only gives one equation for T referencing orbits, which is v=2pir/T

The Attempt at a Solution



v=2pi/T
7723.55 = 2pi/T
7723.55T = 2pi
T = 2pi/7723.55
T = .000814

I think the homework system even laughed at me when I entered that answer :)
 
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  • #2
BitterSuites said:

Homework Equations



The book only gives one equation for T referencing orbits, which is v=2pir/T
Right.

The Attempt at a Solution



v=2pi/T
Wrong.

Compare the two equations. (You left off the r.)

And don't forget to convert your answer to the desired units.
 
  • #3
*sigh* I keep making really silly mistakes.

So I input the correct equation but it came out correct.

v=2pir/t
7723.55 m/s = 2pi * 6689000m/T
7723.55T = 4.20282e7
T = 5221.57 seconds

Convert to hours

5221.57/60 = 90.6928 minutes
90.6928/60 = 1.51155 hours

Thank you so much.
 
Last edited:

1. What is the formula for calculating centripetal acceleration?

The formula for calculating centripetal acceleration is a = v²/r, where a is the centripetal acceleration, v is the velocity, and r is the radius of the circular motion.

2. How does centripetal acceleration differ from regular acceleration?

Centripetal acceleration refers to the acceleration towards the center of a circular motion, while regular acceleration refers to the change in velocity over time. Centripetal acceleration is always perpendicular to the velocity, whereas regular acceleration can be in any direction.

3. What is the relationship between centripetal acceleration and centripetal force?

Centripetal acceleration is directly proportional to the centripetal force. This means that as the force increases, the acceleration also increases. The two are related by the formula a = F/m, where F is the force and m is the mass of the object in circular motion.

4. Can an object have centripetal acceleration without centripetal force?

No, an object cannot have centripetal acceleration without centripetal force. According to Newton's second law of motion, an object cannot accelerate without a force acting upon it. Therefore, in circular motion, there must be a force acting towards the center to cause the centripetal acceleration.

5. How does centripetal acceleration affect the motion of an object?

Centripetal acceleration causes an object to change direction constantly, resulting in circular motion. It also affects the speed of the object, as a higher centripetal acceleration will result in a faster circular motion. Additionally, centripetal acceleration can cause objects to feel a force pushing them outwards, known as centrifugal force.

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