Quick question about Oribtal Velocities

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In summary, the conversation discusses the work energy theorem and its application to orbital velocities. It explains that the total work done by the force on a body in an elliptical orbit is equal to the change in kinetic energy, as there are no other forces at play. It also mentions the exclusion of gravitational potential energy in this equation.
  • #1
ZedCar
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Homework Statement



I was reading in a book a little section about orbital velocities.

It states:

For elliptical orbits, consider a body moving from point A to point B. The total work done by the force on the body is given by

W = KE (for B) - KE (for A)

Homework Equations


The Attempt at a Solution



Since W=Fd, does the KE simply represent the kinetic energy?

Thank you.
 
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  • #2
Hi ZedCar! :smile:

Yes, the work energy theorem says that the change in energy equals the work done.

Since the only energy that changes for an orbiting body is the kinetic energy, and the only force is gravity, that means the change in kinetic energy equals the work done by gravity.

(We ignore the gravitational potential energy, since it is defined as minus the work done by a conservative force, such as gravity … and we cannot count it twice! :wink:)
 

1. What is orbital velocity?

Orbital velocity is the speed at which an object must travel in order to maintain a stable orbit around another object, such as a planet or a star. It is determined by the gravitational pull of the object being orbited and the distance between the two objects.

2. How is orbital velocity calculated?

The formula for calculating orbital velocity is V = √(GM/r), where V is the orbital velocity, G is the gravitational constant, M is the mass of the object being orbited, and r is the distance between the two objects.

3. What factors affect orbital velocity?

The main factors that affect orbital velocity are the mass of the object being orbited, the distance between the two objects, and any external forces acting on the orbiting object, such as atmospheric drag or gravitational forces from other nearby objects.

4. How does orbital velocity differ for objects in different orbits?

The orbital velocity for objects in different orbits will vary depending on their distance from the object being orbited. Objects in a lower orbit will have a higher orbital velocity than objects in a higher orbit, as they are closer to the gravitational pull of the object being orbited.

5. Why is orbital velocity important?

Orbital velocity is important because it determines the stability of an object's orbit. If an object's orbital velocity is too low, it will eventually spiral towards the object it is orbiting and potentially crash into it. If the orbital velocity is too high, the object will escape the orbit and continue on a path away from the object being orbited.

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