Solving Rotational Problem: Satellite Elliptical Orbit, Torque & Speed

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In summary, the conversation discusses a satellite following an elliptical orbit with the only force being gravity from the planet. The speed of the satellite at point A is given as 8000m/s and it is 6000km away. Point B is 24000km east of the planet and Point C is 9000km in the i-direction and 12000km in the j-direction from the planet. The question of whether there is any torque acting on the satellite is raised, and the speed at Point B and C is also requested. The equations of torque and conservation of angular momentum are mentioned as possible approaches to solving the problem.
  • #1
Anthonyphy2013
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Homework Statement




A satellite follows an elliptical orbit. The only force on the satellite is the gravity atraction from the planet. The satellites speed at point A is 8000m/s, and it is 6000km away, Point B is 24000km east of the planet, and Point C is component vector 9000ikm+12000jkm away, if the you take the planet as the origin.

a. Is there any torque acting on the satellite?
b. satellite speed at Point B
c, satellite speed at Point C

Homework Equations



torque = force*R

The Attempt at a Solution


part a, I consider there is no torque since the only force is parallel to the pivot . Does it make sense.
part b ,since my professor does not mention gravitational force on this question , I use the f=mv^2/r to this question. i know there is no torque , and I know the radius is changing and I assume the gravitational force for at point a , b and c are the same and then I apply f=mva^2/ra = mvb^2/r2 . is that a good way to solve this problem ?
 
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  • #2
Have you guys covered conservation of angular momentum?
 
  • #3
yes , but how could angular momentum , L=mvr could apply to this question ?
 
  • #4
Well the mass of the satellite does not change. And it has the same angular momentum at every place in its orbit with respect to the planet...
 
  • #5
V*r = V'*r'

Familiar?
 

1. How do you calculate the torque on a satellite in an elliptical orbit?

To calculate the torque on a satellite in an elliptical orbit, you can use the formula: T = Iα, where T is the torque, I is the moment of inertia, and α is the angular acceleration. The moment of inertia for a satellite in an elliptical orbit can be calculated using the formula: I = mr², where m is the mass of the satellite and r is the distance from the center of mass to the axis of rotation.

2. What factors affect the speed of a satellite in an elliptical orbit?

The speed of a satellite in an elliptical orbit is affected by several factors, including the mass of the satellite, the distance from the center of mass to the axis of rotation, and the gravitational force exerted by the central body. It is also affected by the eccentricity of the orbit, as well as any external forces acting on the satellite, such as atmospheric drag.

3. How is the speed of a satellite in an elliptical orbit related to its distance from the central body?

The speed of a satellite in an elliptical orbit is inversely proportional to its distance from the central body. This means that as the satellite moves closer to the central body, its speed increases, and as it moves further away, its speed decreases. This is due to the conservation of angular momentum, which states that the product of an object's moment of inertia and angular velocity remains constant as long as there are no external torques acting on the object.

4. What is the difference between a circular and an elliptical orbit?

A circular orbit is a type of elliptical orbit with an eccentricity of 0, meaning that the distance between the satellite and the central body remains constant throughout the orbit. In contrast, an elliptical orbit has an eccentricity greater than 0, causing the distance between the satellite and the central body to vary at different points along the orbit. Additionally, the speed of a satellite in a circular orbit is constant, while the speed in an elliptical orbit varies depending on the distance from the central body.

5. How does torque affect the shape of a satellite's orbit?

The torque acting on a satellite can cause changes in its orbit, particularly in the shape and orientation of the elliptical orbit. If the torque is greater than the angular momentum of the satellite, the orbit may become more circular. Conversely, if the torque is less than the angular momentum, the orbit may become more elliptical. Torque can also cause the orientation of the orbit to change, resulting in a precession or wobble of the orbit. This can be seen in the precession of the orbit of the Earth around the Sun, caused by the gravitational pull of other planets in the solar system.

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