Orbits for classical mechanics

In summary, for solving the problem of finding the orbits for the m mass under the force F(r)=-A/r^2+B/r^3, where A>0 and B is positive or negative, it is necessary to make an attempt at a solution. This can be done by reading a chapter on central force motion in a classical mechanics book, such as chp 8 in Thornton and Marion's Classical Dynamics, where the steps for solving such a problem will be outlined. Thank you for your help.
  • #1
madwolf
4
0
Find the orbits for the m mass under the F(r)=-A/r^2+B/r^3 . Where A>0 and B is positive or negative.
Friends, please help me for homework
 
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  • #2
It is necessary for you to make some attempt at a solution. If you have not already done so, read a chapter in a classical mechanics book on central force motion. For example chp 8 in thornton and marion Classical Dynamics. The steps for solving such a problem will be outlined for you there.
 
  • #3
AlexChandler said:
It is necessary for you to make some attempt at a solution. If you have not already done so, read a chapter in a classical mechanics book on central force motion. For example chp 8 in thornton and marion Classical Dynamics. The steps for solving such a problem will be outlined for you there.

thank you very much
 

1. What is an orbit in classical mechanics?

An orbit in classical mechanics is the path that an object takes around another object due to their mutual gravitational attraction. This is described by Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.

2. How do you calculate the trajectory of an orbit?

To calculate the trajectory of an orbit, you need to know the masses of the two objects, their distance apart, and their initial velocities. This information can be used to solve the equations of motion, such as Newton's second law of motion and the law of conservation of angular momentum, to determine the shape, size, and orientation of the orbit.

3. What factors affect the shape of an orbit?

The shape of an orbit is affected by the mass of the two objects, their distance apart, and their initial velocities. The shape can also be affected by external forces, such as the gravitational pull of other nearby objects or the effects of relativity.

4. How does the eccentricity of an orbit affect its motion?

The eccentricity of an orbit is a measure of how elongated or circular the orbit is. A perfectly circular orbit has an eccentricity of 0, while a highly elliptical orbit has an eccentricity close to 1. The eccentricity affects the speed of the orbiting object, with higher eccentricity resulting in faster speeds at the closest point to the central object and slower speeds at the farthest point.

5. Can the orbit of an object change over time?

Yes, the orbit of an object can change over time due to various factors. For example, the gravitational pull of other objects can cause the orbit to become more elliptical or even result in the object being ejected from its original orbit. The orbit can also be affected by external forces, such as atmospheric drag or the effects of general relativity.

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