How Do Orbital Dynamics Change Under Different Force Laws?

In summary, if a particle under the influence of a "1/r^3" force is nudged in its circular orbit, its energy and angular momentum will change slightly. The behavior of the particle will be similar to a particle on a flat line given a nudge, and will eventually impact the surface due to conservation of angular momentum. If the force varies with distance as 1/r^2, the particle's orbit will become elliptical with some eccentricity. The effective potential in this case will no longer be zero, making the problem more complicated.
  • #1
Odyssey
87
0
Suppose a particle is under the influence of a "1/r^3" force. The particle travels in a circular orbit, but its nudged so that its energy and angular momentum changes slightly. What would happen?

What if the force varies with distance as 1/r^2 (like Earth)? (Earth's orbit is almost circular) What would happen?:confused:
 
Physics news on Phys.org
  • #2
Answer to the second question: a nudge off inverse-square central force orbiting body from circular orbit would make its orbit elliptical. (Of course a circle is an ellipse, but I mean an ellipse with some eccentricity.) I used to know the answer to the first question, but have forgotten. Someone here will know.
 
  • #3
Janitor said:
Answer to the second question: a nudge off inverse-square central force orbiting body from circular orbit would make its orbit elliptical. (Of course a circle is an ellipse, but I mean an ellipse with some eccentricity.) I used to know the answer to the first question, but have forgotten. Someone here will know.

Thank you Janitor. :smile:
 
  • #4
Odyssey said:
Suppose a particle is under the influence of a "1/r^3" force. The particle travels in a circular orbit, but its nudged so that its energy and angular momentum changes slightly. What would happen?

What if the force varies with distance as 1/r^2 (like Earth)? (Earth's orbit is almost circular) What would happen?:confused:

Look for the other thread (two threads) on the inverse cube force law.

https://www.physicsforums.com/showthread.php?t=45277

https://www.physicsforums.com/showthread.php?t=45330

The effective potential for an particle in a circular orbit is flat (zero). So the behavior of a particle given a small radial nudge will be the same as a particle on a flat line given a nudge, i.e. dr/dt will be positive or negative and constant. I'd assume this continues on blissfully until the particle impacts the surface, at which point it will be moving quite rapidly in because of the conservation of angular momentum.

If you give the particle a nudge that increases its angular momentum, the effective potential won't be zero anymore, making the problem a little more difficult, so I'll refer you to the first thread above.
 

Related to How Do Orbital Dynamics Change Under Different Force Laws?

1. How is it possible to get particles off orbit?

Particles can be removed from orbit through various methods such as using a spacecraft to capture and remove them, using a laser to vaporize them, or using a gravitational slingshot technique to change their trajectory.

2. What are the challenges in getting particles off orbit?

The main challenges in getting particles off orbit include accurately tracking and identifying the particles, developing and implementing effective removal methods, and ensuring the safety of other objects in orbit.

3. How do scientists decide which particles to remove from orbit?

Scientists typically prioritize removing particles that pose a risk to active spacecraft or the International Space Station, as well as those that contribute to the growing problem of space debris.

4. Can particles be recycled or reused after being removed from orbit?

Yes, some particles can be recycled or reused for future space missions. For example, some spacecraft have been designed to collect and deorbit old satellites to reduce the amount of space debris in orbit.

5. How does removing particles from orbit impact the environment?

Removing particles from orbit can help reduce the amount of space debris and minimize the risk of collisions with active spacecraft. However, the removal process itself can also create new debris and must be carefully managed to avoid further cluttering the space environment.

Similar threads

I When is weak interaction a force?
Replies
4
Views
2K
B The Sun's Influence on the Moon's Orbit: Is it Negligible?
Replies
4
Views
1K
B Do changes in speed always affect orbit size, and vice versa?
Replies
30
Views
2K
From circular orbit to elliptical orbit
Replies
3
Views
1K
I Can a Gyroscope on a Satellite Detect Orbit?
Replies
20
Views
2K
I Can a Satellite Maintain its Angular Velocity with Continuous Low Thrust?
Replies
2
Views
1K
Doubt about the elliptic orbits of the planets
Replies
1
Views
832
Initial states ppbar can proceed to npi^0 with parity conserved
Replies
1
Views
1K
Clarification on angular momentum
Replies
1
Views
984
I What would a hypothetical quark-quark collision yield?
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top