How Do Orbital Dynamics Change Under Different Force Laws?

  • Thread starter Thread starter Odyssey
  • Start date Start date
  • Tags Tags
    Orbit Particles
Odyssey
Messages
84
Reaction score
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
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.
 
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:
 
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.
 
Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'

Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'

Well, I'm simulating a neutron-proton scattering phase shift. The equation that I solve numerically is the Phase function method and is $$ \frac{d}{dr}[\delta_{i+1}] = \frac{2\mu}{\hbar^2}\frac{V(r)}{k^2}\sin(kr + \delta_i)$$ ##\delta_i## is the phase shift for triplet and singlet state, ##\mu## is the reduced mass for neutron-proton, ##k=\sqrt{2\mu E_{cm}/\hbar^2}## is the wave number and ##V(r)## is the potential of interaction like Yukawa, Wood-Saxon, Square well potential, etc. I first...
View full post »

Thread 'Toponium Discovered'

Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark. Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true. But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
View full post »

Thread 'Dirac-Delta from Normalization of Continuous Eigenfunctions'

I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
View full post »

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
2K
From circular orbit to elliptical orbit
Replies
3
Views
2K
B Do changes in speed always affect orbit size, and vice versa?
Replies
30
Views
3K
I Tong Dynamics: cannot cancel angle from orbit energy expression calculation
Replies
2
Views
1K
Initial states ppbar can proceed to npi^0 with parity conserved
Replies
1
Views
1K
Doubt about the elliptic orbits of the planets
Replies
1
Views
1K
I Can a Gyroscope on a Satellite Detect Orbit?
Replies
20
Views
3K
I Can a Satellite Maintain its Angular Velocity with Continuous Low Thrust?
Replies
2
Views
2K
Clarification on angular momentum
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top