Tagged Questions
3
votes
2answers
76 views
Runge-Lenz vector and Keplerian Orbits
Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
1
vote
3answers
87 views
Condition for closed orbit [closed]
I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
3
votes
3answers
182 views
Is there a mathematical relationship here or am I looking for relations when there are none?
When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. This lead me to think about the two situations depicted above. Left: Shows two balls of equal mass ...
0
votes
2answers
328 views
Does effective potential for a gravitational force have a maximum below $E=0$?
The relevant figure is below (taken from Goldstein's Classical Mechanics). This figure plots the effective potential for a gravitational force. Does the effective potential $V'$ go flat below $E_2=0$? ...
0
votes
1answer
169 views
Energy required to kick a planet orbiting the Sun from an elliptical to a parabolic path
I am trying to solve the following problem from Goldstein's Classical Mechanics:
A planet of mass $M$ is in orbit of eccentricity $e=1-\alpha$ where $\alpha<<1$, about the Sun. Assume that the ...
1
vote
3answers
345 views
What is the difference between a bounded orbit and a closed orbit?
Goldstein's Classical Mechanics has a puzzling few sentences in his discussion of orbits.
Referring to the case of orbit where the energy is low enough for the orbit to be bounded, he says :"This ...
1
vote
1answer
71 views
What's the amount of deviation of cellestial orbits from perfect ellipses
It's well known that the planets don't orbit the sun in perfect circles and the characteristics of the elliptical orbits which serve as better approximations to their motion have been calculated ...
16
votes
4answers
1k views
What symmetry causes the Runge-Lenz vector to be conserved?
Noether's theorem relates symmetries to conserved quantities. For a central potential $V \propto \frac{1}{r}$, the Laplace-Runge-Lenz vector is conserved. What is the symmetry associated with the ...
3
votes
4answers
530 views
Does mass affect speed of orbit at a certain distance?
Does the mass of both the parent object, and the child object affect the speed at which the child object orbits the parent object?
I though it didn't (something like T^2 = R^3) until I saw an planet ...
6
votes
3answers
199 views
The feasibility of a satellite orbiting at a fixed time
I was speaking with some friends of mine, one of whom was an aerospace engineer. He posited the infeasibility of a hypothetical "Margaritaville Satellite" that orbited earth in such a way that ...
1
vote
2answers
1k views
Why an object travels a circular path?
It might sound stupid but seriously I couldn't find why?
We have a mass with a constant speed, which is acted on by a unit force which is always at right angles to its direction of motion.
Why do ...
