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In the last section "Orbit inside a radial shaft", it says that gravity is proportional to the distance from the center, and therefore supposedly results in simple harmonic motion like a spring. I am not an expert, but this seems obviously untrue. The spring force is indeed F=kx, but g ~ 1/x^2 . This means that the spring force is increasing with distance and the gravity force is decreasing. Moreover, the later effect is actually complicated by the fact that much of the mass of the planet will be "behind" the point mass as it approaches the center, making the force approach zero. The motion is going to be periodic, though, due to conservation of energy. -Evan — Preceding unsigned comment added by 69.123.96.13 ( talk) 04:43, 28 September 2011 (UTC)
Some scaling seems wrong: , but the separation at time t the bodies would have if they were on a parabolic trajectory is also given as
Patrick ( talk) 22:21, 19 January 2010 (UTC)
Thanks for pointing that out, it's all fixed now.
Apparently we both had been up all night editing the same file. I had to merge your last two edits with my mine, I hope I didn't screw up anything you were working on.
Be advised, the definitions given in escape orbit, and capture orbit are profoundly incorrect. The distinction made between an "escape" and a "capture" orbit is misleading at best.
For all open orbits, if the objects are moving closer when the time is negative, they will be moving apart when the time becomes positive, and vice versa. Flipping the sign of the velocity is a coordinate transform equivalent to flipping the sign of the time, it does not change the essence of the orbit type or or the mathematical analysis.
--
Norbeck (
talk)
18:08, 20 January 2010 (UTC)
so... the above formula doesn't seem compatible with the general formula here:
http://en.wikipedia.org/wiki/Free_fall#Inverse-square_law_gravitational_field
what's going on?
207.68.247.230 (
talk)
21:53, 2 May 2010 (UTC)
The topic is "radial trajectory", but we are really only talking about idealized kepler orbits. The first sentence of the article defines a "radial trajectory" as a kepler orbit, but this is not possible since "orbit" and "trajectory" are not synonymous. A trajectory describes a single body, an orbit describes two.
Since Hyperbolic trajectory, Parabolic trajectory, Radial trajectory exclusively describe orbits, I suggest they be renamed to "- orbit", and that "- trajectory" be redirected to "- orbit".
-- Norbeck ( talk) 18:08, 21 January 2010 (UTC)
What happens at t=0? an think of four possibilities:
Kepler orbits can exist only in closed systems. Since the orbital constants must stay constant the orbit cannot decay or spontaneously change. This rules out inelastic collisions. The remaining possibilites are all periodic.
I can't find the reference but there is a source supporting #3 "wrap around". To rule out the other possibilities we must define radial orbits as having "insignificant but nonzero" angular momentum (L). This is equivalent to defining radial orbits as standard orbits in the limit of L->0, which is equivalent to claiming radial elliptic orbits are degenerate elliptic orbits.
Since no real orbit is perfectly straight the rigorous definition of a radial orbit is: "a radial trajectory is a Kepler orbit with insignificant but nonzero L". I felt this was too technical. On the other hand, the L=0 definition is strictly incorrect and potentially very misleading. -- Norbeck ( talk) 23:11, 22 January 2010 (UTC)
![]() | This article has not yet been rated on Wikipedia's content assessment scale. |
In the last section "Orbit inside a radial shaft", it says that gravity is proportional to the distance from the center, and therefore supposedly results in simple harmonic motion like a spring. I am not an expert, but this seems obviously untrue. The spring force is indeed F=kx, but g ~ 1/x^2 . This means that the spring force is increasing with distance and the gravity force is decreasing. Moreover, the later effect is actually complicated by the fact that much of the mass of the planet will be "behind" the point mass as it approaches the center, making the force approach zero. The motion is going to be periodic, though, due to conservation of energy. -Evan — Preceding unsigned comment added by 69.123.96.13 ( talk) 04:43, 28 September 2011 (UTC)
Some scaling seems wrong: , but the separation at time t the bodies would have if they were on a parabolic trajectory is also given as
Patrick ( talk) 22:21, 19 January 2010 (UTC)
Thanks for pointing that out, it's all fixed now.
Apparently we both had been up all night editing the same file. I had to merge your last two edits with my mine, I hope I didn't screw up anything you were working on.
Be advised, the definitions given in escape orbit, and capture orbit are profoundly incorrect. The distinction made between an "escape" and a "capture" orbit is misleading at best.
For all open orbits, if the objects are moving closer when the time is negative, they will be moving apart when the time becomes positive, and vice versa. Flipping the sign of the velocity is a coordinate transform equivalent to flipping the sign of the time, it does not change the essence of the orbit type or or the mathematical analysis.
--
Norbeck (
talk)
18:08, 20 January 2010 (UTC)
so... the above formula doesn't seem compatible with the general formula here:
http://en.wikipedia.org/wiki/Free_fall#Inverse-square_law_gravitational_field
what's going on?
207.68.247.230 (
talk)
21:53, 2 May 2010 (UTC)
The topic is "radial trajectory", but we are really only talking about idealized kepler orbits. The first sentence of the article defines a "radial trajectory" as a kepler orbit, but this is not possible since "orbit" and "trajectory" are not synonymous. A trajectory describes a single body, an orbit describes two.
Since Hyperbolic trajectory, Parabolic trajectory, Radial trajectory exclusively describe orbits, I suggest they be renamed to "- orbit", and that "- trajectory" be redirected to "- orbit".
-- Norbeck ( talk) 18:08, 21 January 2010 (UTC)
What happens at t=0? an think of four possibilities:
Kepler orbits can exist only in closed systems. Since the orbital constants must stay constant the orbit cannot decay or spontaneously change. This rules out inelastic collisions. The remaining possibilites are all periodic.
I can't find the reference but there is a source supporting #3 "wrap around". To rule out the other possibilities we must define radial orbits as having "insignificant but nonzero" angular momentum (L). This is equivalent to defining radial orbits as standard orbits in the limit of L->0, which is equivalent to claiming radial elliptic orbits are degenerate elliptic orbits.
Since no real orbit is perfectly straight the rigorous definition of a radial orbit is: "a radial trajectory is a Kepler orbit with insignificant but nonzero L". I felt this was too technical. On the other hand, the L=0 definition is strictly incorrect and potentially very misleading. -- Norbeck ( talk) 23:11, 22 January 2010 (UTC)