by flash » Fri Oct 05, 2012 12:07 am
neufer wrote:
A perturbation mechanism that turns many orbiting Oort bodies into (virtually
angular momentum dead) comets
but
one that doesn't (at the same time) scatter the vast majority of Oort bodies out into interstellar space is the mystery
I fear you may be thinking that a highly eccentric orbit (such as a sun-grazing comet) has much less angular momentum than a circular orbit (with radius the same as the apogee of the comet). That is not the case. In fact, the two orbits may have the same angular momentum. What differs is their eccentricity. In velocity space orbit diagrams there are certain prperties that are associated with physical invariants of the orbits. For instance, the radius of the (necessarily) circular orbit in velocity space is associated with the angular momentum of the orbit in position space. The distance from of the center of the velocity space orbit circle to the velocity space origin is associated with the eccentricity of the orbit in position space.
What makes velocity space useful is that when an object in orbit is perturbed (hit by something, or given a net force), the force acting on the mass produces an acceleration (which is to say a delta-v) which acts not on the object's position, but on its velocity. In velocity space this is easily seen. An object in a high circular orbit (such as an Oort body) has a low velocity, resulting in a small velocity space circle. The radius being small indicates that there is little angular momentum in its orbit. And the circularity of the orbit in position space (the eccentricity of the orbit is zero) means that the circle in velocity space is centered at the origin. It can bee seen that it takes only a very small delta-v to move the velocity space circle such that it's center is relatively far from the velocity space origin, making the new orbit highly eccentric. If the velocity space circle moves so that the distance from the origin is equal to the radius of the velocity space circle, then the velocity space circle will intersect the velocity space origin, and the new orbit in position space is parabolic. If the kick is large enough, it moves the velocity space circle so that the origin is outside the circle, and the orbit is hyperbolic. All this becomes obvious once the orbit is viewed through velocity space.
It seems to me that if two Oort bodies approach each other closely enough, they will each be kicked in mostly opposite directions (all this analysis assumes they are in the same plane), and so their velocity space circles will be displaced in different directions. The delta-v introduced by each to the other may be quite large when compared to their tangential velocity, and so they might easily be either be driven into a hyperbolic orbit, or merely become highly eccentric and so graze the Sun.
[quote="neufer"]
A perturbation mechanism that turns many orbiting Oort bodies into (virtually [b][u]angular momentum [color=#FF0000]dead[/color][/u][/b]) comets [b][u]but[/u][/b]
one that doesn't (at the same time) scatter the vast majority of Oort bodies out into interstellar space is the mystery :!:[/quote]
I fear you may be thinking that a highly eccentric orbit (such as a sun-grazing comet) has much less angular momentum than a circular orbit (with radius the same as the apogee of the comet). That is not the case. In fact, the two orbits may have the same angular momentum. What differs is their eccentricity. In velocity space orbit diagrams there are certain prperties that are associated with physical invariants of the orbits. For instance, the radius of the (necessarily) circular orbit in velocity space is associated with the angular momentum of the orbit in position space. The distance from of the center of the velocity space orbit circle to the velocity space origin is associated with the eccentricity of the orbit in position space.
What makes velocity space useful is that when an object in orbit is perturbed (hit by something, or given a net force), the force acting on the mass produces an acceleration (which is to say a delta-v) which acts not on the object's position, but on its velocity. In velocity space this is easily seen. An object in a high circular orbit (such as an Oort body) has a low velocity, resulting in a small velocity space circle. The radius being small indicates that there is little angular momentum in its orbit. And the circularity of the orbit in position space (the eccentricity of the orbit is zero) means that the circle in velocity space is centered at the origin. It can bee seen that it takes only a very small delta-v to move the velocity space circle such that it's center is relatively far from the velocity space origin, making the new orbit highly eccentric. If the velocity space circle moves so that the distance from the origin is equal to the radius of the velocity space circle, then the velocity space circle will intersect the velocity space origin, and the new orbit in position space is parabolic. If the kick is large enough, it moves the velocity space circle so that the origin is outside the circle, and the orbit is hyperbolic. All this becomes obvious once the orbit is viewed through velocity space.
It seems to me that if two Oort bodies approach each other closely enough, they will each be kicked in mostly opposite directions (all this analysis assumes they are in the same plane), and so their velocity space circles will be displaced in different directions. The delta-v introduced by each to the other may be quite large when compared to their tangential velocity, and so they might easily be either be driven into a hyperbolic orbit, or merely become highly eccentric and so graze the Sun.