APOD: Introducing Comet ISON (2012 Oct 01)

[neufer]

134 m/s is not a tiny delta-V

But that isn't the delta-V required to put a distant Oort body into a parabolic orbit.

Yes it is.

[flash]

134 m/s is not a tiny delta-V

But that isn't the delta-V required to put a distant Oort body into a parabolic orbit.

Yes it is.

No, it's not... Given an object in a circular orbit, ANY delta-V will result in an either an elliptical or parabolic (if the change is great enough to exceed excape velocity) orbit. The delta-v causes a change in the object's angular momentum which is conserved throughout the object's orbit. Thus a small reduction in orbital velocity causes a small reduction in angular monentum. The object, (which must sweep equal areas in equal times in order to conserve angular momentum) leaves its circular orbit and begins orbiting in an elliptical (or parabolic) path, (at least in the elliptical case) to return to the initial point (at the initial distance) with the same reduced orbital speed.

The whole physical process is something of a mystery to me, frankly.

Here's a link that contains an explanation of orbital mechanics from a very unusual (and simple, but correct) point of view using the concept of velocity space that might be of interest... A perhaps little-known feature of our world is that in an inverse square field (such as gravity), ALL ORBITS ARE CIRCULAR IN VELOCITY SPACE, and that the radius of these circular orbits (in velocity space) corresponds to the angular momentum of the orbit in normal position space.
http://dspace.mit.edu/bitstream/handle/ ... sequence=2

Enjoy!

[neufer]

The whole physical process is something of a mystery to me, frankly.

Here's a link that contains an explanation of orbital mechanics from a very unusual (and simple, but correct) point of view using the concept of velocity space that might be of interest... A perhaps little-known feature of our world is that in an inverse square field (such as gravity), ALL ORBITS ARE CIRCULAR IN VELOCITY SPACE, and that the radius of these circular orbits (in velocity space) corresponds to the angular momentum of the orbit in normal position space.
http://dspace.mit.edu/bitstream/handle/ ... sequence=2

Orbital mechanics is not the mystery....rather:

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

[flash]

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.

[neufer]

The whole physical process is something of a mystery to me, frankly.

Here's a link that contains an explanation of orbital mechanics from a very unusual (and simple, but correct) point of view using the concept of velocity space that might be of interest... A perhaps little-known feature of our world is that in an inverse square field (such as gravity), ALL ORBITS ARE CIRCULAR IN VELOCITY SPACE, and that the radius of these circular orbits (in velocity space) corresponds to the angular momentum of the orbit in normal position space.
http://dspace.mit.edu/bitstream/handle/ ... sequence=2

Orbital mechanics is not the mystery....rather:

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

[b][color=#0000FF]The upcoming close passage of the Alpha Centaur binary will smear out Oort cloud velocities by ~0.5 km/s RMS. [u]Dozens[/u] of such passages over millions of years are required to constantly replenish our parabolic orbit comet supply.[/color][/b]

---

OK...I think I understand now: It is more of a slow evolutionary cumulative perturbation process which constantly but slowly replenishes our parabolic orbit comet supply over millions & billions of years.

The actual situation is that the outer Oort cloud contains not just distant circular orbits (as I was assuming) but rather the aphelion of a whole variety of orbital eccentricities & velocities. Those with an orbital angular velocity of under 3 m/s [= 30 km/s (x sqrt(2*12)/50,000)] would make for a cometary perihelion of 12 AU or less where they could be affected by the giant planets and eventually removed as a parabolic orbit comet. However, close stellar encounters like the passage of the two solar mass binary Alpha Centauri in 27,000 years will smear out the Oort cloud velocities by about 0.5 km/s RMS and, thereby, essentially fill in the gap of sub 3 m/s orbital angular velocity Oort bodies after around 36 such passages (over around 10 million years ~ one Oort body year).