Universe Simulator

Rudolf,

A few points to ponder:

* If one star approaches another with an initial velocity that is above escape velocity (this will happen more often than not) they will never become gravitationally bound.

* If the stars begin with zero relative velocity but are far enough appart initially, they will reach escape velocity by the time they have fallen to minimum separation.

* There is a chapter on celestial mechanics in Dr. Van Flandern's book "Dark Matter ...". He covers some of the odd things related to gravitational interactions that we see when we look at stuff out there. Much of what we see is not intuitive, until you "adjust your intuition". Pay special attention to the parts about gravitational capture of one body by another. It is a VERY RARE OCCURANCE. And besides that it doesn't happen very often.

* In a situation where particle density is well above normal (as in a galaxy to galaxy collision or in the debris field of an exploded planet or star) the number of captures per unit time can go up to the point where you might actually see it occur.

* Bottom line - most of what happens when galaxies collide is the result of individual stars being deflected from their original trajectory (perhaps several times), not the result of individual stars going into orbit around each other.

* Even if the individual stars don't go into orbit around each other the galaxies themselves might. Or they might merge. The "friction" of passing through each other even if there are no actual star collsions might remove enough relative velocity to allow things like this to happen.

Regards,
LB

LB, Have you done the gravity math about how two objects attract? You say the excape velocity will be reached in the process and that won't happen using Kepler and Newton math. You say the objects will not develop orbits about each other if the velocity begins above the excape velocity and this is not always the case. The relative velocity of the object to the excape velocity can slow if the angle of approch is not too far from dead on. It is angular velocity that determines if an orbit will develop. Maybe I am missing something here.

[Jim] "Have you done the gravity math about how two objects attract?"

I've done several gravity and magnet simulators over the years. Nothing as ambitious as Rudolf's current project, though. Just goofing around. It's fun to watch the little points of light swirling around each other. Every once in a while one will zing off into infinity.

I did some homework problems involving this many years ago. Sophmore or Junior level mechanics, IIRC. And I have read a number of articles over the years that refer to it. As well as a number of (hard) science fiction stories where celestial mechanics came into play as part of the story line. A lot of SF authors are practicing scientists, and the better ones do a lot of research to make sure they get details like this correct.



[Jim] "You say the excape velocity will be reached in the process and that won't happen using Kepler and Newton math. You say the objects will not develop orbits about each other if the velocity begins above the excape velocity and this is not always the case."

Sort of true, but the exceptions involve the addition of a non-gravitational force or more than one target particle for gravity-only interactions.

* If the approaching particle looses enough kinetic energy via a non-gravitational interaction to prevent it from leaving the area of the target permanently, it will enter either a stable or an unstable orbit.

Examples are forces such as atmospheric drag in a near miss (always resulting in an unstable orbit) or collision with an existing mass already in orbit of the target (sometimes resulting in a stable orbit). Or a collision with the target (always resulting in either a lot of unstable orbits for the various pieces or no orbit).

* The other possibility, involving only gravitational force, requires two or more target particles. It works like a gravitational slingshot in reverse. If the incomming particle is diverted in just the right way by each of several masses, it can transfer enough energy to them to drop below escape velocity. The other masses will gain energy and it is possible that one or more of the target masses will gain enough that they will be ejected from the system.

It is a very low probability situation, and can just as easily transfer energy from the targets to the incomming particle.



[Jim] "The relative velocity of the object to the excape velocity can slow if the angle of approch is not too far from dead on."

Two particles only? Gravity only? This doesn't sound right. You'll have to draw me a picture.


Regards,
LB

LB, There is not need to have anything else other than two masses to show they will behave as I have said above. If the sun is one mass and another mass(relativity small for simplicity) is say 100AU distance from the sun it will fall into the sun as per Kepler's law. Now, a mass of the same mass and distance but moving toward the sun at the excape velocity(~4,000m/s@100AU or so) will be accelerated at a different rate(rate may be the wrong word here) due to the fact it covers the distance in less time. Both of these masses will be moving into the inner solar system at about the same speed and both are never getting out of the gravity field without help from other forces which are not part of the two body force. So, they both orbit the sun in stable orbits as do comets and asteriods ans stuff like that.

???

If it is already moving at or above escape velocity, then it will escape. Period. That is THE reason it is called what it is called.

LB

LB, Not so do the math.