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I posted similar questions a few days ago, and got "answers" that did not help. I really need somebody with a good knowledge of the pertinent physics.
I have written a VB application which computes the positions of objects acting under the influence of gravity. I am using classical equations, not general relativity equations.
First question relates to objects light years apart. Should I make corrections for such distances, which are not necessary for objects closer to each other? If corrections are required, do you know of a book or Web site which provides equations/algorithms?
Second question is more complex. It relates to two systems based on 3 massive stars (20 solar masses each). In both systems the three stars are initially equally spaced on a circle around the origin in the XY-Plane. They have initial velocities which result in their maintaining almost circular orbits around the origin and in the XY-Plane. The following two systems are based on this 3-Star system.
The first has a fourth star (5 solar masses) which is initially motionless on the Z-Axis about 1-2 light hours from the origin. Obviously, the fourth object will accelerate toward the origin and pass the 3 circling stars. It will then decelerate and reverse direction, again passing through the three circling stars.
The second system has a fourth star which is initially at the origin with a significant velocity along the Z-Axis. It will obviously reach some maximum distance from the origin, stop, and then accelerate toward the circling stars. When the fourth objects stops, this system seems very similar to the initial condition of the first system.
I expected these systems to be similar to each other, with the differing initial conditions causing them to start at different places in essentially similar histories.
My VB application indicated that in the first system, the three stars orbiting the Z-Axis moved off the XY-Plane in the direction of the initial velocity vector of the fourth object. They continue moving ever farther from the XY-Plane and seem unlikely to return to it. It seems as though they stole momentum from the fourth object.
My VB application indicates that in the second system, the three stars stay near the XY-plane. At least they do not move as far from the XY-Plane as for the first system.
If my application is correct, my intuition about these systems was seriously in error. While not surprised that my intuition was wrong, I was surprised at how bad it was.
My second question is: Could my application have some error, and my intuition be not so far off the mark? Other simulations indicate that the application is correct, but I do not have any independent data for use in verifying my results.
If you are a physicist with some pertinent knowledge, might you have a worthwhile opinion on the above? I would appreciate reliable advice.
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physics....
ok mate...its been a while since i was studying physics at uni, but ill give it a bash.
1) use newtons equations for these objects, they are massive and far apart and of similar masses....the problems come when they get really close together....were talking subatomic here...newton works fine for all objects ranging in size from galaxies to electron orbits.
if you are assuming that space is flat in your conditions and you dont want ridiculous amounts of accuracy (which you wont need in this i think) then dont worry about relativity and special rel....
the other thing is, you could simplify your studies by assuming that the 3 circular orbiting stars are just one star at the origin with 3 times the mass(albeit it a hollow one to allow the fourth stars to pass through) - treat it as a point source, and reduce your equations to 2 dimensions
2.1) remember that gravity is an attractive force. the fourth star will pull the other 3 towards its position along the z axis initially, as will the 3 stars pull the fourth toward them. so you would asssume that the 3 stars would initially accelerate toward the fourth(albeit not by much due to the mass difference), and the fourth toward the 3 quite a lot.
..also, the radius of the 3 stars orbit around the z axis should decrease slightly because the fourth star is attracting them toward the z axis....their velocity around the orbit will increase as the radius gets smaller(conservation of angular momentum/ energy)
as the fourth star approaches the centre of the orbit of the three it will be accelerating more and more...then it will pass through and begin to decelerate(the 3 stars pull it back toward them). it depends on how fast the 4th star is travelling as to what happens next...if the fourth star has enough energy to escape to infinty then it will not return, if it does not, then it will decelerate until it stops and then begin to accelerate back toward the 3 star system. anjd the system will reciprocate like that.
what you basically have is a pendulum...the tension in the string is gravity,
the anchor point of the string (the 3 stars) will move as well as the bob is attracting them (it is quite a significant percentage of the mass of the rest of the clock(or 3 star system. ....also the 3 strs orbit radius will reduce, but this wont effect the combined pull on the 4th....like i sadi you could replace the 3 stars with a single point mass equal to 3 times their mass...)
2.2)
this system is the same as the first...the only difference being that the fourth star has more velocity than the first systems fourth star, so the likelyhood that it will escape the system is bigger.
i cant remember off the top of my head what the equation for limiting factors would be to decide if the fourth star will stop or not...i can work it out if you want it...would be a good bit of revision for me!
so i think you have something wrong with your code.
start it simple, just use the 2d model and see if it works...the equations will be the same as those for a pendulum.
if you dont want to be so accurate, make the 3 star system much more massive than the fourth star and ignore the fact that they will move as well.
hope this helps....
if i can help more, give me a shout.
btw, do you know how to get a MAPI statement to choose a certain user profile automatically?
cheers
kev
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