| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1110.1 | Problems... | ARTMIS::MILLSH | and 50g scepticism, at gas mark 4.... | Mon Aug 14 1989 08:20 | 10 |
|
Correct me if I'm wrong, but...
The three body problem is unsolvable with Newtonian methods,
The two body problem is unsolvable in relativity (Special or General)
The one body problem is unsolvable in quantum physics (Heisenberg
uncertainty principle)
Relativistic Quantum physics runs into problems with a vacuum :-)
HRM
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| 1110.2 | | HPSTEK::XIA | In my beginning is my end. | Mon Aug 14 1989 16:40 | 24 |
| re .0 .1
If you have only two bodies, then there are essentially three
solutions for the Newtonian physics:
1. Hyperbolic solution. In this case the two bodies pass near each
other and curve each other's orbits then go their separate ways.
2. Elliptic solution. Simply known as "earth orbiting the sun".
3. Collision.
If you want to go for other fancy theories, then here is what you have:
General Relativity (Special Relativity does not make sense here since
the theory does not work when you have gravity): There are
approximation methods for the two body problem.
QM: You can solve the problem exactly for two bodies (Hydrogen atom is
an example).
Eugene
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| 1110.3 | | HPSTEK::XIA | In my beginning is my end. | Mon Aug 14 1989 17:33 | 6 |
| Here is a little puzzle I just come up with. Suppose you have two
objects A and B (with mass M and m). We know the initial positions and
velocities of both objects, and we know the position of object A at all
time. Derive a simple method to find object B at all time.
Eugene
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| 1110.4 | | BEING::POSTPISCHIL | Always mount a scratch monkey. | Mon Aug 14 1989 18:00 | 8 |
| Re .3:
Given initial positions, velocities, and masses, the center of mass
always travels in a known straight line. B's position is linearly
dependent upon A's position and the center of mass.
-- edp
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| 1110.5 | | HPSTEK::XIA | In my beginning is my end. | Mon Aug 14 1989 18:25 | 6 |
| re -1
Ain't that a nice problem :-)?
Eugene
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| 1110.6 | | ANT::JANZEN | cf. ANT::CIRCUITS,ANT::UWAVES | Mon Aug 14 1989 21:53 | 3 |
| The two body problem also has a parabolic solution newtonianly.
like when you throw a rock
Tom
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| 1110.7 | | DWOVAX::YOUNG | in the iron grip of bureaucracy | Mon Aug 14 1989 23:47 | 6 |
| I was looking more for a closed solution. I know that one exists
because I had to derive it on a test in college. Well, my math isn't
as sharp today as it was then, so I was hoping that someone else could
help me out.
Should I post this in Physics instead?
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| 1110.8 | | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Tue Aug 15 1989 03:31 | 8 |
| I vaguely recall that the math is a little tricky, but
for the "Sun - Earth" solution (assume no relativistic
effects, assume a large mass that is fixed with a smaller
mass moving around it) you eventually get the "conic
sections". I play around with it a bit on paper and see
if I can reconstruct it.
Dan
|