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Re: [Phys-l] Fun orbital problem



On 01/04/2008 01:07 PM, Ludwik Kowalski wrote:


Assuming Carl is away from the Internet access, I just simulated his
situation with I.P. The two stars have identical mass of 2e30 kg; the
distance between them is 1.5*10^15 m. The stars orbited exactly the
same circle many times, as expected. Then the simulation was stopped
and a much less massive satellite (m=2*10^25 kg) was added at r=
3.595e^15 m. The three particles were initially on the horizontal line,
at locations -1.5e15, +1.5e15 and 3.595e15 meters. The speeds of large
stars were 149.1 m/s (clockwise) while the speed of the satellite was
357.36 m/s (also clockwise).

Under such initial conditions, the three particles were initially
collinear. But not for too long. After about one T (period for each
star) the satellite started approaching the nearest star. Then it
started orbiting around it. But this also did not last too long. It
less than 2*T it hit the small circle representing the star which was
initially far away from it.

If you are interested in stability, this is your chance to
investigate stability.

It looks like there is roundoff error in the initial conditions
on the order of few parts in 10^4 since I doubt that 149.1 m/s
is the exact answer. So run the simulation several times with
various initial conditions, perturbed by something on the order
of parts in 10^4, and see what effect the perturbations have on
the trajectory.