Re: [Phys-l] Sharing a problem for students

[Ludwik Kowalski <kowalskil@mail.montclair.edu>]

On Dec 22, 2007, at 4:01 PM, John Mallinckrodt wrote:

> On Dec 22, 2007, at 7:45 AM, Ludwik Kowalski wrote:
>
> > ... I just simulated the sun (M=2e30 kg) with two identical planets
> > (m=6e24 kg) revolving on a circular orbit (R=1.5e11 m). The system
> > potential energy is -1e55 J while its kinetic energy is only +5e33
> > J. For obvious reason, the magnitude of potential energy is much
> > higher than kinetic energy.
>
> What is that obvious reason?  In general the gravitational PE of a
> circularly orbiting pair of bodies will be -2 times the KE.  If you
> have two Earths orbiting the Sun, you'll just get twice as much of
> both.  It seems pretty clear, then, that your potential energy is off
> by precisely 22 orders of magnitude, just the kind of erroneous
> result you'd expect, for instance, if you used G = 6.67 x 10^11 N m^2
> kg^-2.

Thanks John,

1) I obviously do not have intuition for this kind of results, 
otherwise i would immediately recognized the nonsensical outcome. You 
are correct, the mechanical error was in entering +11 instead of -11 in 
the G.

2) Another indication of my limited experience with astronomical 
numbers was when I started simulating a double star system (each mass 
2e30kg, and the circular orbit of radius 1.5e15 m = 10000 AU). I 
calculated the required speed and the answer was 149 m/s. How can it 
be? I suspected an error.  But it was not an error. The simulation 
confirmed this, about an hour ago. The period of one revolution turns 
out to be 2 million years. And that what the IP clock read at the end 
of the first revolution.

3) The double star is an interesting object because its center of mass 
is empty.
_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/