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

[John Mallinckrodt <ajm@csupomona.edu>]

Correction. I wrote:

> 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.

when I should have written:

> your potential energy is off by precisely 21 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 and then made an additional  
> error of a factor of ten (perhaps during a multiplication of 5 by 2?)

John Mallinckrodt
Cal Poly Pomona

Original message:

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.