Re: A weighty subject

[Richard Tarara <rtarara@SAINTMARYS.EDU>]

----- Original Message -----
From: John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>

> I've proposed exercises that I thought might reveal some conceptual
> difficulties previously in this thread.  Nobody took me up on them, so
> maybe I shouldn't bother trying to do it again.  Nevertheless, undaunted
> ...
>
> Consider two identical, spherically symmetric, nonrotating planets of
> radius R and mass M orbiting their common center of mass in a circle of
> radius 2R (and don't worry about Roche limits and all that!)
>
> a) What is the Newtonian "force of gravity" on an object of mass m near
> the surface of one planet when the other is directly overhead.

8/9(GMm/R^2)        from GMm/R^2 - GMn/(3R)^2

> b) What would a properly functioning scale read if it were used to
> weigh the object?

8/9(GMm/R^2)

> c) If the object were allowed to fall, what would be its acceleration
> relative to the nearby planet?

8/9(GM/R^2)  (approximately over a short range near the surface)


> John Mallinckrodt      mailto:ajm@csupomona.edu
> Cal Poly Pomona          http://www.csupomona.edu/~ajm

I would say all in agreement with W = m x (Grav Field).  What am I missing?
The second planet certainly affects the net gravitational force, the field,
and hence the weight and acceleration.

Rick