On 2008-03-03, Eivind Kjorstad <eivindorama@[EMAIL PROTECTED]
> wrote:
> You make it sound as if the gravity-field of earth is divided in a
> "inside" and "outside" part, which is false.
Odd, it doesn't sound like that to me.
It's not a difficult concept: suppose that the field has an "energy
density" pro****tional to the square of the acceleration due to gravity
at each point.
(This is exactly analogous to the case for electrostatic fields, with
electric field strength instead of gravitational acceleration)
A very distant mass does change the field, but only very weakly. In
the limit where the separation is unbounded, the total field "energy"
is exactly the sum of the individual fields.
(This is also analogous to the case for electrostatic fields)
Choosing a suitable constant of pro****tionality and integrating over
all space gives a negative field "energy" that can be proven exactly
equal to the gravitational binding energy of all matter in the space.
(This once again is analogous to the case for electrostatic fields,
except that gravity has only one type of charge and the sign on the
constant of pro****tionality is reversed)
Note that this does not carry over to general relativity. Energy
considerations are much more complex there.
- Tim
|
