Re: [Phys-l] Mass and Energy

[John Denker <jsd@av8n.com>]

Josh Gates-fac wrote:
> John, from your webpage:
>
> As for gravitational mass, it is the thing that shows up (twice) in the
> expression
> Fg = G M m / r2              ([
> http://www.av8n.com/physics/mass.htm#eq-grav ]8)
> which is valid provided the gravitation is not too strong and not too
> rapidly changing.
>  
> can you explain this?  I'm not sure that I follow what effects you're
> alluding to here.

Newtonian gravity is an approximation to general relativity.

1) The full GR treatment is nonlinear.  If the field is not too strong,
we can neglect higher-order terms and recover a linear theory.
Newtonian gravity is linear, i.e. the field from two sources is
just the sum of the fields of each source separately.

2) The full GR treatment is time dependent.  This includes gravitational
waves.  Newtonian gravity is instantaneous.  This corresponds to the
limit where the fields are not rapidly changing on timescales of
interest.