Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: flr on 06/04/2013 17:51:02

1.
The energy E of an object having the momentum p and the rest mass m0 is:
E^2 = (m0*c^2)^2+(p*c)^2
To define both E and pc, I need a frame and these quantities depends on the frame.
m0*c^2 is the same in all frames.
2.
The gravity law says that
F = G*M*m / r^2; where M is the mass of (say) Earth and m is the mass of then object moving, and having its rest mass m0.
If the object does not move relative to Earth, gravity law becames:
F = G*M*m0 / r^2;

My question is: If objects move relative to Earth, which mass should I use in:
F = G*M*m? / r^2;
still the rest mass m0 or the relativistic mass m_relativitic = E/c^2 = sqrt((m0*c)^2+(p)^2) = gamma*m0*c^2

See http://home.comcast.net/~peter.m.brown/gr/grav_force.htm

Thanks for the link. Interesting, but a bit too mathematical. Maybe in time you will explain more in words. Nevertheless, very interesting indeed.
Back to my question: From your Equation 21, it follows that the relativistic mass: m=sqrt((m0*c)^2+(p)^2) = gamma*m0*c^2 and not the rest mass m0, should be used in F = G*M*m? / r^2;.
Do I understand this correctly? Could you confirm it?

If so, it means that the relative speed between objects determine how much gravitational attraction there is. Is that right?

Thanks for the link. Interesting, but a bit too mathematical. Maybe in time you will explain more in words. Nevertheless, very interesting indeed.
Back to my question: From your Equation 21, it follows that the relativistic mass: m=sqrt((m0*c)^2+(p)^2) = gamma*m0*c^2 and not the rest mass m0, should be used in F = G*M*m? / r^2;.
Do I understand this correctly? Could you confirm it?

If so, it means that the relative speed between objects determine how much gravitational attraction there is. Is that right?
For particle moving in a gravitational field the mass is function of both speed and position (i.e. gravitational potential). See Eq. (16) in http://arxiv.org/abs/0709.0687
I've never worked it out for a spherical body like the earth, only for a uniform gravitational field. See Eq.(12) at http://home.comcast.net/~peter.m.brown/gr/uniform_force.htm
The gravitational force has the form F = mg where m = relativistic mass = "time component of 4momentum"/c = P^{0}/c.
Does that help?