On the Interactions of Point Masses
The formula for the
gravitational field (g) of a
point mass (m1), whose motion up until time t < r/c is known, is(1)
dot u)3 [u(c2-vret2)
+ r x (u
In this equation
and aret are m1’s
retarded velocity and acceleration
points from the retarded position of m1
to point r;
u=c<r> – vret is a utility vector;
the unit vector of r.
The formula for m1’s
gravitomagnetic field is
= <r>/c x g(r,t).
The force experienced by a
second mass, m2, at (r,t)
and moving with velocity v2,
= m2(g + v2 x O).
g and O are mathematically imaginary. Thus the force, experienced
by m2 in the field of m1, has a radial attractive
component toward m1 and a transverse component found by application
of the left-hand rule to v2
In order to calculate the
motion of m2, Newton’s relativistically correct 2nd law
must be applied.
1. See INTRODUCTION TO ELECTRDYNAMICS, Griffiths, Second Edition,