Re: Are the relative speeds of two moving bodies symmetric?
- From: Albertito <albertito1992@xxxxxxxxx>
- Date: Sun, 11 May 2008 05:02:22 -0700 (PDT)
On May 11, 10:38 am, Albertito <albertito1...@xxxxxxxxx> wrote:
Let two bodies, A and B, with equal masses, move inertially
along a straight line. Velocity of A wrt B is V_ab, and velocity
of B wrt A is V_ba. Since both bodies are inertially moving
along a straight line, we assume V_ab = - V_ba will always
hold, so we say both velocities are symmetrical. Suppose
now, body A accelerates during a time t at constant a_A along
the same straight line to yield a final velocity V_ab'. Can we
still claim the new velocity of B wrt A is V_ba' = -V_ab'? IOW,
isn't it reasonable to claim that the new V_ba' is actually not
that new, but V_ba' = - k*V_ab', for a real k < > 1? If it is true
that
V_ba' = - k*V_ab', for a real k < > 1, after the acceleration a_A
and V_ab' < > V_ab, then, can we conclusively say that
acceleration a_A has created an eventual gravitational field,
by claiming that both masses are no longer equal?
In the gravitational field of the Earth, a test body located
at a distance equal to R =1 AU, would feel a escape
speed of v_e=sqrt(2GM_e/R), with M_e the mass of the
Earth. In the gravitational field of the Sun, a test body located
at a distance equal to R =1 AU, would feel a escape speed
of v_s=sqrt(2GM_s/R), with M_s the mass of the Sun.
This means both bodies, the Earth and the Sun, are
free falling toward each other with different relative speeds.
If the mass of the Earth were equal to the mass of the Sun,
then it would be v_s = - v_e. But, since M_s > M_e, then
|v_s| > |v_e|. If you could stop the orbital motion of the Earth
around the Sun, it would free fall towards the Sun along a
straight line, and would impact it after a time of t_e = R/v_e,
measured with a local clock in the earth. The same collision,
measured by a local clock at the center of the Sun, would
occur after a time of t_s = R/v_s.
.
- References:
- Are the relative speeds of two moving bodies symmetric?
- From: Albertito
- Are the relative speeds of two moving bodies symmetric?
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