Transcript Implication of Mass Increase From GPS

Implication of Mass Increase
From GPS
Ron Hatch
Natural Philosophy Alliance
June 5, 2000
GPS in a Sun-Centered Frame (1)
• Show what is needed to make GPS work properly
in the sun-centered isotropic light speed inertial
frame. Consider clock slowing, length contraction,
and mass increase with velocity.
– For simplicity assume that the velocity vector of the
earth’s orbit lies in one of the GPS orbital planes. This
gives a velocity scale factor of:
v2
v2
vo2
vs2 vo  vs
  1 2  1 2  1 2  2  2
c
2c
2c 2c
c
GPS in a Sun-Centered Frame (2)
• Who cares about the length contraction of the
satellite? (No one) Of the Earth? (Yes – the orbital
velocity effect)
• But the slower clock rate has a term linear in the
spin velocity. Its integral means that the clock
will accumulate a bias which is peak negative
(earlier) upstream and peak positive (later)
downstream of earth’s velocity vector).
GPS in a Sun-Centered Frame (3)
• If velocity causes an inertial mass increase, then
the satellite will increase in mass with a term due
to the cross product of the orbital and spin
velocities. Conservation of momentum means that
it will slow down going upstream and speed up
going downstream. This will cause an apparent
length contraction of the orbit—the earth keeps
going at the same orbital speed.
• The satellite orbit longitudinal contraction
together with the satellite clock biases will make it
look to the earth observer like the speed of light is
isotropic on the earth relative to the GPS satellite.
GPS in a Sun-Centered Frame (4)
• A GRW law of kinetic force (analogous to the
magnetic force) solves two inertial mass increase
problems.
• A spin velocity kinetic force will ensure a
gravitational equivalent of the Trouton-Noble null
result.
• An orbital velocity kinetic force will lead to
energy conservation of the GPS satellite orbit.