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Shapiro time delay

What you are seeing: a light signal traveling from an emitter to a receiver passes near a massive body (the Sun at the origin). In flat space the signal would travel in a straight line parallel to the xx-axis at impact parameter bb. In General Relativity the signal experiences a time delay δt=2Mln(4rErR/b2)\delta t = 2M \ln(4 r_E r_R / b^2) relative to the flat-space expectation, where rEr_E and rRr_R are the emitter and receiver distances from the Sun.

The delay is logarithmic in bb, growing rapidly as the signal grazes the body. For light grazing the Sun, the round-trip Cassini delay was about 250250 microseconds; Bertotti, Iess and Tortora measured it to high precision in 2003 to test the PPN parameter gamma.

Figure 1. Shapiro delay. Method: closed-form PPN formula with full Schwarzschild overlay.
b (units M)20
r_E = r_R1000
speed2

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.