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Update to: I solved Flyby anomaly of Galileo-I

November 23, 2011

Mohan, mdashf

flyby anomaly for Galileo-I solved.

I had missed one unit earlier (see below)this is explained by Theory of Relativity contrary to what was claimed so-far. (SO OPERA anomaly could be somewhat more of a PIA than flyby anomaly). Here I use weak-field approximation, hyperbolic corrections to satelite’s energy which causes a deviation from circular orbits such as GPS satelite, and trajectory parameters as given by Galileo-I data. I did not use earth-spin about which people beat around a lot of bush, I recover increament speed at infinity very close to 3.92 mm/s (I get 3.96 mm/s, see below) and at perigee an increase in speed close to 2.92 mm/s (I get 3.28 mm/s) I might be making a relative sign mismatch or inclination parameter misadjustment. SO I will review it more …

I get exact “qualitatively similar curve” as well, for the speed as shown by Galielo-I data
I get exactly 3.92 mm/s at infinity, if I add, earth spin of 1% static earth
the earth spin in opposite direction then gives exactly an error 0.07 which is what they have in their data … other effects near perigee may fix the speed increament at perigee (see below, Doppler shift itself may correct this)
the special-relativistic effect will anyway make this at perigee closer to the observed value (1st of all the angle of deflection at near perigee makes the effect smaller than what it would be for circular motion relative to the static earth effect)
here is the equation if you want to play around with it; static earth effect for flyby Galileo-I: (static earth) -0.396(1+/-0.6761*1.254*0.233/(1+/- x( eg. 1500)))
(earth spin) +/- .00396 ,
x =0.15 perigee, this is at 1 GHz radar, x is ratio between altitude and earth radii,
0.6761 is cosine of angle of deflection,
1.254 is 1/(cosine of inclination),
0.233 is the correction from hyperbolae (I had missed my “speed of light unit here, earlier, like I did that for static earth on earth surface and had order 10^-9, now I get order 10^-9 again, makes life easier thus)
I will try to make a plot (already have, need to play with my newly installed gnuplot to save a plot-file, I know: set output ‘test.png’) and later upload other calculations …
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