This article is a compilation of technical results that I obtained through my research. The ideas of this article thus will be comprehended mostly perhaps by only an expert of satellite technology and/or a general Physicist, nevertheless only after he/she also goes through preceding analysis and descriptive-content, the last one is linked below.

Flyby-Anomaly for Galileo-I, solved.

I had missed one unit earlier (– see below) in the computations I had carried out, this anomaly 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, — I would call flyby anomaly: a puzzle rather and opera anomaly: an adventure of hype.

Here (in flyby analysis) I use weak-field approximation, hyperbolic corrections to satellite’s energy which causes a deviation from circular orbits such as GPS-satellite, and trajectory parameters as given by Galileo-I radar-data.

I did not (?) use earth-spin about which people beat around a lot of bush, I recover increment-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 maladjustment. So I will review it more

I get exact qualitatively “similar curve” as well, for the speed as shown by Galileo-I radar-data.

I get exactly 3.92 mm/s at infinity, if I add, earth-spin: of 1% of static earth.

The earth-spin in opposite direction then gives exactly an error of 0.07 which is what they have in their dataother effects near perigee may fix the speed-increment-at-perigee ( — see below, Doppler shift itself may correct this)

The special-relativistic effect will anyway make this speed-increment 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: (– Again static earth)



x ( eg. 1500)

(earth spin) + or – 0.00396.

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 hyperbola.

I had missed my “speed of light unit” here, earlier, like I fixed that for static earth on earth surface and had order of 10^-{9}, now I get order of 10^-{9} again, makes life easier thus.

I will try to make a plot, I do already have a plot, need to play with my newly installed gnuplot, to save a plot-file, I know: set output ‘test.png’. Later I would upload scanned copies of other calculations …