The gravitational lenses of Alpha Centauri A, B, C and of Barnard’s Star
The gravitational lenses of the three nearest stars, Alpha Centauri A, B, and C (Proxima Centauri), are studied in this chapter. For each star, the minimal focal distance is found, and turns out to equal 679.262 AU, 563.484 AU and 112.138 AU, respectively, plus or minus the (large) uncertainties deriving from the uncertainties in the estimates of the star masses and radii. A comparison of these three minimal focal distances against the corresponding value for the Sun (550 AU, or, more correctly, 548.214 AU) is then made, but it is clearly pointed out that all these minimal focal distances are just the theoretical values given by Einstein’s deflection formula for a corresponding “naked star” (i.e., a star as if it had no corona!). The study of the true focal distances that follow from taking the corona into account is much more difficult and uncertain, and has to be delayed for further research. For the naked stars, we study the deflection of radio waves for four different frequencies: the water maser at 22 GHz, NASA’s Interstellar Probe (ISP) telecommunication frequency at 32 GHz (Ka band), the Cosmic Microwave Background peak frequency at 160.378 GHz and finally the positronium frequency at 203 GHz. For each frequency the antenna patterns of the three naked stars’ gravitational lenses are given. Finally, all the above data are derived also for the fourth star in increasing distance from the Sun—Barnard’s Star.
KeywordsRadio Wave Cosmic Microwave Background Star Mass Antenna Pattern Gravitational Lens
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