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HandWiki. Stellar Aberration (Derivation from Lorentz Transformation). Encyclopedia. Available online: https://encyclopedia.pub/entry/31480 (accessed on 23 September 2026).
HandWiki. Stellar Aberration (Derivation from Lorentz Transformation). Encyclopedia. Available at: https://encyclopedia.pub/entry/31480. Accessed September 23, 2026.
HandWiki. "Stellar Aberration (Derivation from Lorentz Transformation)" Encyclopedia, https://encyclopedia.pub/entry/31480 (accessed September 23, 2026).
HandWiki. (2022, October 27). Stellar Aberration (Derivation from Lorentz Transformation). In Encyclopedia. https://encyclopedia.pub/entry/31480
HandWiki. "Stellar Aberration (Derivation from Lorentz Transformation)." Encyclopedia. Web. 27 October, 2022.
Stellar Aberration (Derivation from Lorentz Transformation)
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Stellar aberration is an astronomical phenomenon "which produces an apparent motion of celestial objects". It can be proven mathematically that stellar aberration is due to the change of the astronomer's inertial frame of reference. The formula is derived with the use of Lorentz transformation of the star's coordinates. As the astronomer John Herschel has already explained in 1844, the stellar aberration does not depend on the relative velocity of the star towards Earth. Otherwise eclipsing binary stars would appear to be separated, in stark contrast to observation: both stars are rotating with high speed —and ever changing and different velocity vectors— around each other, but they appear as one spot all the time.

eclipsing binary stars stellar aberration inertial frame

References

  1. Emden, R. (1926). "Aberration und Relativitätstheorie". Die Naturwissenschaften 14 (16): 329–335. doi:10.1007/BF01506966. Bibcode: 1926NW.....14..329E.  (14. Jahrgang, Heft 16) https://dx.doi.org/10.1007%2FBF01506966
  2. R. Emden's (rhetorical) question "How will the direction of the light rays of stars incident upon Earth be influenced by the motion of Earth and the motion (not the location) of the star at the time of emission?" is answered by him with "Not at all."
  3. See for example equation (4) in Klaus Kassner (2002). "Why the Bradley aberration cannot be used to measure absolute speeds. A comment". Europhysics Letters (EPL) 58 (4): 637–638. doi:10.1209/epl/i2002-00443-7. Bibcode: 2002EL.....58..637K.  https://dx.doi.org/10.1209%2Fepl%2Fi2002-00443-7
  4. I.e. the stars can rotate very fast like eclipsing binary stars as long as the change in position is much smaller than the star-earth distance.
  5. It's easy to (technically) compensate the deviation of the direction of the axes due to Earth's rotation and earth's orbit but it almost impossible to (technically) compensate a velocity in the order of several 1000 m/s. This can only be achieved with help of mathematics.
  6. Of course every inertial frame of reference is physically equal, but the rest system of the barycenter has the mathematical advantage, that it's the mean frame of reference and since the time of Galileo Galilei it's the preferred frame of reference
  7. The lines of x-axis and x'-axis lie on top of each other
  8. An even better quasi-inertial frame of reference would be a frame of reference in which the center of mass of the Milky Way would rest or be in uniform motion.
  9. Here the solution with cot 0 = -π/2 has to be used, see Plot of arccot (x) https://www.google.com/imgres?imgurl=http://www.efunda.com/math/trig_functions/images/arccot_plot.gif&imgrefurl=http://www.efunda.com/math/trig_functions/display.cfm?name%3Darccot&h=329&w=485&sz=3&tbnid=a0hRF-qzOibryM:&tbnh=82&tbnw=121&zoom=1&usg=__rTZwdunutqIAiG-l4WbgNeG82pY=&docid=KYfggGmcAxqigM&sa=X&ei=Z52XUZTAK6nk4QSDxIEQ&ved=0CEMQ9QEwAw&dur=197
  10. Spezielle Relativitätstheorie für Studienanfänger, Jürgen Freund, vdf-Verlag (Zürich), 2nd. Ed. (2005)
  11. For the star this period lies in the past.
  12. see e.g. The Constant of Aberration and the Solar Parallax http://adsabs.harvard.edu/full/1964SvA.....7..737M
  13. see hypertextbook.com http://hypertextbook.com/facts/2002/StacyLeong.shtml
  14. NASA - StarChild Question of the Month for February 2000 http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question18.html
  15. This is a hint from H.-H. Voigt: Abriss der Astronomie, 6. Auflage. Herausgegeben von H.-J. Röser und W. Tscharnuter. 2012 Wiley-VCH Verlag GmbH & Co. KGaA., page 35 of extract http://www.science-shop.de/sixcms/media.php/370/Leseprobe.1162646.pdf
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