Stellar Aberration from Earth and from a Satellite

Abstract

In his endeavor to find a concrete evidence in favor of the Copernican picture of the solar system, the English astronomer James Bradley made a series of astronomical observations during the period (1725-1728) aiming to detect a stellar parallax. His findings, which manifested indeed an annual apparent cyclic motion of a star, were however at conflict with what is expected in a parallax. To his surprise, the result of every measurement obtained corresponded to what he expected to get in a measurement done three months earlier. Bradley realized that he was witnessing a new physical effect, and he presented an explanation that conceived light as a corpuscular stream travelling at finite velocity. Despite that Bradley’s explanation of the stellar aberration effect was inadequate, the equation which he derived to quantify the aberration angle, predicted a better estimation of light velocity, and the aberration phenomenon itself was a concrete support of heliocentrism. Stellar aberration as well as some other optical experiments, whose explanations posed challenges to the existing physical theories in the late nineteenth century paved the way for the emergence of the special theory of relativity. In the current work we employ the theory of universal space and time to show that a given direction in a frame of reference is tilted when observed in a moving frame by an angle that depends on the direction itself and the velocity of the moving frame. The latter fact is utilized to explain stellar aberration, determine the deviation of a star’s vision direction from its true one, and deduce its apparent position at any instant as a function of its latitude and time. The novel concept of aberration correction vector is employed to derive the apparent elliptic path of an observed celestial object at any time. The concept of graded inertial frames is introduced and utilized to deal with aberration when observed from a satellite in a similar way to its treatment when observed from Earth. The transformation matrix between a geocentric frame and a satellite’s non-rotating frame is derived and used to transform temporary Earthly vision directions to the satellite’s frame. Furthermore, the transformed vectors are adopted as transient fixed directions relative to which the vision directions of a star from the satellite are specified throughout one revolution. Satellites connective matrices are constructed to make geometric information regarding the celestial sphere in one frame immediately usable by observers on Earth and in all other satellites.