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The Curvature of Light Due to Relativistic Aberration

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The Curvature of Light Due to Relativistic Aberration The curvature of light due to relativistic aberration Bart Leplae - [email protected] 16-Oct-2012 This paper summarizes the different forms of aberration for nearby and remote objects and provides supporting evidence that the physics of the aberration of light must be a combination of local and remote effects whereby light follows a curved path as a consequence of relativistic aberration. The reference frames that are at the basis of relativistic aberration are put into the context of the relativistic effects on atomic clocks such as used in GPS satellites. 1 Table of content Aberration of light ................................................................................................................................................... 3 Stellar aberration – Definition ............................................................................................................................ 3 Stellar aberration – A complication related to nearby objects ........................................................................... 4 Nearby objects – No aberration ..................................................................................................................... 5 The Moon – Diurnal aberration ...................................................................................................................... 5 Planets – Planetary aberration ....................................................................................................................... 6 Stars within the Milky Way – Secular aberration ........................................................................................... 7 Remote galaxies – Secular aberration ............................................................................................................ 7 Hubble telescope - Orbital aberration ............................................................................................................ 8 Where does the aberration of light take place? ...................................................................................................... 9 Occultation of stars and planets ........................................................................................................................... 10 Airy’ Water Telescope ........................................................................................................................................... 10 Venus transit ......................................................................................................................................................... 11 Relativistic aberration ........................................................................................................................................... 12 The reference frame within the Solar System ....................................................................................................... 13 Simulation of light path ......................................................................................................................................... 14 Complex light curve ............................................................................................................................................... 15 Annual aberration ................................................................................................................................................. 16 Why does only the motion of the observer matter?.............................................................................................. 17 Global Positioning system ..................................................................................................................................... 18 The Hafele-Keating experiment ............................................................................................................................. 19 The effect on GPS clocks ........................................................................................................................................ 20 Summary / Conclusion........................................................................................................................................... 21 2 Aberration of light Stellar aberration – Definition As per Wikipedia: The aberration of light (also referred to as astronomical aberration or stellar aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations. At the instant of any observation of an object, the apparent position of the object is displaced from its true position by an amount which depends solely upon the transverse component of the velocity of the observer, with respect to the vector of the incoming beam of light (i.e., the line actually taken by the light on its path to the observer). The result is a tilting of the direction of the incoming light which is independent of the distance between object and observer. In the case of an observer on Earth, the direction of a star's velocity varies during the year as Earth revolves around the Sun (or strictly speaking, the barycenter of the solar system), and this in turn causes the apparent position of the star to vary. This particular effect is known as annual aberration or stellar aberration, because it causes the apparent position of a star to vary periodically over the course of a year. The maximum amount of the aberrational displacement of a star is approximately 20 arcseconds in right ascension or declination. Light from location 1 will appear to be coming from location 2 for a moving telescope due to the finite speed of light. The aberration can be calculated as: There are a number of types of aberration, caused by the differing components of the Earth's motion: Annual aberration is due to the revolution of the Earth around the Sun. Planetary aberration is the combination of aberration and light-time correction. Diurnal aberration is due to the rotation of the Earth about its own axis. Secular aberration is due to the motion of the Sun and solar system relative to other stars in the galaxy. 3 Stellar aberration – A complication related to nearby objects A complication when considering a more nearby object (whether it is a planet, the Moon, or a satellite) is that the source itself has a significant motion. It is the velocity of the observer relative to the velocity of the source that becomes relevant. As a specific example, if the source and observer move with the same relative transverse velocity, the aberration term is zero. Considering the above illustration, the question now arises why photons following the same path but originating from different sources can show a different behavior at the moment of entering a telescope. 4 Nearby objects – No aberration V = 0 m/s From the perspective of the observer on Earth, the observed position of the objects located on Earth do not change in the course of a day or in the course of a year. The Moon – Diurnal aberration V = + or -464 m/s at the Earth’s equator due to the rotation of the Earth around its axis. The resulting diurnal aberration = maximum 0.32" (with a periodicity of 1 day) The light-time correction for the Moon: −0.704". Light originating from the Moon is not subject to Annual aberration: to calculate the occurrence of a New Moon, we need only to take into account the constant displacement of the Sun (20.5”) and the light-time correction for the Moon (−0.704”). http://en.wikipedia.org/wiki/New_moon ) The observed position of the Moon is displaced with a maximum of 0.32 arcsec (+0.7 arcsec light- time correction) in the course of a day due to the effect of diurnal aberration. 5 Planets – Planetary aberration V depends on the relative motion of the observed planet and the Earth. Planetary aberration is the combination of aberration and light-time correction: Light-time correction: the distance the celestial object has moved while light travelled towards the observer once light has been emitted from the source Aberration: planetary aberration depends on the relative motion between source (planet) and observer (Earth). As a specific example, if source and observer move with the same relative transverse velocity (e.g. the Moon), the aberration term is zero (and only light-time correction applies) The following table depicts the aberration values (in arcsec) when all planets would be aligned with the Sun and with a distant star: Light Distance Source > from Orbital Sun Speed Observer on (AU) (km/s) v Sun Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Star 0 0 Sun 0.0 -32.9 -24.1 -20.5 -16.6 -9.0 -6.7 -4.7 -3.7 0.0 0,4 47,9 Mercury 32.9 0.0 8.8 12.4 16.4 23.9 26.3 28.3 29.2 32.9 0,7 35,0 Venus 24.1 -8.8 0.0 *3.6 7.5 15.1 17.4 19.4 20.4 24.1 1 29,8 Earth 20.5 -12.4 -3.6 0.0 3.9 11.5 13.8 15.8 16.8 20.5 1,5 24,1 Mars 16.6 -16.4 -7.5 -3.9 0.0 7.6 9.9 11.9 12.8 16.6 5,2 13,1 Jupiter 9.0 -23.9 -15.1 -11.5 -7.6 0.0 2.3 4.3 5.3 9.0 9,5 9,7 Saturn 6.7 -26.3 -17.4 -13.8 -9.9 -2.3 0.0 2.0 2.9 6.7 19,6 6,8 Uranus 4.7 -28.3 -19.4 -15.8 -11.9 -4.3 -2.0 0.0 0.9 4.7 30 5,4 Neptune 3.7 -29.2 -20.4 -16.8 -12.8 -5.3 -2.9 -0.9 0.0 3.7 Example whereby the observed aberration of 3.6 arcsec for Venus is referred to: “A Letter from Richard Price, D. D. F. R. S. to Benjamin Franklin, L L. D. F. R. S. on the Effect of the Aberration of Light on the Time of a Transit of Venus Over the Sun. (December 1770):” http://www.jstor.org/stable/105919?seq=1 From the perspective of the observers on Earth, the apparent position of the planets is subject to Diurnal aberration as well.
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