Light-time correction
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Light-time correction is a slight angular shift in the apparent position of a celestial object, especially a planet, from its geometric position on the celestial sphere caused by the object's motion during the time it takes its light to reach Earth.
Thus light-time correction moves a celestial object back from where it is at a particular instant of Earth time to where it was when its light left it, so that its calculated position does indeed predict its observed position (at least due to this effect). It depends only on the motion of the celestial object during its light-time—it does not depend on the motion of Earth. It is calculated iteratively. An approximate light-time is calculated by dividing the object's geometric distance from Earth by the speed of light. Then the object's velocity is multiplied by this approximate light-time to determine its approximate displacement through space during that time. Its previous position is used to calculate a more precise light-time. This process is repeated if necessary, but one iteration is usually sufficient given the slow movements of planets. This precise light-time is then used to calculate its precise displacement, which, combined with its past and present distances (at the beginning and end of its light-time) from the present position of Earth enable the calculation of its angular shift using trigonometry. The complement of light-time correction, which takes into account the angular shift of a celestial body due to Earth's orbital velocity, is called the aberration of light.
A celestial object's geometric position is calculated via Sir Isaac Newton's theory of universal gravitation, which assumes that an object's gravity affects all other objects simultaneously, no matter how far away they are, that is, that the speed of gravity is infinite.
A false light-time correction of the Sun is often mentioned as an example of the aberration of light. There is an apparent 20.5" (arc-second) shift of the Sun's position along the ecliptic relative to the fixed stars due to Earth's displacement along its orbit during the 8.3 minutes that it takes the Sun's light to reach Earth. This approximates the magnitude of the aberration of light from other stars, which obviously have vastly greater light-times, thus the phenomena are totally different. Furthermore, the geometric position of the Sun is always calculated at an instant of Earth time, thus Earth does not get a chance to move. Actually, during its light-time, the Sun does move slightly around the barycenter (center of mass) of the solar system as a counter-balance to the massive jovian planets (Jupiter, Saturn, Uranus, and Neptune). Thus the true light-time correction of the Sun is extremely small, usually much smaller than 0.03".
Bibliography
- P. Kenneth Seidelmann, Explanatory Supplement to the Astronomical Almanac (Mill Valley, Calif., University Science Books, 1992), 23, 393.