Light-time correction is a displacement in the ''apparent'' position of a

celestial object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often u ...

from its ''true'' position (or geometric position) caused by the object's

motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and m ...

during the time it takes its

light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...

to reach an observer. Light-time correction occurs in principle during the observation of any moving object, because the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...

is finite. The magnitude and direction of the displacement in position depends upon the distance of the object from the observer and the motion of the object, and is measured at the instant at which the object's light reaches the observer. It is ''independent'' of the motion of the observer. It should be contrasted with the

aberration of light In astronomy, aberration (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is a phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of t ...

, which depends upon the instantaneous

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...

of the observer at the time of observation, and is independent of the motion or distance of the object. Light-time correction can be applied to any object whose distance and motion are known. In particular, it is usually necessary to apply it to the motion of a

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...

or other

Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...

object. For this reason, the combined displacement of the apparent position due to the effects of light-time correction and aberration is known as ''planetary aberration''. By convention, light-time correction is not applied to the positions of stars, because their

and distance may not be known accurately.

Calculation

A calculation of light-time correction usually involves an

iterative Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...

process. An approximate light-time is calculated by dividing the object's geometric distance from

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

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 as necessary. For planetary motions, a few (3–5) iterations are sufficient to match the accuracy of the underlying

ephemerides In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly ...

Discovery

The effect of the finite speed of light on observations of celestial objects was first recognised by Ole Rømer in 1675, during a series of observations of eclipses of the

moons of Jupiter There are 82 known moons of Jupiter, not counting a number of moonlets likely shed from the inner moons. All together, they form a satellite system which is called the Jovian system. The most massive of the moons are the four Galilean moons: ...

. He found that the interval between eclipses was less when Earth and Jupiter are approaching each other, and more when they are moving away from each other. He correctly deduced that this difference was caused by the appreciable time it took for light to travel from Jupiter to the observer on Earth.

References

*P. Kenneth Seidelmann (ed.), ''Explanatory Supplement to the Astronomical Almanac'' (Mill Valley, Calif., University Science Books, 1992), 23, 393. *Arthur Berry, ''A Short History of Astronomy'' (John Murray, 1898 – republished by Dover, 1961), 258–265. Astrometry Time {{time-stub