Light-time correction
Encyclopedia
Light-time correction is a displacement in the apparent position of a celestial object from its true position (or geometric position) caused by the object's motion during the time it takes its light to reach an observer.
Light-time correction occurs in principle during the observation of any moving object, because the speed of light
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
, which depends upon the instantaneous velocity
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
or other solar system
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 motion
and distance may not be known accurately.
process. 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 as necessary. For planetary motions, a few (3-5) iterations are sufficient to match the accuracy of the underlying ephemerides.
s of the moons of Jupiter
. 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.
Light-time correction occurs in principle during the observation of any moving object, because the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
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
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
, which depends upon the instantaneous velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
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
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
or other solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
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 motion
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...
and distance may not be known accurately.
Calculation
A calculation of light-time correction usually involves an iterativeIteration
Iteration means the act of repeating a process usually with the aim of approaching a desired goal or target or result. Each repetition of the process is also called an "iteration," and the results of one iteration are used as the starting point for the next iteration.-Mathematics:Iteration in...
process. An approximate light-time is calculated by dividing the object's geometric distance from Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
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.
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 eclipseEclipse
An eclipse is an astronomical event that occurs when an astronomical object is temporarily obscured, either by passing into the shadow of another body or by having another body pass between it and the viewer...
s of the moons of Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
. 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.