Convert Astronomical Units to Light Years

Astronomical Unit - An astronomical unit (abbreviated as AU, au, a.u., or sometimes ua) is a unit of length roughly equal to the mean distance between the Earth and the Sun. It is approximately 150 million kilometres (93 million miles). The symbol ua is recommended by the International Bureau of Weights and Measures, but au is more common in Anglosphere countries. The International Astronomical Union recommends au, while international standard ISO 31-1 uses AU. In general, capital letters are only used for the symbols of units which are named after individual scientists, while au or a.u. can also mean atomic unit or even arbitrary unit; however, the use of AU to refer to the astronomical unit is widespread. The astronomical constant whose value is one astronomical unit is referred to as unit distance and given the symbol A.

Originally, the AU was defined as the length of the semi-major axis of the Earth's elliptical orbit around the Sun. In 1976, the International Astronomical Union revised the definition of the AU for greater precision, defining it as that length for which the Gaussian gravitational constant (k) takes the value 0.017 202 098 95 when the units of measurement are the astronomical units of length, mass and time. An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.017 202 098 95 radians per day, or that length for which the heliocentric gravitational constant (the product GM) is equal to (0.017 202 098 95)2 AU3/d2. It is approximately equal to the mean Earth-Sun distance.

The metre is defined to be a unit of proper length, but the SI definition does not specify the metric tensor to be used in determining it. Indeed, the International Committee for Weights and Measures (CIPM) notes that "its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored." As such, the metre is undefined for the purposes of measuring distances within the solar system. The 1976 definition of the astronomical unit is incomplete, in particular because it does not specify the frame of reference in which time is to be measured, but has proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity has been proposed.

Light Year - A light-year or light year (symbol: ly) is a unit of length, equal to just under ten trillion kilometres. As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year. The light-year is often used to measure distances to stars and other distances on a galactic scale, especially in non-specialist and popular science publications. The preferred unit in astrometry is the parsec, because it can be more easily derived from, and compared with, observational data. The parsec is defined as the distance at which an object will appear to move one arcsecond of parallax when the observer moves one astronomical unit perpendicular to the line of sight to the observer, and is equal to approximately 3.26 light-years. The related unit of the light-month, roughly one-twelfth of a light-year, is also used occasionally for approximate measures.

Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in the IAU (1964) System of Astronomical Constants, used from 1968 to 1983. The product of Simon Newcomb's J1900.0 mean tropical year of 31,556,925.9747 ephemeris seconds and a speed of light of 299,792.5 km/s produced a light-year of 9.460530 x 1015 metres (rounded to the seven significant digits in the speed of light) found in several modern sources was probably derived from an old source such as a reputable 1973 reference which was not updated until 2000.

Other high precision values are not derived from a coherent IAU system. A value of 9.460536207 x 1015 metres found in some modern sources is the product of a mean Gregorian year of 365.2425 days (31,556,952 s) and the defined speed of light (299,792,458 m/s). The Live Search value, 9.460528405 x 1015 metres, is the product of the J1900.0 mean tropical year and the defined speed of light.