Astronomical constant
Encyclopedia
An astronomical constant is a physical constant
used in astronomy
. A formal set of constants, along with recommended values, was defined by the International Astronomical Union
(IAU) in 1976, and a new set of recommended values was produced in 1994. This set of constants is widely reproduced in publications such as the Astronomical Almanac
of the United States Naval Observatory
and Her Majesty's Nautical Almanac Office.
The IAU system of constants defines a system of astronomical units for length, mass and time (in fact, several such systems), and also includes constants such as the speed of light
and the constant of gravitation which allow transformations between astronomical units and SI units. Slightly different values for the constants are obtained depending on the frame of reference
used. Values quoted in barycentric dynamical time
(TDB) or equivalent time scales such as the Teph
of the Jet Propulsion Laboratory
ephemerides
represent the mean values that would be measured by an observer on the Earth's surface (strictly, on the surface of the geoid
) over a long period of time. The IAU also recommends values in SI units, which are the values which would be measured (in proper length
and proper time
) by an observer at the barycentre of the Solar System: these are obtained by the following transformations:
(k) takes the value when the units of measurement are the astronomical units of length, mass and time.
Notes
* The theories of precession
and nutation
have advanced since 1976, and these also affect the definition of the ecliptic
. The values here are appropriate for the older theories, but additional constants are required for current models.
† The definitions of these derived constants have been taken from the references cited, but the values have been recalculated to take account of the more precise values of the primary constants cited in the table.
Physical constant
A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
used in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
. A formal set of constants, along with recommended values, was defined by the International Astronomical Union
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
(IAU) in 1976, and a new set of recommended values was produced in 1994. This set of constants is widely reproduced in publications such as the Astronomical Almanac
Astronomical Almanac
The Astronomical Almanac is an almanac published by the United States Naval Observatory and Her Majesty's Nautical Almanac Office, containing solar system ephemeris and catalogs of selected stellar and extragalactic objects....
of the United States Naval Observatory
United States Naval Observatory
The United States Naval Observatory is one of the oldest scientific agencies in the United States, with a primary mission to produce Positioning, Navigation, and Timing for the U.S. Navy and the U.S. Department of Defense...
and Her Majesty's Nautical Almanac Office.
The IAU system of constants defines a system of astronomical units for length, mass and time (in fact, several such systems), and also includes constants such as 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...
and the constant of gravitation which allow transformations between astronomical units and SI units. Slightly different values for the constants are obtained depending on the frame of reference
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...
used. Values quoted in barycentric dynamical time
Barycentric Dynamical Time
Barycentric Dynamical Time is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar system...
(TDB) or equivalent time scales such as the Teph
Ephemeris time
The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...
of the Jet Propulsion Laboratory
Jet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...
ephemerides
Ephemeris
An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...
represent the mean values that would be measured by an observer on the Earth's surface (strictly, on the surface of the geoid
Geoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...
) over a long period of time. The IAU also recommends values in SI units, which are the values which would be measured (in proper length
Proper length
In relativistic physics, proper length is an invariant measure of the distance between two spacelike-separated events, or of the length of a spacelike path within a spacetime....
and proper time
Proper time
In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...
) by an observer at the barycentre of the Solar System: these are obtained by the following transformations:
Astronomical system of units
The astronomical unit of time is a time interval of one day (D) of 86400 seconds. The astronomical unit of mass is the mass of the Sun (S). The astronomical unit of length is that length (A) for which the Gaussian gravitational constantGaussian gravitational constant
The Gaussian gravitational constant is an astronomical constant first proposed by German polymath Carl Friedrich Gauss in his 1809 work Theoria motus corporum coelestium in sectionibus conicis solem ambientum , although he had already used the concept to great success in predicting the...
(k) takes the value when the units of measurement are the astronomical units of length, mass and time.
Table of astronomical constants
| Quantity | Symbol | Value | Relative uncertainty | Ref. |
|---|---|---|---|---|
| Defining constants | ||||
| Gaussian gravitational constant Gaussian gravitational constant The Gaussian gravitational constant is an astronomical constant first proposed by German polymath Carl Friedrich Gauss in his 1809 work Theoria motus corporum coelestium in sectionibus conicis solem ambientum , although he had already used the concept to great success in predicting the... |
k | 0.017 202 098 95 A3/2 S−1/2 D−1 | defined | |
| 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... |
c | 299 792 458 m s−1 | defined | |
| Mean ratio of the TT second Terrestrial Time Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth.... to the TCG second Geocentric Coordinate Time Geocentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to precession, nutation, the Moon, and artificial satellites of the Earth... |
1 − LG | 1 − 6.969 290 134 | defined | |
| Mean ratio of the TCB second Barycentric Coordinate Time Barycentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar system... to the TDB second Barycentric Dynamical Time Barycentric Dynamical Time is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar system... |
1 − LB | 1 − 1.550 519 767 72 | defined | |
| Primary constants | ||||
| Mean ratio of the TCB second Barycentric Coordinate Time Barycentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar system... to the TCG second Geocentric Coordinate Time Geocentric Coordinate Time is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to precession, nutation, the Moon, and artificial satellites of the Earth... |
1 − LC | 1 − 1.480 826 867 41 | 1.4 | |
| Light-time for unit distance | τA | 499.004 786 3852 s | 4.0 | |
| Equatorial radius for 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... |
ae | 6.378 1366 m | 1.6 | |
| Potential of the geoid | W0 | 6.263 685 60 m2 s−2 | 8.0 | |
| Dynamical form-factor for 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... |
J2 | 0.001 082 6359 | 9.2 | |
| Flattening factor for 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... |
1/ƒ | 0.003 352 8197 = 1/298.256 42 |
3.4 | |
| Geocentric gravitational constant | GE | 3.986 004 391 m3 s−2 | 2.0 | |
| Constant of gravitation | G | 6.674 28 m3 kg−1 s−2 | 1.0 | |
| Ratio of mass of Moon to mass of Earth | μ | 0.012 300 0383 = 1/81.300 56 |
4.0 | |
| General precession in longitude, per Julian century, at standard epoch 2000 | ρ | 5029.796 195″ | * | |
| Obliquity of the ecliptic, at standard epoch 2000 | ε | 23° 26′ 21.406″ | * | |
| Derived constants | ||||
| Constant of nutation, at standard epoch 2000 | N | 9.205 2331″ | * | |
| Unit distance = cτA | A | 149 597 870 691 m | 4.0 | |
| Solar parallax = arcsin(ae/A) | π☉ | 8.794 1433″ | 1.6 | † |
| Constant of aberration, at standard epoch 2000 | κ | 20.495 52″ | ||
| Heliocentric gravitational constant = A3k2/D2 | GS | 1.327 2440 m3 s−2 | 3.8 | |
| Ratio of mass of Sun to mass of Earth = (GS)/(GE) | S/E | 332 946.050 895 | ||
| Ratio of mass of Sun to mass of (Earth + Moon) | (S/E) (1 + μ) |
328 900.561 400 | ||
| Mass of Sun = (GS)/G | S | 1.9818 kg | 1.0 | † |
| System of planetary masses: Ratios of mass of Sun to mass of planet | ||||
| Mercury Mercury (planet) Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits... |
6 023 600 | |||
| Venus Venus Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows... |
408 523.71 | |||
| 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... + Moon Moon The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more... |
328 900.561 400 | |||
| Mars Mars Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance... |
3 098 708 | |||
| 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,... |
1047.3486 | |||
| Saturn Saturn Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,... |
3497.898 | |||
| Uranus Uranus Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus... |
22 902.98 | |||
| Neptune Neptune Neptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times... |
19 412.24 | |||
| Pluto Pluto Pluto, formal designation 134340 Pluto, is the second-most-massive known dwarf planet in the Solar System and the tenth-most-massive body observed directly orbiting the Sun... |
135 200 000 | |||
| Other constants (outside the formal IAU System) | ||||
| Parsec Parsec The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres .... = A/tan(1") |
pc | 3.085 677 581 28×1016 m | 4.0 | † |
| Light-year Light-year A light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres... = 365.25cD |
ly | 9.460 730 472 5808 m | defined | † |
| Hubble constant | H0 | 70.1 km s−1 Mpc−1 | 0.019 | |
| Solar luminosity | L☉ | 3.939 W = 2.107 S D−1 |
variable, ±0.1% |
|
Notes
* The theories of precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
and nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...
have advanced since 1976, and these also affect the definition of the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
. The values here are appropriate for the older theories, but additional constants are required for current models.
† The definitions of these derived constants have been taken from the references cited, but the values have been recalculated to take account of the more precise values of the primary constants cited in the table.
External links
- Tables of constants — from Nick Strobel's Astronomy Notes
- Astronomical constants index — James Q. Jacobs