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Constants

The Constants module provides frequently occuring fundamental mathematical and astronomical constants.

Mathematical

Mathematical constants provide quick-reference to common factors.

Constant Description
DEG2RAD Factor to convert from degrees and radians.
RAD2DEG Factor to convert from radians to degrees.
AS2RAD Factor to convert from arc-seconds to radians.
RAD2AS Factor to convert from radians to arc-seconds.

Time

Time constants are used for conversions between different time systems.

Constant Description Value Units Source
MJD_ZERO Offset between Modified Julian Date and Julian Date time scales. $t_{mjd} + {mjd}{0} = t{jd $ \(2400000.5\) Days Montenbruck and Gill 1
MJD_J2000 Modified Julian date of J2000 Epoch. January 1, 2000 12:00:00. \(51544.5\) Days Montenbruck and Gill 1
GPS_TAI Constant offset from TAI to GPS time scale. \(t_{gps} = t_{tai} + \Delta_{GPS-TAI}\) \(19.0\) \(s\) Montenbruck and Gill 1
TAI_GPS Constant offset from GPS to TAI time scale. \(t_{tai} = t_{gps}<br/><br/><br/> + \Delta_{TAI-GPS}\) \(-19.0\) \(s\) Montenbruck and Gill 1
TT_TAI Constant offset from TT to TAI time scale. \(t_{tt} = t_{tai} <br/><br/><br/>+ \Delta_{TT-TAI}\) \(32.184\) \(s\) Montenbruck and Gill 1
TAI_TT Constant offset from TAI to TT time scale. \(t_{tai} = t_{tt} <br/><br/><br/>+ \Delta_{TAI-TT}\) \(-32.184\) \(s\) Montenbruck and Gill 1
GPS_TT Constant offset from GPS to TT time scale. \(t_{gps} = t_{tt} <br/><br/><br/>+ \Delta_{GPS-TT}\) \(-51.184\) \(s\) Montenbruck and Gill 1
TT_GPS Constant offset from TT to GPS time scale. \(t_{tt} = t_{gps} <br/><br/><br/>+ \Delta_{TT-GPS}\) \(51.184\) \(s\) Montenbruck and Gill 1
GPS_ZERO Modified Julian Date of the start of the GPS time scale in the GPS time scale. This date is January 6, 1980 00:00:00 hours reckoned in the UTC time scale \(44244.0\) Days Montenbruck and Gill 1

Physical Constants

Physical constants are fundamental physical constants or properties of astronomical bodies. While these values are estimated they are considered to be well known and do not change frequently.

Constant Description Value Units Source
C_LIGHT Speed of light in vacuum. \(299792458.0\) \(\frac{m}{s}\) Vallado 2
AU Astronominal Unit. TDB reference frame compatible value equal to the mean distance of the Earth from the Sun. \(1.49597870700 \times 10^{11}\) \(m\) Gérard and Luzum 3
R_EARTH Earth's semi-major axis as defined by the Grace GGM05S gravity model. \(.378136.3\) \(m\) Ries et al. 4
WGS84_A Earth geoid model's semi-major axis as defined by the World Geodetic System 1984 edition. \(6378137.0\) \(m\) NIMA Technical Report 5
WGS84_F Earth geoid model's flattening as defined by the World Geodetic System 1984 edition. \(\frac{1.0}{298.257223563}\) Dimensionless NIMA Technical Report 5
GM_EARTH Gravitational Constant of the Earth. \(3.986004415 \times 10^{14}\) \(\frac{m^3}{s^2}\) Montenbruck and Gill 1
ECC_EARTH Earth geoid model's eccentricity. \(8.1819190842622 \times 10^{-2}\) Dimensionless NIMA Technical Report 5
J2_EARTH Earth's first zonal harmonic. Also known as Earth's oblateness. \(0.0010826358191967\) Dimensionless Montenbruck and Gill 1
OMEGA_EARTH Earth's axial rotation rate. \(7.292115146706979 \times 10^{-5}\) \(\frac{rad}{s}\) Vallado 2
GM_SUN Gravitational constant of the Sun. \(1.32712440041939400 \times 10^{20}\) \(\frac{m^3}{s^2}\) Montenbruck and Gill 1
R_SUN Nominal photosphere radius of the Sun. \(6.957 \times 10^{8}\) \(m\) Montenbruck and Gill 1
P_SUN Nominal solar radiation pressure at 1 AU. \(4.560 \times 10^{-6}\) \(\frac{N}{m^2}\) Montenbruck and Gill 1
R_SUN Equatorial radius of the Moon. \(1.738 \times 10^{6}\) \(m\) Montenbruck and Gill 1
GM_MOON Gravitational constant of the Moon. \(4.902800066 \times 10^{12}\) \(\frac{m^3}{s^2}\) Montenbruck and Gill 1
GM_MERCURY Gravitational constant of the Mercury. \(2.2031780 \times 10^{13}\) \(\frac{m^3}{s^2}\) Montenbruck and Gill 1
GM_VENUS Gravitational constant of the Venus. \(3.248585920 \times 10^{12}\) \(\frac{m^3}{s^2}\) Montenbruck and Gill 1
GM_MARS Gravitational constant of Mars (planet only, without Phobos and Deimos). \(4.282837362069909 \times 10^{13}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_MARS_SYSTEM Gravitational constant of the Mars system barycenter (NAIF ID 4). \(4.28283758157561 \times 10^{13}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_JUPITER Gravitational constant of Jupiter (planet only, without its satellites). \(1.266865319003704 \times 10^{17}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_JUPITER_SYSTEM Gravitational constant of the Jupiter system barycenter (NAIF ID 5). \(1.267127641 \times 10^{17}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_SATURN Gravitational constant of Saturn (planet only, without its satellites). \(3.793120623436167 \times 10^{16}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_SATURN_SYSTEM Gravitational constant of the Saturn system barycenter (NAIF ID 6). \(3.79405848418 \times 10^{16}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_URANUS Gravitational constant of Uranus (planet only, without its satellites). \(5.793951256527211 \times 10^{15}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_URANUS_SYSTEM Gravitational constant of the Uranus system barycenter (NAIF ID 7). \(5.7945564 \times 10^{15}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_NEPTUNE Gravitational constant of Neptune (planet only, without its satellites). \(6.835103145462294 \times 10^{15}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_NEPTUNE_SYSTEM Gravitational constant of the Neptune system barycenter (NAIF ID 8). \(6.836527100580399 \times 10^{15}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_PLUTO Gravitational constant of Pluto (planet only, without its satellites). \(8.696138177608748 \times 10^{11}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6
GM_PLUTO_SYSTEM Gravitational constant of the Pluto system barycenter (NAIF ID 9). \(9.755 \times 10^{11}\) \(\frac{m^3}{s^2}\) NAIF gm_de440.tpc 6

  1. O. Montenbruck, and E. Gill, Satellite Orbits: Models, Methods and Applications, 2012 ↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩

  2. D. Vallado, Fundamentals of Astrodynamics and Applications (4th Ed.), 2010 ↩↩

  3. P. Gérard and B. Luzum, IERS Technical Note 36, 2010 ↩

  4. J. Ries, S. Bettadpur, R. Eanes, Z. Kang, U. Ko, C. McCullough, P. Nagel, N. Pie, S. Poole, T. Richter, H. Save, and B. Tapley, Development and Evaluation of the Global Gravity Model GGM05, 2016 ↩

  5. Department of Defense World Geodetic System 1984, Its Definition and Relationships With Local Geodetic Systems ↩↩↩

  6. NAIF gm_de440.tpc (JPL/Horizons DE440 "ASTRO-VALUES" constant set; barycentric system GMs are the DE440 planetary-solution values, planet-only and satellite GMs are Horizons-curated satellite-solution values). Because the two sets come from estimation solutions of different epochs, a system GM does not exactly equal the sum of its planet and satellite GMs (e.g. GM_MARS_SYSTEM exceeds GM_MARS + GM_PHOBOS + GM_DEIMOS by ~1.4×10⁶ m³/s²); pair system values with DE-kernel barycenter positions and body values with satellite-kernel body-center dynamics. R.S. Park, W.M. Folkner, J.G. Williams, and D.H. Boggs, The JPL Planetary and Lunar Ephemerides DE440 and DE441, The Astronomical Journal, 161:105, 2021 ↩↩↩↩↩↩↩↩↩↩↩↩