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 |
MJD2000 |
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. $t_{tai} = t_{gps} + \Delta_{TAI-GPS}$ |
$-19.0$ | $s$ | Montenbruck and Gill 1 |
TT_TAI |
Constant offset from TT to TAI time scale. $t_{tt} = t_{tai} + \Delta_{TT-TAI}$ |
$32.184$ | $s$ | Montenbruck and Gill 1 |
TAI_TT |
Constant offset from TAI to TT time scale. $t_{tai} = t_{tt} + \Delta_{TAI-TT}$ |
$-32.184$ | $s$ | Montenbruck and Gill 1 |
GPS_TT |
Constant offset from GPS to TT time scale. $t_{gps} = t_{tt} + \Delta_{GPS-TT}$ |
$-51.184$ | $s$ | Montenbruck and Gill 1 |
TT_GPS |
Constant offset from TT to GPS time scale. $t_{tt} = t_{gps} + \Delta_{TT-GPS}$ |
$51.184$ | $s$ | 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 the Mars. | $4.282837521 \times 10^{13}$ | $\frac{m^3}{s^2}$ | Montenbruck and Gill 1 |
GM_JUPITER |
Gravitational constant of the Jupiter. | $1.267127648 \times 10^{17}$ | $\frac{m^3}{s^2}$ | Montenbruck and Gill 1 |
GM_SATURN |
Gravitational constant of the Saturn. | $3.79405852 \times 10^{16}$ | $\frac{m^3}{s^2}$ | Montenbruck and Gill 1 |
GM_URANUS |
Gravitational constant of the Uranus. | $5.7945486 \times 10^{15}$ | $\frac{m^3}{s^2}$ | Montenbruck and Gill 1 |
GM_NEPTUNE |
Gravitational constant of the Neptune. | $6.836527100580 \times 10^{15}$ | $\frac{m^3}{s^2}$ | Montenbruck and Gill 1 |
GM_PLUTO |
Gravitational constant of the Pluto. | $9.770 \times 10^{11}$ | $\frac{m^3}{s^2}$ | Montenbruck and Gill 1 |
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O. Montenbruck, and E. Gill, Satellite Orbits: Models, Methods and Applications, 2012 ↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩
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D. Vallado, Fundamentals of Astrodynamics and Applications (4th Ed.), 2010 ↩↩
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P. Gérard and B. Luzum, IERS Technical Note 36, 2010 ↩
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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 ↩
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Department of Defense World Geodetic System 1984, Its Definition and Relationships With Local Geodetic Systems ↩↩↩