.. _constants: ``constants`` ============= This module contains constants that are used in the tudatpy library or commonly used in astrodynamic calculations. .. References .. ---------- .. .. [1] NASA SSD. Astrodynamic Parameters, http://ssd.jpl.nasa.gov/?constants#ref, 6th September, 2011, last accessed: 21st February, 2012. .. .. [2] Standish, E.M. (1995) "Report of the IAU WGAS Sub-Group on Numerical Standards", in Highlights of Astronomy (I. Appenzeller, ed.), Table 1, Kluwer Academic Publishers, Dordrecht .. .. [3] IAU 2012, Resolution B2. https://www.iau.org/static/resolutions/IAU2012_English.pdf .. .. [4] Anderson, J.D. Jr. Hypersonic and High-Temperature Gas Dynamics, Second Edition, p469, 2006 .. .. [5] NIST reference on constants, units and uncertainty. http://physics.nist.gov/cuu/Constants/index.html, last accessed: 11th January, 2013 .. .. [6] Wolfram Research, http://scienceworld.wolfram.com/physics/Stefan-BoltzmannLaw.html, last accessed: 11th January 2013. Physical Constants ------------------ .. currentmodule:: tudatpy.constants Fundamental physical constants used in physics and astronomy. .. autodata:: tudatpy.constants.SEA_LEVEL_GRAVITATIONAL_ACCELERATION Standard gravitational acceleration at Earth's sea level in :math:`\mathrm{m}/\mathrm{s}^2`. .. autodata:: tudatpy.constants.SPEED_OF_LIGHT Speed of light in vacuum in :math:`\mathrm{m}/\mathrm{s}` :cite:p:`standish1995`. .. autodata:: tudatpy.constants.SPEED_OF_LIGHT_LONG Speed of light in vacuum, high-precision (long double) variant in :math:`\mathrm{m}/\mathrm{s}` :cite:p:`standish1995`. .. autodata:: tudatpy.constants.GRAVITATIONAL_CONSTANT Newtonian gravitational constant in :math:`\mathrm{m}^3/(\mathrm{kg} \, \mathrm{s}^2)` :cite:p:`standish1995`. .. autodata:: tudatpy.constants.ASTRONOMICAL_UNIT Astronomical Unit - mean Earth-Sun distance in :math:`\mathrm{m}` :cite:p:`iau2012`. .. autodata:: tudatpy.constants.SPECIFIC_GAS_CONSTANT_AIR Specific gas constant for air in :math:`\mathrm{J}/(\mathrm{kg} \, \mathrm{K})` :cite:p:`anderson2006`. .. autodata:: tudatpy.constants.MOLAR_GAS_CONSTANT Universal molar gas constant in :math:`\mathrm{J}/(\mathrm{mol} \, \mathrm{K})` :cite:p:`nistconstants`. Also known as universal gas constant. .. autodata:: tudatpy.constants.PLANCK_CONSTANT Planck constant in :math:`\mathrm{J} \, \mathrm{s}` :cite:p:`nistconstants`. .. autodata:: tudatpy.constants.BOLTZMANN_CONSTANT Boltzmann constant - gas constant per particle in :math:`\mathrm{m}^{2} \, \mathrm{kg} / ( \mathrm{s}^{2} \, \mathrm{K} )` :cite:p:`nistconstants`. .. autodata:: tudatpy.constants.STEFAN_BOLTZMANN_CONSTANT Stefan-Boltzmann constant for black body radiation in :math:`\mathrm{W}/(\mathrm{m}^{2} \, \mathrm{K}^{4})` :cite:p:`wolfram2013`. .. autodata:: tudatpy.constants.INVERSE_SQUARE_SPEED_OF_LIGHT Precomputed :math:`1/c^2` in :math:`\mathrm{s}^2/\mathrm{m}^2`. .. autodata:: tudatpy.constants.INVERSE_CUBIC_SPEED_OF_LIGHT Precomputed :math:`1/c^3` in :math:`\mathrm{s}^3/\mathrm{m}^3`. .. autodata:: tudatpy.constants.INVERSE_QUARTIC_SPEED_OF_LIGHT Precomputed :math:`1/c^4` in :math:`\mathrm{s}^4/\mathrm{m}^4`. .. autodata:: tudatpy.constants.INVERSE_QUINTIC_SPEED_OF_LIGHT Precomputed :math:`1/c^5` in :math:`\mathrm{s}^5/\mathrm{m}^5`. .. autodata:: tudatpy.constants.VACUUM_PERMEABILITY Magnetic permeability of free space :math:`\mu_0` in :math:`\mathrm{H}/\mathrm{m}`. Defined as :math:`\mu_0 = 4\pi \times 10^{-7}` :math:`\mathrm{H}/\mathrm{m}`. .. autodata:: tudatpy.constants.VACUUM_PERMITTIVITY Electric permittivity of free space :math:`\varepsilon_0` in :math:`\mathrm{F}/\mathrm{m}`. Computed as :math:`\varepsilon_0 = 1/(\mu_0 c^2)`. Time Constants -------------- Time conversion factors and relativistic time scale parameters. .. autodata:: tudatpy.constants.JULIAN_DAY Number of seconds in a Julian day in :math:`\mathrm{s}` :cite:p:`NASASSD2011`. .. autodata:: tudatpy.constants.JULIAN_DAY_LONG Number of seconds in a Julian day, high-precision (long double) variant in :math:`\mathrm{s}` :cite:p:`NASASSD2011`. .. autodata:: tudatpy.constants.JULIAN_YEAR_IN_DAYS Number of days in a Julian year :cite:p:`NASASSD2011`. .. autodata:: tudatpy.constants.JULIAN_YEAR_IN_DAYS_LONG Number of days in a Julian year, high-precision (long double) variant :cite:p:`NASASSD2011`. .. autodata:: tudatpy.constants.JULIAN_YEAR Number of seconds in a Julian year in :math:`\mathrm{s}`. Result of ``JULIAN_YEAR_IN_DAYS * JULIAN_DAY``. .. autodata:: tudatpy.constants.SIDEREAL_DAY Number of seconds in a sidereal day in :math:`\mathrm{s}` :cite:p:`NASASSD2011`. .. autodata:: tudatpy.constants.SIDEREAL_YEAR_IN_DAYS Number of days in a sidereal year in quasar reference frame :cite:p:`NASASSD2011`. .. autodata:: tudatpy.constants.SIDEREAL_YEAR Number of seconds in a sidereal year in quasar reference frame in :math:`\mathrm{s}`. Result of ``SIDEREAL_YEAR_IN_DAYS * JULIAN_DAY``. .. autodata:: tudatpy.constants.LG_TIME_RATE_TERM Relative time rate difference between Geocentric Coordinate Time (TCG) and Terrestrial Time (TT). Defines the linear drift rate: TCG progresses faster than TT by approximately 0.7 parts per billion. Over one year, TCG gains about 22 milliseconds relative to TT. .. autodata:: tudatpy.constants.LG_TIME_RATE_TERM_LONG Relative time rate difference between TCG and TT, high-precision (long double) variant. Epoch Constants --------------- .. autodata:: tudatpy.constants.JULIAN_DAY_ON_J2000 Julian Day Number at the J2000.0 epoch (2000-01-01 12:00:00 TT). .. autodata:: tudatpy.constants.JULIAN_DAY_AT_0_MJD Julian Day Number at Modified Julian Date zero (1858-11-17 00:00:00). Mathematical Constants ---------------------- Fundamental mathematical constants. .. autodata:: tudatpy.constants.E Euler's number, base of natural logarithm. Also known as Napier's constant. .. autodata:: tudatpy.constants.GOLDEN_RATIO The golden ratio, also known as the divine proportion, golden mean, or golden section. A number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. .. autodata:: tudatpy.constants.COMPLEX_I Imaginary unit :math:`i = \sqrt{-1}`. Independent root of -1. .. autodata:: tudatpy.constants.PI The constant :math:`\pi`, ratio of circle's circumference :math:`C` to its diameter :math:`d = 2r`. .. autodata:: tudatpy.constants.TUDAT_NAN Tudat Not-a-Number (NaN) value indicating undefined/invalid results. High-Precision Constants ------------------------ The following constants have high-precision ``_LONG`` variants using ``long double`` precision instead of standard ``double`` precision. These provide extended precision for calculations requiring high accuracy over long time spans (the high-accuracy may only be realized in C++, on architectures/compilers where ``long double`` will map to 80-bit precision). **When to use high-precision variants:** - Long-duration orbital propagations (decades to centuries) - High-accuracy ephemeris calculations - Relativistic corrections in precise orbit determination - Time scale transformations requiring sub-nanosecond accuracy **Available high-precision variants:** - :data:`JULIAN_DAY_LONG` - For time conversions - :data:`JULIAN_YEAR_IN_DAYS_LONG` - For long-term propagations - :data:`SPEED_OF_LIGHT_LONG` - For relativistic corrections - :data:`LG_TIME_RATE_TERM_LONG` - For TCG-TT transformations