diff --git a/doc/calc-help/constants.md b/doc/calc-help/constants.md index 4800ae16..c5a11cab 100644 --- a/doc/calc-help/constants.md +++ b/doc/calc-help/constants.md @@ -994,6 +994,14 @@ Mercury gravitational parameter It is measured by radio tracking of spacecraft (Mariner 10, MESSENGER). [Reference 4](#reference-4) +### M☿ constant + +Mercury mass + +Mercury's mass, derived from the gravitational parameter `GM☿` and the measured +gravitational constant `G` as `GM☿/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req☿ constant Mercury equatorial radius @@ -1044,6 +1052,13 @@ Mercury's sidereal rotation period is a measured quantity. It is the true time it takes to spin 360° on its axis. Mercury is in a 3:2 spin-orbit resonance with the Sun, rotating three times for every two orbits. [Reference 22](#reference-22) +### ωrot☿ constant + +Mercury rotation angular velocity + +Mercury's sidereal rotation angular velocity, computed as `2π/Prot☿` from the +sidereal rotation period. The unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ☿ constant Mercury axial tilt @@ -1110,6 +1125,14 @@ Venus gravitational parameter Venus's gravitational parameter, measured by radio tracking of spacecraft (Magellan, Venus Express). [Reference 4](#reference-4) +### M♀ constant + +Venus mass + +Venus's mass, derived from the gravitational parameter `GM♀` and the measured +gravitational constant `G` as `GM♀/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req♀ constant Venus equatorial radius @@ -1161,6 +1184,15 @@ Measured. Venus's sidereal rotation period is the true time it takes to spin 360 on its axis. Venus rotates retrograde (opposite to its orbital motion), with a rotation period longer than its orbital period. [Reference 22](#reference-22) +### ωrot♀ constant + +Venus rotation angular velocity + +Venus's sidereal rotation angular velocity, computed as `2π/Prot♀` from the +sidereal rotation period. The value is negative because Venus rotates retrograde +(opposite to its orbital motion); the uncertainty uses the positive magnitude. +The unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ♀ constant Venus axial tilt @@ -1223,6 +1255,14 @@ Earth gravitational parameter Exact nominal value (IAU 2015). Earth's gravitational parameter. An exact nominal value defined by the IAU (2015). [Particle Data Group 2023](#particle-data-group-2023) +### M♁ constant + +Earth mass + +Earth's mass, derived from the gravitational parameter `GM♁` and the measured +gravitational constant `G` as `GM♁/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Particle Data Group 2023](#particle-data-group-2023) [Reference 5](#reference-5) + ### Req♁ constant Earth equatorial radius @@ -1274,6 +1314,13 @@ Earth sidereal rotation period Measured. Earth's sidereal rotation period (one sidereal day), the time for one rotation relative to the fixed stars. [Reference 24](#reference-24) +### ωrot♁ constant + +Earth rotation angular velocity + +Earth's sidereal rotation angular velocity, computed as `2π/Prot♁` from the +sidereal rotation period. The unit is radians per second (`r/s`). [Reference 24](#reference-24) + ### ϵ♁ constant Earth axial tilt @@ -1333,6 +1380,74 @@ year). Value in JDN. It is the most recent point in its orbit when it was closest to the Sun. [Materials 20](#materials-20) +### a♁GPS constant + +Earth equatorial radius (WGS-84) + +The semi-major axis of the WGS-84 reference ellipsoid, a defining constant of the +World Geodetic System 1984 used by GPS. Exact by definition. [WGS-84](#wgs-84) + +### f♁GPS constant + +Earth flattening (WGS-84) + +The flattening of the WGS-84 reference ellipsoid, `1/298.257223563`, a defining +constant. Exact by definition. [WGS-84](#wgs-84) + +### ω♁GPS constant + +Earth nominal mean angular velocity (WGS-84) + +The nominal mean angular velocity of the Earth in the WGS-84 system. Exact by +definition, and distinct from the sidereal value `ωrot♁` derived from `Prot♁`. [WGS-84](#wgs-84) + +### GM♁GPS constant + +Earth gravitational parameter (WGS-84) + +The geocentric gravitational constant of the WGS-84 system, including the mass of +the Earth's atmosphere. Exact by definition, and distinct from the IAU nominal +`GM♁`. [WGS-84](#wgs-84) + +### e12♁GPS constant + +Earth first eccentricity squared (WGS-84) + +The square of the first eccentricity of the WGS-84 reference ellipsoid, computed +from the flattening as `2·f♁GPS−f♁GPS²`. This is an ellipsoid (shape) eccentricity, +not the orbital eccentricity `e♁`. [WGS-84](#wgs-84) + +### e22♁GPS constant + +Earth second eccentricity squared (WGS-84) + +The square of the second eccentricity of the WGS-84 reference ellipsoid, computed +from the first as `e12♁GPS/(1−e12♁GPS)`. An ellipsoid eccentricity, distinct from +the orbital eccentricity `e♁`. [WGS-84](#wgs-84) + +### Ytrop♁ constant + +Tropical year + +The tropical (seasonal) year, equinox to equinox, about 365.24219 days at J2000. +It is distinct from `Porb♁` (the anomalistic year, perihelion to perihelion, used +by `T₀♁`) and from the calendar years `YJul♁` and `YGreg♁`. [Reference 24](#reference-24) + +### YJul♁ constant + +Julian year + +The Julian year, exactly 365.25 days. It is the year used to define the +light-year. [Reference 24](#reference-24) + +### YGreg♁ constant + +Gregorian mean year + +The mean year of the Gregorian calendar, exactly 365.2425 days +(365 + 1/4 − 1/100 + 1/400). [Reference 24](#reference-24) + + ## Moon constants ### GM☽ constant @@ -1342,6 +1457,14 @@ Moon gravitational parameter Measured. Moon's gravitational parameter, measured by lunar laser ranging and spacecraft radio tracking. [Reference 4](#reference-4) +### M☽ constant + +Moon mass + +The Moon's mass, derived from the gravitational parameter `GM☽` and the measured +gravitational constant `G` as `GM☽/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req☽ constant Moon equatorial radius @@ -1393,6 +1516,14 @@ Measured. Moon's sidereal rotation period is the true time it takes to spin 360° on its axis. The Moon is tidally locked to Earth, so its rotation period equals its orbital period. [Reference 22](#reference-22) +### ωrot☽ constant + +Moon rotation angular velocity + +The Moon's sidereal rotation angular velocity, computed as `2π/Prot☽` from the +sidereal rotation period. Because the Moon is tidally locked, this equals its +orbital mean motion. The unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ☽ constant Moon axial tilt @@ -1458,6 +1589,14 @@ Mars gravitational parameter Measured. Mars system gravitational parameter, including the contribution of its moons Phobos and Deimos, measured by spacecraft radio tracking. [Reference 4](#reference-4) +### M♂ constant + +Mars mass + +Mars's mass, derived from the gravitational parameter `GM♂` and the measured +gravitational constant `G` as `GM♂/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req♂ constant Mars equatorial radius @@ -1507,6 +1646,13 @@ Measured. Mars's sidereal rotation period is the true time it takes to spin 360° on its axis. A Martian day (sol) is very similar in length to an Earth day. [Reference 22](#reference-22) +### ωrot♂ constant + +Mars rotation angular velocity + +Mars's sidereal rotation angular velocity, computed as `2π/Prot♂` from the +sidereal rotation period. The unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ♂ constant Mars axial tilt @@ -1570,6 +1716,14 @@ Jupiter gravitational parameter Exact nominal value (IAU 2015). Jupiter system gravitational parameter. An exact nominal value defined by the IAU (2015). [Particle Data Group 2023](#particle-data-group-2023) +### M♃ constant + +Jupiter mass + +Jupiter's mass, derived from the gravitational parameter `GM♃` and the measured +gravitational constant `G` as `GM♃/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Particle Data Group 2023](#particle-data-group-2023) [Reference 5](#reference-5) + ### Req♃ constant Jupiter equatorial radius @@ -1623,6 +1777,13 @@ Measured. Jupiter's sidereal rotation period is the true time it takes to spin 360° on its axis (System III, based on radio emissions from its magnetosphere). [Reference 22](#reference-22) +### ωrot♃ constant + +Jupiter rotation angular velocity + +Jupiter's sidereal rotation angular velocity, computed as `2π/Prot♃` from the +sidereal rotation period (System III). The unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ♃ constant Jupiter axial tilt @@ -1688,6 +1849,14 @@ Saturn gravitational parameter Measured. Saturn system gravitational parameter, measured by radio tracking of the Cassini spacecraft. [Reference 4](#reference-4) +### M♄ constant + +Saturn mass + +Saturn's mass, derived from the gravitational parameter `GM♄` and the measured +gravitational constant `G` as `GM♄/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req♄ constant Saturn equatorial radius @@ -1740,6 +1909,13 @@ Measured. Saturn's sidereal rotation period is the true time it takes to spin 360° on its axis (System III, based on Cassini radio measurements). [Reference 22](#reference-22) +### ωrot♄ constant + +Saturn rotation angular velocity + +Saturn's sidereal rotation angular velocity, computed as `2π/Prot♄` from the +sidereal rotation period (System III). The unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ♄ constant Saturn axial tilt @@ -1805,6 +1981,14 @@ Uranus gravitational parameter Measured. Uranus system gravitational parameter, measured by Voyager 2 radio tracking. [Reference 4](#reference-4) +### M⛢ constant + +Uranus mass + +Uranus's mass, derived from the gravitational parameter `GM⛢` and the measured +gravitational constant `G` as `GM⛢/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req⛢ constant Uranus equatorial radius @@ -1856,6 +2040,15 @@ Measured. Uranus's sidereal rotation period is the true time it takes to spin 360° on its axis. Uranus rotates retrograde relative to its orbital motion. [Reference 22](#reference-22) +### ωrot⛢ constant + +Uranus rotation angular velocity + +Uranus's sidereal rotation angular velocity, computed as `2π/Prot⛢` from the +sidereal rotation period. The value is negative because Uranus rotates retrograde +relative to its orbital motion; the uncertainty uses the positive magnitude. The +unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ⛢ constant Uranus axial tilt @@ -1923,6 +2116,14 @@ Neptune gravitational parameter Measured. Neptune system gravitational parameter, measured by Voyager 2 radio tracking and Hubble Space Telescope astrometry of Triton. [Reference 4](#reference-4) +### M♆ constant + +Neptune mass + +Neptune's mass, derived from the gravitational parameter `GM♆` and the measured +gravitational constant `G` as `GM♆/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req♆ constant Neptune equatorial radius @@ -1974,6 +2175,13 @@ Measured. Neptune's sidereal rotation period is the true time it takes to spin 360° on its axis (System III, from Voyager 2 radio measurements). [Reference 22](#reference-22) +### ωrot♆ constant + +Neptune rotation angular velocity + +Neptune's sidereal rotation angular velocity, computed as `2π/Prot♆` from the +sidereal rotation period (System III). The unit is radians per second (`r/s`). [Reference 22](#reference-22) + ### ϵ♆ constant Neptune axial tilt @@ -2040,6 +2248,14 @@ Pluto gravitational parameter Measured. Pluto system gravitational parameter, measured by New Horizons radio tracking. [Reference 4](#reference-4) +### M♇ constant + +Pluto mass + +Pluto's mass, derived from the gravitational parameter `GM♇` and the measured +gravitational constant `G` as `GM♇/G`. The relative uncertainty is carried as +`ⓇG` (the dominant term), so the mass self-corrects whenever `G` is updated. [Reference 4](#reference-4) [Reference 5](#reference-5) + ### Req♇ constant Pluto equatorial radius @@ -2089,6 +2305,15 @@ Measured. Pluto's sidereal rotation period is the true time it takes to spin 360° on its axis. Pluto rotates retrograde and is tidally locked to its moon Charon. [Reference 26](#reference-26) +### ωrot♇ constant + +Pluto rotation angular velocity + +Pluto's sidereal rotation angular velocity, computed as `2π/Prot♇` from the +sidereal rotation period. The value is negative because Pluto rotates retrograde; +the uncertainty uses the positive magnitude. The unit is radians per second +(`r/s`). [Reference 26](#reference-26) + ### ϵ♇ constant Pluto axial tilt @@ -2220,6 +2445,14 @@ by tracking surface features using Doppler techniques. It is the true time it takes to spin 360° on its axis. [Reference 20](#reference-20) [Reference 21](#reference-21) +### ωrot☉ constant + +Solar rotation angular velocity + +The Sun's sidereal rotation angular velocity at the equator (System I), computed +as `2π/Prot☉` from the sidereal rotation period. The unit is radians per second +(`r/s`). [Reference 20](#reference-20) [Reference 21](#reference-21) + ## Cosmology constants ### Λ constant @@ -3319,6 +3552,10 @@ Particle Data Group (2024). "Review of Particle Physics — Astrophysical Consta Particle Data Group 2023 Prša, A., et al. (2016). "Nominal values for selected solar and planetary quantities: IAU 2015 Resolution B3". The Astronomical Journal, 152(2), 41. arXiv:1605.09788 — DOI: 10.3847/0004-6256/152/2/41 +### WGS-84 + +National Geospatial-Intelligence Agency (2014). Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems, NGA.STND.0036_1.0.0_WGS84, 3rd ed. (Defining parameters of the WGS-84 reference ellipsoid used by GPS.) + ### Reference 4 Park, R.S., et al. (2021). "The JPL Planetary and Lunar Ephemerides DE440 and DE441". The Astronomical Journal, 161(3), 105. DOI: 10.3847/1538-3881/abd414 diff --git a/src/constants.cc b/src/constants.cc index a3d5d122..132a350c 100644 --- a/src/constants.cc +++ b/src/constants.cc @@ -1214,6 +1214,11 @@ static const cstring basic_constants[] = " 0.0000000091E13_m³/s² " " 'ROUND(ⓈGM☿/ⒸGM☿;-2)' " " 2.203E13_m³/s² ]", + // *Mercury mass - Calculation from GM and G + "M☿", "[ 'ROUND(CONVERT(ⒸGM☿/ⒸG;1_kg);XPON(UVAL(ⒸGM☿/ⒸG·ⓇG))-XPON(UVAL(ⒸGM☿/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM☿*ⒸM☿);-2);1_kg)' " + " 'ⓇG' " + " 3.301E23_kg ]", // *Mercury equatorial radius - Measurement [22] "Req☿", "[ 2439.7_km " " 0.1_km " @@ -1247,6 +1252,10 @@ static const cstring basic_constants[] = " 0.1_s " " 'ROUND(ⓈProt☿/ⒸProt☿;-2)' " " 5.067E6_s ]", + // *Mercury rotation angular velocity - Calculation from Prot + "ωrot☿", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt☿;1_r/s);XPON(UVAL(Ⓡωrot☿*(2*Ⓒπ*1_r)/ⒸProt☿))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt☿))-2)' " + " 'CONVERT(ROUND(Ⓡωrot☿*(2*Ⓒπ*1_r)/ⒸProt☿;-2);1_r/s)' " + " 'ⓇProt☿' ]", // *Mercury axial tilt - Measurement [22] "ϵ☿", "[ 0.034_° " " 0.001_° " @@ -1289,6 +1298,11 @@ static const cstring basic_constants[] = " 0.00000012E14_m³/s² " " 'ROUND(ⓈGM♀/ⒸGM♀;-2)' " " 3.249E14_m³/s² ]", + // *Venus mass - Calculation from GM and G + "M♀", "[ 'ROUND(CONVERT(ⒸGM♀/ⒸG;1_kg);XPON(UVAL(ⒸGM♀/ⒸG·ⓇG))-XPON(UVAL(ⒸGM♀/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM♀*ⒸM♀);-2);1_kg)' " + " 'ⓇG' " + " 4.867E24_kg ]", // *Venus equatorial radius - Measurement [22] "Req♀", "[ 6051.8_km " " 0.1_km " @@ -1322,6 +1336,10 @@ static const cstring basic_constants[] = " 8.64_s " " 'ROUND(ⓈProt♀/ⒸProt♀;-2)' " " 2.100E7_s ]", + // *Venus rotation angular velocity - Calculation from Prot [retrograde] + "ωrot♀", "[ 'ROUND(CONVERT(-(2*Ⓒπ*1_r)/ⒸProt♀;1_r/s);XPON(UVAL(Ⓡωrot♀*(2*Ⓒπ*1_r)/ⒸProt♀))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt♀))-2)' " + " 'CONVERT(ROUND(Ⓡωrot♀*(2*Ⓒπ*1_r)/ⒸProt♀;-2);1_r/s)' " + " 'ⓇProt♀' ]", // *Venus axial tilt - Measurement [22] "ϵ♀", "[ 177.36_° " " 0.01_° " @@ -1364,6 +1382,11 @@ static const cstring basic_constants[] = "GM♁", "[ 3.986004E14_m³/s² " " 0_m³/s² " " 0 ]", + // *Earth mass - Calculation from GM and G + "M♁", "[ 'ROUND(CONVERT(ⒸGM♁/ⒸG;1_kg);XPON(UVAL(ⒸGM♁/ⒸG·ⓇG))-XPON(UVAL(ⒸGM♁/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM♁*ⒸM♁);-2);1_kg)' " + " 'ⓇG' " + " 5.972E24_kg ]", // *Earth equatorial radius - Exact nominal value [3] "Req♁", "[ 6378.1_km " " 0_km " @@ -1373,7 +1396,7 @@ static const cstring basic_constants[] = " 0_km " " 0 ]", // *Earth oblateness - Calculation from nominal value [3] - "f♁", "[ 'ROUND(1-ⒸRp♁/ⒸReq♁;XPON(UVAL(Ⓡf♁*(1-ⒸRp♁/ⒸReq♁)))-XPON(1-ⒸRp♁/ⒸReq♁)-2)' " + "f♁", "[ 'ROUND(1-ⒸRp♁/ⒸReq♁;-5)' " " 'ROUND(Ⓡf♁*Ⓒf♁;-2)' " " 'ⓇRp♁+ⓇReq♁' ]", // *Earth mean density - Calculation from nominal value [3] @@ -1395,6 +1418,10 @@ static const cstring basic_constants[] = " 0.0001_s " " 'ROUND(ⓈProt♁/ⒸProt♁;-2)' " " 8.616E4_s ]", + // *Earth rotation angular velocity - Calculation from Prot + "ωrot♁", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt♁;1_r/s);XPON(UVAL(Ⓡωrot♁*(2*Ⓒπ*1_r)/ⒸProt♁))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt♁))-2)' " + " 'CONVERT(ROUND(Ⓡωrot♁*(2*Ⓒπ*1_r)/ⒸProt♁;-2);1_r/s)' " + " 'ⓇProt♁' ]", // *Earth axial tilt - Measurement [24] "ϵ♁", "[ 23.4393_° " " 0.0001_° " @@ -1431,6 +1458,48 @@ static const cstring basic_constants[] = " 0_date " " 0 ]", + // ------------------------------------------------------------------------ + // WGS-84 / GPS reference ellipsoid (defining constants, exact) + // *Earth equatorial radius - WGS-84 defining constant [WGS-84] + "a♁GPS", "[ 6378137_m " + " 0_m " + " 0 ]", + // *Earth flattening - WGS-84 defining constant 1/298.257223563 [WGS-84] + "f♁GPS", "[ '1/298.257223563' " + " 0 " + " 0 ]", + // *Earth nominal mean angular velocity - WGS-84 [WGS-84] + "ω♁GPS", "[ 7.2921150E-5_r/s " + " 0_r/s " + " 0 ]", + // *Earth gravitational parameter (incl. atmosphere) - WGS-84 [WGS-84] + "GM♁GPS", "[ 3.986004418E14_m³/s² " + " 0_m³/s² " + " 0 ]", + // *Earth first eccentricity squared - WGS-84 ellipsoid, from flattening [WGS-84] + "e12♁GPS", "[ '2*Ⓒf♁GPS-Ⓒf♁GPS²' " + " 0 " + " 0 ]", + // *Earth second eccentricity squared - WGS-84 ellipsoid, from first [WGS-84] + "e22♁GPS", "[ 'Ⓒe12♁GPS/(1-Ⓒe12♁GPS)' " + " 0 " + " 0 ]", + + // ------------------------------------------------------------------------ + // Calendar and astronomical years + // *Tropical year (equinox to equinox, J2000) - seasonal year [24] + "Ytrop♁", "[ 365.24219_d " + " 0_d " + " 0 ]", + // *Julian year - exact, defines the light-year [24] + "YJul♁", "[ 365.25_d " + " 0_d " + " 0 ]", + // *Gregorian mean year - exact: 365 + 1/4 - 1/100 + 1/400 [24] + "YGreg♁", "[ 365.2425_d " + " 0_d " + " 0 ]", + "Astronomy/Moon", nullptr, // *Moon gravitational parameter - Measurement [4] @@ -1438,6 +1507,11 @@ static const cstring basic_constants[] = " 0.0000000009E12_m³/s² " " 'ROUND(ⓈGM☽/ⒸGM☽;-2)' " " 4.903E12_m³/s² ]", + // *Moon mass - Calculation from GM and G + "M☽", "[ 'ROUND(CONVERT(ⒸGM☽/ⒸG;1_kg);XPON(UVAL(ⒸGM☽/ⒸG·ⓇG))-XPON(UVAL(ⒸGM☽/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM☽*ⒸM☽);-2);1_kg)' " + " 'ⓇG' " + " 7.346E22_kg ]", // *Moon equatorial radius - Measurement [22] "Req☽", "[ 1738.1_km " " 0.1_km " @@ -1471,6 +1545,10 @@ static const cstring basic_constants[] = " 0.1_s " " 'ROUND(ⓈProt☽/ⒸProt☽;-2)' " " 2.361E6_s ]", + // *Moon rotation angular velocity - Calculation from Prot + "ωrot☽", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt☽;1_r/s);XPON(UVAL(Ⓡωrot☽*(2*Ⓒπ*1_r)/ⒸProt☽))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt☽))-2)' " + " 'CONVERT(ROUND(Ⓡωrot☽*(2*Ⓒπ*1_r)/ⒸProt☽;-2);1_r/s)' " + " 'ⓇProt☽' ]", // *Moon axial tilt - Measurement [22] "ϵ☽", "[ 1.5424_° " " 0.0001_° " @@ -1513,6 +1591,11 @@ static const cstring basic_constants[] = " 0.00000000091E13_m³/s² " " 'ROUND(ⓈGM♂/ⒸGM♂;-2)' " " 4.283E13_m³/s² ]", + // *Mars mass - Calculation from GM and G + "M♂", "[ 'ROUND(CONVERT(ⒸGM♂/ⒸG;1_kg);XPON(UVAL(ⒸGM♂/ⒸG·ⓇG))-XPON(UVAL(ⒸGM♂/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM♂*ⒸM♂);-2);1_kg)' " + " 'ⓇG' " + " 6.417E23_kg ]", // *Mars equatorial radius - Measurement [22] "Req♂", "[ 3396.2_km " " 0.1_km " @@ -1546,6 +1629,10 @@ static const cstring basic_constants[] = " 0.1_s " " 'ROUND(ⓈProt♂/ⒸProt♂;-2)' " " 8.864E4_s ]", + // *Mars rotation angular velocity - Calculation from Prot + "ωrot♂", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt♂;1_r/s);XPON(UVAL(Ⓡωrot♂*(2*Ⓒπ*1_r)/ⒸProt♂))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt♂))-2)' " + " 'CONVERT(ROUND(Ⓡωrot♂*(2*Ⓒπ*1_r)/ⒸProt♂;-2);1_r/s)' " + " 'ⓇProt♂' ]", // *Mars axial tilt - Measurement [22] "ϵ♂", "[ 25.19_° " " 0.01_° " @@ -1586,6 +1673,11 @@ static const cstring basic_constants[] = "GM♃", "[ 1.26686534E17_m³/s² " " 0_m³/s² " " 0 ]", + // *Jupiter mass - Calculation from GM and G + "M♃", "[ 'ROUND(CONVERT(ⒸGM♃/ⒸG;1_kg);XPON(UVAL(ⒸGM♃/ⒸG·ⓇG))-XPON(UVAL(ⒸGM♃/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM♃*ⒸM♃);-2);1_kg)' " + " 'ⓇG' " + " 1.898E27_kg ]", // *Jupiter equatorial radius - Exact nominal value [3] "Req♃", "[ 71492_km " " 0_km " @@ -1595,7 +1687,7 @@ static const cstring basic_constants[] = " 0_km " " 0 ]", // *Jupiter oblateness - Calculation from nominal value [3] - "f♃", "[ 'ROUND(1-ⒸRp♃/ⒸReq♃;XPON(UVAL(Ⓡf♃*(1-ⒸRp♃/ⒸReq♃)))-XPON(1-ⒸRp♃/ⒸReq♃)-2)' " + "f♃", "[ 'ROUND(1-ⒸRp♃/ⒸReq♃;-5)' " " 'ROUND(Ⓡf♃*Ⓒf♃;-2)' " " 'ⓇRp♃+ⓇReq♃' ]", // *Jupiter mean density - Calculation from nominal value [3] @@ -1616,6 +1708,10 @@ static const cstring basic_constants[] = "Prot♃", "[ 35730_s " " 1_s " " 'ROUND(ⓈProt♃/ⒸProt♃;-2)' ]", + // *Jupiter rotation angular velocity - Calculation from Prot + "ωrot♃", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt♃;1_r/s);XPON(UVAL(Ⓡωrot♃*(2*Ⓒπ*1_r)/ⒸProt♃))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt♃))-2)' " + " 'CONVERT(ROUND(Ⓡωrot♃*(2*Ⓒπ*1_r)/ⒸProt♃;-2);1_r/s)' " + " 'ⓇProt♃' ]", // *Jupiter axial tilt - Measurement [22] "ϵ♃", "[ 3.13_° " " 0.01_° " @@ -1657,6 +1753,11 @@ static const cstring basic_constants[] = " 0.00000000091E16_m³/s² " " 'ROUND(ⓈGM♄/ⒸGM♄;-2)' " " 3.794E16_m³/s² ]", + // *Saturn mass - Calculation from GM and G + "M♄", "[ 'ROUND(CONVERT(ⒸGM♄/ⒸG;1_kg);XPON(UVAL(ⒸGM♄/ⒸG·ⓇG))-XPON(UVAL(ⒸGM♄/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM♄*ⒸM♄);-2);1_kg)' " + " 'ⓇG' " + " 5.685E26_kg ]", // *Saturn equatorial radius - Measurement [22] "Req♄", "[ 60268_km " " 4_km " @@ -1690,6 +1791,10 @@ static const cstring basic_constants[] = " 50_s " " 'ROUND(ⓈProt♄/ⒸProt♄;-2)' " " 3.836E4_s ]", + // *Saturn rotation angular velocity - Calculation from Prot + "ωrot♄", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt♄;1_r/s);XPON(UVAL(Ⓡωrot♄*(2*Ⓒπ*1_r)/ⒸProt♄))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt♄))-2)' " + " 'CONVERT(ROUND(Ⓡωrot♄*(2*Ⓒπ*1_r)/ⒸProt♄;-2);1_r/s)' " + " 'ⓇProt♄' ]", // *Saturn axial tilt - Measurement [22] "ϵ♄", "[ 26.73_° " " 0.01_° " @@ -1731,6 +1836,11 @@ static const cstring basic_constants[] = " 0.0000040E15_m³/s² " " 'ROUND(ⓈGM⛢/ⒸGM⛢;-2)' " " 5.795E15_m³/s² ]", + // *Uranus mass - Calculation from GM and G + "M⛢", "[ 'ROUND(CONVERT(ⒸGM⛢/ⒸG;1_kg);XPON(UVAL(ⒸGM⛢/ⒸG·ⓇG))-XPON(UVAL(ⒸGM⛢/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM⛢*ⒸM⛢);-2);1_kg)' " + " 'ⓇG' " + " 8.682E25_kg ]", // *Uranus equatorial radius - Measurement [22] "Req⛢", "[ 25559_km " " 4_km " @@ -1764,6 +1874,10 @@ static const cstring basic_constants[] = " 10_s " " 'ROUND(ⓈProt⛢/ⒸProt⛢;-2)' " " 6.206E4_s ]", + // *Uranus rotation angular velocity - Calculation from Prot [retrograde] + "ωrot⛢", "[ 'ROUND(CONVERT(-(2*Ⓒπ*1_r)/ⒸProt⛢;1_r/s);XPON(UVAL(Ⓡωrot⛢*(2*Ⓒπ*1_r)/ⒸProt⛢))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt⛢))-2)' " + " 'CONVERT(ROUND(Ⓡωrot⛢*(2*Ⓒπ*1_r)/ⒸProt⛢;-2);1_r/s)' " + " 'ⓇProt⛢' ]", // *Uranus axial tilt - Measurement [22] "ϵ⛢", "[ 97.77_° " " 0.01_° " @@ -1805,6 +1919,11 @@ static const cstring basic_constants[] = " 0.00000010058E15_m³/s² " " 'ROUND(ⓈGM♆/ⒸGM♆;-2)' " " 6.837E15_m³/s² ]", + // *Neptune mass - Calculation from GM and G + "M♆", "[ 'ROUND(CONVERT(ⒸGM♆/ⒸG;1_kg);XPON(UVAL(ⒸGM♆/ⒸG·ⓇG))-XPON(UVAL(ⒸGM♆/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM♆*ⒸM♆);-2);1_kg)' " + " 'ⓇG' " + " 1.024E26_kg ]", // *Neptune equatorial radius - Measurement [22] "Req♆", "[ 24764_km " " 15_km " @@ -1837,6 +1956,10 @@ static const cstring basic_constants[] = "Prot♆", "[ 58000_s " " 100_s " " 'ROUND(ⓈProt♆/ⒸProt♆;-2)' ]", + // *Neptune rotation angular velocity - Calculation from Prot + "ωrot♆", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt♆;1_r/s);XPON(UVAL(Ⓡωrot♆*(2*Ⓒπ*1_r)/ⒸProt♆))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt♆))-2)' " + " 'CONVERT(ROUND(Ⓡωrot♆*(2*Ⓒπ*1_r)/ⒸProt♆;-2);1_r/s)' " + " 'ⓇProt♆' ]", // *Neptune axial tilt - Measurement [22] "ϵ♆", "[ 28.32_° " " 0.01_° " @@ -1877,6 +2000,11 @@ static const cstring basic_constants[] = "GM♇", "[ 9.755E11_m³/s² " " 0.005E11_m³/s² " " 'ROUND(ⓈGM♇/ⒸGM♇;-2)' ]", + // *Pluto mass - Calculation from GM and G + "M♇", "[ 'ROUND(CONVERT(ⒸGM♇/ⒸG;1_kg);XPON(UVAL(ⒸGM♇/ⒸG·ⓇG))-XPON(UVAL(ⒸGM♇/ⒸG))-2)' " + " 'CONVERT(ROUND(UBASE(ⓇM♇*ⒸM♇);-2);1_kg)' " + " 'ⓇG' " + " 1.462E22_kg ]", // *Pluto equatorial radius - Measurement [26] "Req♇", "[ 1188.3_km " " 1.6_km " @@ -1910,6 +2038,10 @@ static const cstring basic_constants[] = " 0.1_s " " 'ROUND(ⓈProt♇/ⒸProt♇;-2)' " " 5.519E5_s ]", + // *Pluto rotation angular velocity - Calculation from Prot [retrograde] + "ωrot♇", "[ 'ROUND(CONVERT(-(2*Ⓒπ*1_r)/ⒸProt♇;1_r/s);XPON(UVAL(Ⓡωrot♇*(2*Ⓒπ*1_r)/ⒸProt♇))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt♇))-2)' " + " 'CONVERT(ROUND(Ⓡωrot♇*(2*Ⓒπ*1_r)/ⒸProt♇;-2);1_r/s)' " + " 'ⓇProt♇' ]", // *Pluto axial tilt - Measurement [26] "ϵ♇", "[ 119.591_° " " 0.001_° " @@ -1992,6 +2124,10 @@ static const cstring basic_constants[] = " 864_s " " 'ROUND(ⓈProt☉/ⒸProt☉;-2)' " " 2.193E6_s ]", + // *Sun rotation angular velocity - Calculation from Prot + "ωrot☉", "[ 'ROUND(CONVERT((2*Ⓒπ*1_r)/ⒸProt☉;1_r/s);XPON(UVAL(Ⓡωrot☉*(2*Ⓒπ*1_r)/ⒸProt☉))-XPON(UVAL((2*Ⓒπ*1_r)/ⒸProt☉))-2)' " + " 'CONVERT(ROUND(Ⓡωrot☉*(2*Ⓒπ*1_r)/ⒸProt☉;-2);1_r/s)' " + " 'ⓇProt☉' ]", "Astronomy/Cosmology", nullptr,