1MODULE earthConstants_mod
2 ! MODULE earthConstants_mod (prefix='ec' category='8. Low-level utilities and constants')
3 !
4 !:Purpose: Define public constants related to the Earth.
5 !
6 ! Prefixes:
7 ! * ec_ (Earth constants), for miscellaneous values from diverse sources or
8 ! * ec_wgs_ (World Geodetic Syatem) when they are explicitly from WGS84 specification.
9 !
10 use mathPhysConstants_mod
11 !
12 ! The following constants should ultimately be taken from module
13 ! modgps02wgs84const OR module modgps06gravity. They have been placed here
14 ! as an intermediate step.
15 real(8), parameter :: ec_Omega = 7292000.D-11 ! Approximation, see for instance ec_wgs_Omega below.
16 real(8), parameter :: ec_rg = 9.80616000000000000000D+00 ! ...616 ? This is Lambert IGF at 45 lat (g45). The WMO standard for conversions is ...665.
17 real(8), parameter :: ec_ra = 6371229.00000000000000D+00 ! ECMWF topographical mean radius (Authalic radius, eg ec_wgs_R2,+average topography)
18 real(8), parameter :: ec_r1sa = 1.D0/ec_ra ! 1.56955588945241177170D-07 ! Modified to explicitly 1/ec_ra
19 !real(8), parameter :: RV = 4.61524993308387870310D+02 ! WV gas constant? Seems unused.
20 real(8), parameter :: ec_rayt = 6371220.00000000000000D+00 ! Another topographical mean (NOAA)
21 !
22 ! Further values through the code:
23 !
24 real(8), parameter :: ec_RDay = 86400.D0 ! Standard day
25 real(8), parameter :: ec_JYear = 365.25D0 ! Standard (Julian) year
26 real(8), parameter :: ec_SidYear = ec_JYear*ec_RDAY*2.D0*MPC_PI_R8/6.283076D0 ! Not really sidereal year, seems rather anomalistic year (odd).
27 real(8), parameter :: ec_SidDay = ec_RDAY/(1.D0+ec_RDAY/ec_SidYear) ! Approx sidereal day (wrt perihelion?), odd expression.
28 real(8), parameter :: ec_ROmega = 2.D0*MPC_PI_R8/ec_SidDay ! Angular rotation (approx., again)
29 ! ! ec_SidDay ~= 86164.0996
30 ! ! ec_ROmega ~= 7292115.D-11
31 ! ! First seven digits as ec_wgs_Omega
32
33 ! WGS (World Geodetic System, 1984) constants
34
35 ! Semimajor axis (a) (m) [*Defining constant*]
36 real(8), parameter :: ec_wgs_a = 6378137.0D0
37
38 ! Flattening (f) [*Defining constant*]
39 real(8), parameter :: ec_wgs_f = 1.D0 / 298.257223563D0
40
41 ! m = omega^2 a^2 b / GM
42 real(8), parameter :: ec_wgs_m = 0.00344978650684D0
43
44 ! Theoretical (Normal) Gravity Formula Constant:
45 real(8), parameter :: ec_wgs_TNGk = 0.00193185265241D0
46
47 ! First eccentricity squared:
48 real(8), parameter :: ec_wgs_e2 = 6.69437999014D-3
49
50 ! Theoretical (Normal) Gravity at the equator (m/s2):
51 real(8), parameter :: ec_wgs_GammaE = 9.7803253359D0
52
53 ! Earth's Gravitational Constant (GM) (m3/s2). [*Defining constant*]
54 ! This is the GM value with Earth's atmosphere included.
55 real(8), parameter :: ec_wgs_GM = 3986004.418D8
56
57 ! Angular velocity of the Earth (omega) (radians/s). [*Defining constant*]
58 ! Standard Earth, rotating with a constant angular velocity.
59 real(8), parameter :: ec_wgs_Omega = 7292115.D-11
60
61 ! ***********************************************************
62 ! Parameter values for special applications:
63 ! ***********************************************************
64
65 ! Earth's Gravitational Constant (GM_KEP) (m3/s2).
66 !
67 ! This is the old GM value with Earth's atmosphere included,
68 ! but still used for consistency in the transformations
69 ! instantaneous keplerian <-> cartesian state vector.
70 real(8), parameter :: ec_wgs_GM_KEP = 3986005.0D8
71
72 ! Earth's Atmosphere Gravitational Constant (GMA) (m3/s2).
73 ! This is the GM value of the Earth's atmosphere alone.
74 real(8), parameter :: ec_wgs_GMA = 3.5D8
75
76 ! Earth's Gravitational Constant (GMPrime) (m3/s2).
77 ! This is the GM value with Earth's atmosphere excluded.
78 real(8), parameter :: ec_wgs_GMPrime = 3986000.9D8
79
80 ! Angular velocity of the Earth (omegaPrime) (radians/s).
81 ! Standard Earth, rotating with a constant angular velocity (IAU, GRS67).
82 real(8), parameter :: ec_wgs_OmegaPrime = 7292115.1467D-11
83
84 ! Angular velocity of the Earth (omegaStar) (radians/s).
85 ! Standard Earth, in a precessing frame (TU: Julian centuries since J2000.0)
86 ! OmegaStar = OmegaStar0 + OmegaStar1 * TU
87 real(8), parameter :: ec_wgs_OmegaStar0 = 7292115.8553D-11
88 real(8), parameter :: ec_wgs_OmegaStar1 = 4.3D-15
89
90 ! ***********************************************************
91 ! Derived geometric constants:
92 ! ***********************************************************
93
94 ! Inverse flattening: 1/f = ec_wgs_1f
95 real(8), parameter :: ec_wgs_1f = 298.257223563D0
96
97 ! Second degree zonal coefficient:
98 real(8), parameter :: ec_wgs_C20 = -0.484166774985D-3
99
100 ! Semiminor axis:
101 real(8), parameter :: ec_wgs_b = 6356752.3142D0
102
103 ! First eccentricity:
104 real(8), parameter :: ec_wgs_e = 8.1819190842622D-2
105
106 ! Second eccentricity:
107 real(8), parameter :: ec_wgs_ePrime = 8.2094437949696D-2
108
109 ! Second eccentricity squared:
110 real(8), parameter :: ec_wgs_ePrime2 = 6.73949674228D-3
111
112 ! Linear eccentricity:
113 real(8), parameter :: ec_wgs_ELinear = 5.2185400842339D5
114
115 ! Polar radius of curvature:
116 real(8), parameter :: ec_wgs_c = 6399593.6258D0
117
118 ! Focal length:
119 real(8), parameter :: ec_wgs_EFocal = 521854.00897D0
120
121 ! Axis ratio:
122 real(8), parameter :: ec_wgs_ba = 0.996647189335D0
123
124 ! Mean radius of semiaxes:
125 real(8), parameter :: ec_wgs_R1 = 6371008.7714D0
126
127 ! Radius of sphere of equal area:
128 real(8), parameter :: ec_wgs_R2 = 6371007.1809D0
129
130 ! Radius of sphere of equal volume:
131 real(8), parameter :: ec_wgs_R3 = 6371000.7900D0
132
133 ! ***********************************************************
134 ! Derived physical constants:
135 ! ***********************************************************
136
137 ! Theoretical (Normal) Gravity potential of the ellipsoid (m2/s2):
138 real(8), parameter :: ec_wgs_U0 = 62636860.8497D0
139
140 ! Theoretical (Normal) Gravity at the pole (m/s2):
141 real(8), parameter :: ec_wgs_GammaP = 9.8321849378D0
142
143 ! Mean Value of the Theoretical (Normal) Gravity (m/s2):
144 real(8), parameter :: ec_wgs_GammaM = 9.7976432222D0
145
146 ! Mass of the Earth (Atmosphere Included):
147 real(8), parameter :: ec_wgs_Mass = 5.9733328D24
148
149 ! Dynamical Ellipticity H:
150 real(8), parameter :: ec_wgs_H = 1.D0 / 305.4413D0
151
152 ! Universal Constant of Gravitation (m3/kg*s2):
153 ! (value to be used only within WGS, for internal consistency)
154 real(8), parameter :: ec_wgs_G = 6.673D-11
155
156 ! Earth's principal moments of inertia (A, B, C) (kg m2):
157 real(8), parameter :: ec_wgs_PMI_A = 8.0091029D37
158 real(8), parameter :: ec_wgs_PMI_B = 8.0092559D37
159 real(8), parameter :: ec_wgs_PMI_C = 8.0354872D37
160
161end MODULE earthConstants_mod