NewGamePhysics.Physics.GravityEarthWgsModel Class Reference

World Geodetic System 1984 (WGS 1984) model of earth's gravity g. Reference: Hofmann-Wellenhof, B., Moritz, H. (2006), Physical Geodesy (2nd ed.), Springer-Verlag Wien. More...

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Public Member Functions

double Calculate (double latitude, double height)
 Calculate the gravity outside the ellipsoid of the earth at a particular latitude in degrees and height above the surface in m. Obtained from the second order expansion of a small height.

Static Public Attributes

static double a = 6378137.0
 Semimajor axis of the ellipsoid in m.
static double GM = 3986004.418e8
 Geocentric gravitational constant of the earth including the atmosphere in m^3*s^-2.
static double omega = 7292115.0e-11
 Angular velocity of the earth in rad*s^-1.
static double b = 6356752.3142
 Semiminor axis of the ellipsoid in m.
static double E = 5.2185400842339e5
 Linear eccentricity in m.
static double c = 6399593.6258
 Polar radius of curvature in m.
static double e2 = 6.69437999014e-3
 First eccentricity squared.
static double ep2 = 6.73949674228e-3
 Second eccenctricity squared.
static double f = 1.0/298.257223563
 Flattening.
static double U0 = 62636851.7146
 Normal potential of the ellipsoid in m^2*s^-2;.
static double m = 0.00344978650684
 m = omega^2*a^2*b/GM
static double ya = 9.7803253359
 Normal gravity at the equator in m*s^-2.
static double yb = 9.8321849378
 Normal gravity at the pole in m*s^-2.
static double M = 5.9733328e24
 Mass of earth in kg.

Detailed Description

World Geodetic System 1984 (WGS 1984) model of earth's gravity g. Reference: Hofmann-Wellenhof, B., Moritz, H. (2006), Physical Geodesy (2nd ed.), Springer-Verlag Wien.

Definition at line 17 of file GravityEarthWgsModel.cs.

Member Function Documentation

double NewGamePhysics.Physics.GravityEarthWgsModel.Calculate ( double  latitude,
double  height 
)

Calculate the gravity outside the ellipsoid of the earth at a particular latitude in degrees and height above the surface in m. Obtained from the second order expansion of a small height.

Parameters:
latitude The latitude in degrees [-90,90]
height The height above the ellipsoid in meters [0,1000000].
Returns:
The gravity in m*s^-2.

Definition at line 100 of file GravityEarthWgsModel.cs.

00101         {
00102             if ((latitude < -90.0) || (latitude > 90.0))
00103             {
00104                 throw new ArgumentOutOfRangeException("latitude");
00105             }
00106 
00107             if ((height < 0.0) || (height > 1000000.0))
00108             {
00109                 throw new ArgumentOutOfRangeException("height");
00110             }
00111 
00112             // precalculations
00113             double phi = Math.PI * latitude / 180.0;
00114             double sl = Math.Sin(phi);
00115             double s2l = Math.Sin(2.0 * phi);
00116             double sl2 = sl * sl;
00117             double s2l2 = s2l * s2l;
00118 
00119             // calculate gravity flattening
00120             double fs = (yb - ya) / ya;
00121             double f4 = -0.5 * f * f + 2.5 * f * m;
00122 
00123             // calculate latitude dependent gravity
00124             double y = ya * (1.0 + fs * sl2 - 0.25 * f4 * s2l2);
00125 
00126             // calculate the height dependent gravity
00127             double yh = y * (1.0 - 2.0 / a * (1.0 + f + m - 2.0 * f * sl2) * height + 3.0 / (a * a) * (height * height));
00128 
00129             // result
00130             return yh;           
00131         }

Member Data Documentation

double NewGamePhysics.Physics.GravityEarthWgsModel.a = 6378137.0 [static]

Semimajor axis of the ellipsoid in m.

Definition at line 22 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.b = 6356752.3142 [static]

Semiminor axis of the ellipsoid in m.

Definition at line 38 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.c = 6399593.6258 [static]

Polar radius of curvature in m.

Definition at line 48 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.E = 5.2185400842339e5 [static]

Linear eccentricity in m.

Definition at line 43 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.e2 = 6.69437999014e-3 [static]

First eccentricity squared.

Definition at line 53 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.ep2 = 6.73949674228e-3 [static]

Second eccenctricity squared.

Definition at line 58 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.f = 1.0/298.257223563 [static]

Flattening.

Definition at line 63 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.GM = 3986004.418e8 [static]

Geocentric gravitational constant of the earth including the atmosphere in m^3*s^-2.

Definition at line 28 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.M = 5.9733328e24 [static]

Mass of earth in kg.

Definition at line 88 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.m = 0.00344978650684 [static]

m = omega^2*a^2*b/GM

Definition at line 73 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.omega = 7292115.0e-11 [static]

Angular velocity of the earth in rad*s^-1.

Definition at line 33 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.U0 = 62636851.7146 [static]

Normal potential of the ellipsoid in m^2*s^-2;.

Definition at line 68 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.ya = 9.7803253359 [static]

Normal gravity at the equator in m*s^-2.

Definition at line 78 of file GravityEarthWgsModel.cs.

double NewGamePhysics.Physics.GravityEarthWgsModel.yb = 9.8321849378 [static]

Normal gravity at the pole in m*s^-2.

Definition at line 83 of file GravityEarthWgsModel.cs.

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