NewGamePhysics.Physics.GravityEarthGrsModel Class Reference

Geodetic Reference System 1980 (GRS 1980). 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 = 3986005.0e8
 Geocentric gravitational constant of the earth including the atmosphere in m^3*s^-2.
static double J2 = 108263.0e-8
 Dynamic form factor of the earth excluding the tidal deformation.
static double omega = 7292115.0e-11
 Angular velocity of the earth in rad*s^-1.
static double b = 6356752.3141
 Semiminor axis of the ellipsoid in m.
static double E = 521854.0097
 Linear eccentricity in m.
static double c = 6399593.6259
 Polar radius of curvature in m.
static double e2 = 0.00669438002290
 First eccentricity squared.
static double ep2 = 0.00673949677548
 Second eccenctricity squared.
static double f = 1.0/298.257222101
 Flattening.
static double U0 = 62636860.850
 Normal potential of the ellipsoid in m^2*s^-2;.
static double J4 = -0.00000237091222
 Spherical harmonic coefficient 4.
static double J6 = 0.00000000608347
 Spherical harmonic coefficient 6.
static double J8 = -0.00000000001427
 Spherical harmonic coefficient 8.
static double m = 0.00344978600308
 m = omega^2*a^2*b/GM
static double ya = 9.7803267715
 Normal gravity at the equator in m*s^-2.
static double yb = 9.8321863685
 Normal gravity at the pole in m*s^-2.

Detailed Description

Geodetic Reference System 1980 (GRS 1980). 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 GravityEarthGrsModel.cs.

Member Function Documentation

double NewGamePhysics.Physics.GravityEarthGrsModel.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 116 of file GravityEarthGrsModel.cs.

00117         {
00118             if ((latitude < -90.0) || (latitude > 90.0))
00119             {
00120                 throw new ArgumentOutOfRangeException("latitude");
00121             }
00122 
00123             if ((height < 0.0) || (height > 1000000.0))
00124             {
00125                 throw new ArgumentOutOfRangeException("height");
00126             }
00127 
00128             // precalculations
00129             double phi = Math.PI * latitude / 180.0;
00130             double sl = Math.Sin(phi);
00131             double s2l = Math.Sin(2.0 * phi);
00132             double sl2 = sl * sl;
00133             double s2l2 = s2l * s2l;
00134 
00135             // calculate gravity flattening
00136             double fs = (yb - ya) / ya;
00137             double f4 = -0.5 * f * f + 2.5 * f * m;
00138 
00139             // calculate latitude dependent gravity
00140             double y = ya * (1.0 + fs * sl2 - 0.25 * f4 * s2l2);
00141 
00142             // calculate the height dependent gravity
00143             double yh = y * (1.0 - 2.0 / a * (1.0 + f + m - 2.0 * f * sl2) * height + 3.0 / (a * a) * (height * height));
00144 
00145             // result
00146             return yh;
00147         }

Member Data Documentation

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

Semimajor axis of the ellipsoid in m.

Definition at line 22 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.b = 6356752.3141 [static]

Semiminor axis of the ellipsoid in m.

Definition at line 44 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.c = 6399593.6259 [static]

Polar radius of curvature in m.

Definition at line 54 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.E = 521854.0097 [static]

Linear eccentricity in m.

Definition at line 49 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.e2 = 0.00669438002290 [static]

First eccentricity squared.

Definition at line 59 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.ep2 = 0.00673949677548 [static]

Second eccenctricity squared.

Definition at line 64 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.f = 1.0/298.257222101 [static]

Flattening.

Definition at line 69 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.GM = 3986005.0e8 [static]

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

Definition at line 28 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.J2 = 108263.0e-8 [static]

Dynamic form factor of the earth excluding the tidal deformation.

Definition at line 34 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.J4 = -0.00000237091222 [static]

Spherical harmonic coefficient 4.

Definition at line 79 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.J6 = 0.00000000608347 [static]

Spherical harmonic coefficient 6.

Definition at line 84 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.J8 = -0.00000000001427 [static]

Spherical harmonic coefficient 8.

Definition at line 89 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.m = 0.00344978600308 [static]

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

Definition at line 94 of file GravityEarthGrsModel.cs.

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

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

Definition at line 39 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.U0 = 62636860.850 [static]

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

Definition at line 74 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.ya = 9.7803267715 [static]

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

Definition at line 99 of file GravityEarthGrsModel.cs.

double NewGamePhysics.Physics.GravityEarthGrsModel.yb = 9.8321863685 [static]

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

Definition at line 104 of file GravityEarthGrsModel.cs.

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