MakeGravGridPoint (Fortran)

Determine the three components of the gravity vector at a single point.

Usage

value = MakeGravGridPoint (cilm, lmax, gm, r0, r, lat, lon, omega, dealloc)

Parameters

value : output, real(dp), dimension (3)

Vector components (r, theta, phi) of the gravity at (r, lat, lon).

cilm : input, real(dp), dimension (2, lmax+1, lmax+1)

The real 4-pi normalized spherical harmonic coefficients of the gravitational potential. The coefficients C1lm and C2lm refer to the cosine (Clm) and sine (Slm) coefficients, respectively, with Clm=cilm(1,l+1,m+1) and Slm=cilm(2,l+1,m+1).

lmax : input, integer(int32)

The maximum spherical harmonic degree used in evaluating the function.

gm : input, real(dp)

The gravitational constant multiplied by the mass of the planet.

r0: input, real(dp)

The reference radius of the spherical harmonic coefficients.

r: input, real(dp)

The radius to evaluate the gravity field.

lat : input, real(dp)

The latitude of the point in degrees.

lon : input, real(dp)

The longitude of the point in degrees.

omega : optional, input, real(dp)

The angular rotation rate of the planet.

dealloc : input, optional, integer(int32), default = 0

0 (default) = Save variables used in the external Legendre function calls. (1) Deallocate this memory at the end of the funcion call.

Description

MakeGravGridPoint will compute the three components of the gravity vector (gravitational force + centrifugal force) at a single point. The input latitude and longitude are in degrees, and the output components of the gravity are in spherical coordinates (r, theta, phi). The gravitational potential is given by

V = GM/r Sum_{l=0}^lmax (r0/r)^l Sum_{m=-l}^l C_{lm} Y_{lm},

and the gravitational acceleration is

B = Grad V.

The coefficients are referenced to a radius r0, and the output accelerations are in m/s^2. To convert m/s^2 to mGals, multiply by 10^5. If the optional angular rotation rate omega is specified, the gravity vector will be calculated in a body-fixed rotating reference frame and will include the contribution of the centrifugal force.

See also

makegeoidgrid, makegravgradgriddh, normalgravity