These Fortran and C libraries compute the Earth gravity with high order and degree. This paper describes the software implementation for higher order and degree geopotential and derivatives computation. It includes test and application cases.

Fortran source codes including example of utilization with a truncated EGM2008 model. The Fortran code uses the parameters of the geopotential model: Ae, GM, C(n,m), S(n,m) as local variables, which are in the calling parameters of the subroutine computing the geopotential. Besides C and S are two-dimensional arrays so care must be taken with the declaration of their sizes in the main program (recall that Fortran stores matrix columns-wise). We prefer to keep the two-dimensional array for the sake of readability of code. However, The user can modify (at his will) the program to store C(n,m) and S(n,m) as one-dimensional arrays (see C source-codes) and save some memory storage. The following Fortran-source codes together with test case are available:

• Download the Geopotential Fortran codes (zip file).
  
• Download the Geopotential Acceleration Fortran codes (zip file): Besides the geopotential acceleration, the subroutine "Leg_ForCol_Ac" can be modified to compute jointly the geopotential value, by supressing the comments character "!" related to variable "Omega", and including it in the calling parameters. Besides, if only the geopotential gradient in spherical coordinates is desired, it is explicit in the final lines of subroutine "Leg_ForCol_Ac" as "Vl, Vf, Vr" (Partial derivatives of geopotential wrt longitude, colatitude, radius), just before converting them to cartesian coordinates.

The Ansi-C source codes include an example of utilization with a truncated EGM2008 model. These codes use the parameters of the geopotential model Ae, GM, C(n,m), S(n,m) as global variables. Thus they weren't included in the calling parameters of the procedure that computes the geopotential, and must be loaded beforehand. Besides, C(n,m) and S(n,m) are loaded as one-dimensional arrays. Users should use the same strategy to load any other geopotential model, when using the C procedures. The following C-source codes together with test case are available:

• Download the Geopotential C codes
• Donwload the Geopotential Acceleration C codes: Besides the geopotential acceleration, the void procedure "leg_forcol_ac" can be modified to compute jointly the geopotential value, by supressing the comments character "//" related to variable "omega", or including it in the calling parameters if desired. If only the geopotential gradient in spherical coordinates is desired, it is explicit in the final lines of void procedure "leg_forcol_ac" as "vl, vf, vr" (Partial derivatives of geopotential wrt longitude, colatitude, radius), just before converting them to cartesian coordinates.

• The correction of original EGM 2008 values for time drift of harmonic coefficients (see IERS conventions 2010, TN36, Chapter 6) is up to the user.
• For test purposes, only a truncated (to order/degree 10) version of EGM 2008 ("EGM2008_ZeroTide_Truncated.dat") is provided together with source codes. The full (and heavy: more than 200MBytes) EGM 2008 or other models can be downloaded by the user at NGA.
• The original paper published by SBSR in 2013 was replaced here by a corrected version.
  
• Email me for suggestions and questions.