Gravity - Man Page

compute the earth's gravity field


Gravity [ -n name ] [ -d dir ] [ -N Nmax ] [ -M Mmax ] [ -G | -D | -A | -H ] [ -c lat h ] [ -w ] [ -p prec ] [ -v ] [ --comment-delimiter commentdelim ] [ --version | -h | --help ] [ --input-file infile | --input-string instring ] [ --line-separator linesep ] [ --output-file outfile ]


Gravity reads in positions on standard input and prints out the gravitational field on standard output.

The input line is of the form lat lon h.  lat and lon are the latitude and longitude expressed as decimal degrees or degrees, minutes, and seconds; for details on the allowed formats for latitude and longitude, see the GEOGRAPHIC COORDINATES section of GeoConvert(1).  h is the height above the ellipsoid in meters; this quantity is optional and defaults to 0.  Alternatively, the gravity field can be computed at various points on a circle of latitude (constant lat and h) via the -c option; in this case only the longitude should be given on the input lines.  The quantities printed out are governed by the -G (default), -D, -A, or -H options.

All the supported gravity models, except for grs80, use WGS84 as the reference ellipsoid a = 6378137 m, f = 1/298.257223563, omega = 7292115e-11 rad/s, and GM = 3986004.418e8 m^3/s^2.


-n name

use gravity field model name instead of the default egm96.  See “Models”.

-d dir

read gravity models from dir instead of the default.  See “Models”.

-N Nmax

limit the degree of the model to Nmax.

-M Mmax

limit the order of the model to Mmax.


compute the acceleration due to gravity (including the centrifugal acceleration due the the earth's rotation) g.  The output consists of gx gy gz (all in m/s^2), where the x, y, and z components are in easterly, northerly, and up directions, respectively. Usually gz is negative.


compute the gravity disturbance delta = g - gamma, where gamma is the “normal” gravity due to the reference ellipsoid .  The output consists of deltax deltay deltaz (all in mGal, 1 mGal = 10^-5 m/s^2), where the x, y, and z components are in easterly, northerly, and up directions, respectively.  Note that deltax = gx, because gammax = 0.


computes the gravitational anomaly.  The output consists of 3 items Dg01 xi eta, where Dg01 is in mGal (1 mGal = 10^-5 m/s^2) and xi and eta are in arcseconds.  The gravitational anomaly compares the gravitational field g at P with the normal gravity gamma at Q where the P is vertically above Q and the gravitational potential at P equals the normal potential at Q. Dg01 gives the difference in the magnitudes of these two vectors and xi and eta give the difference in their directions (as northerly and easterly components).  The calculation uses a spherical approximation to match the results of the NGA's synthesis programs.


compute the height of the geoid above the reference ellipsoid (in meters).  In this case, h should be zero.  The results accurately match the results of the NGA's synthesis programs.  GeoidEval(1) can compute geoid heights much more quickly by interpolating on a grid of precomputed results; however the results from GeoidEval(1) are only accurate to a few millimeters.

-c lat h

evaluate the field on a circle of latitude given by lat and h instead of reading these quantities from the input lines.  In this case, Gravity can calculate the field considerably more quickly.  If geoid heights are being computed (the -H option), then h must be zero.


toggle the longitude first flag (it starts off); if the flag is on, then on input and output, longitude precedes latitude (except that, on input, this can be overridden by a hemisphere designator, N, S, E, W).

-p prec

set the output precision to prec.  By default prec is 5 for acceleration due to gravity, 3 for the gravity disturbance and anomaly, and 4 for the geoid height.


print information about the gravity model on standard error before processing the input.

--comment-delimiter commentdelim

set the comment delimiter to commentdelim (e.g., “#” or “//”).  If set, the input lines will be scanned for this delimiter and, if found, the delimiter and the rest of the line will be removed prior to processing and subsequently appended to the output line (separated by a space).


print version and exit.


print usage, the default gravity path and name, and exit.


print full documentation and exit.

--input-file infile

read input from the file infile instead of from standard input; a file name of “-” stands for standard input.

--input-string instring

read input from the string instring instead of from standard input. All occurrences of the line separator character (default is a semicolon) in instring are converted to newlines before the reading begins.

--line-separator linesep

set the line separator character to linesep.  By default this is a semicolon.

--output-file outfile

write output to the file outfile instead of to standard output; a file name of “-” stands for standard output.


Gravity computes the gravity field using one of the following models

    egm84, earth gravity model 1984.  See
    egm96, earth gravity model 1996.  See
    egm2008, earth gravity model 2008.  See
    wgs84, world geodetic system 1984.  This returns the normal
      gravity for the WGS84 ellipsoid.
    grs80, geodetic reference system 1980.  This returns the normal
      gravity for the GRS80 ellipsoid.

These models approximate the gravitation field above the surface of the earth.  By default, the egm96 gravity model is used.  This may changed by setting the environment variable GEOGRAPHICLIB_GRAVITY_NAME or with the -n option.

The gravity models will be loaded from a directory specified at compile time.  This may changed by setting the environment variables GEOGRAPHICLIB_GRAVITY_PATH or GEOGRAPHICLIB_DATA, or with the -d option.  The -h option prints the default gravity path and name.  Use the -v option to ascertain the full path name of the data file.

Instructions for downloading and installing gravity models are available at <>.



Override the compile-time default gravity name of egm96.  The -h option reports the value of GEOGRAPHICLIB_GRAVITY_NAME, if defined, otherwise it reports the compile-time value.  If the -n name option is used, then name takes precedence.


Override the compile-time default gravity path.  This is typically /usr/local/share/GeographicLib/gravity on Unix-like systems and C:/ProgramData/GeographicLib/gravity on Windows systems.  The -h option reports the value of GEOGRAPHICLIB_GRAVITY_PATH, if defined, otherwise it reports the compile-time value.  If the -d dir option is used, then dir takes precedence.


Another way of overriding the compile-time default gravity path.  If it is set (and if GEOGRAPHICLIB_GRAVITY_PATH is not set), then $GEOGRAPHICLIB_DATA/gravity is used.


An illegal line of input will print an error message to standard output beginning with ERROR: and causes Gravity to return an exit code of 1.  However, an error does not cause Gravity to terminate; following lines will be converted.


The gravity field from EGM2008 at the top of Mount Everest

    echo 27:59:17N 86:55:32E 8820 | Gravity -n egm2008
    => -0.00001 0.00103 -9.76782

See Also

GeoConvert(1), GeoidEval(1), geographiclib-get-gravity(8).


Gravity was written by Charles Karney.


Gravity was added to GeographicLib, <>, in version 1.16.

Referenced By


2020-11-22 GeographicLib 1.51 GeographicLib Utilities