# Distancia del gran círculo más cambio de altitud

How do you exactly compute the distance traveled between two points at different altitudes on a spherical body? If the two points are at the same altitude it's a simple great-circle calculation. But what is the additional term to account for a steady climb or descent precisely? Say we're talking about a spaceplane that steadily climbs up to a great height over a great distance after taking off.

ilustración:
http://i.imgur.com/nAp1S.png

preguntado el 29 de julio de 12 a las 17:07

The best idea I have at the moment is to fit a second degree polynomial to the end points and a midpoint at half-way up in altitude. Then integrate to compute the length of the segment of the ellipse. I think this would be an approximation because the rate of climb/descent wouldn't be modeled quite right. -

What do you know about the climb and descent? -

The rate of climb/descent is constant over the entire segment length being considered. -

If the speed is also constant you'll end up with a triangle... -

## 1 Respuestas

The National Geodetic Survey (NGS) (a division of NOAA) has some information on this, and even sample Fortran code and working programs on their website and for a PC.

The program that you want is INVERS3D:
http://www.ngs.noaa.gov/PC_PROD/Inv_Fwd/

You will need to look through their code for specifics, but they calculate "ellipsoidal distance, the mark-to-mark distance, and the ellipsoid height difference" using lat/long/altitude.

Desde su página web:

INVERS3D

Program INVERS3D is the three dimensional version of program INVERSE, and is the tool for computing not just the geodetic azimuth and ellipsoidal distance, but also the mark-to-mark distance, the ellipsoid height difference, the DX, DY, DZ (differential X, Y, Z used to express GPS vectors), and the DN, DE, DU (differential North, East, Up using the FROM station as the origin of the NEU-coordinate system). The program requires geodetic coordinates as input, expressed as either: 1) latitude and longitude in degrees, minutes, and seconds or decimal degrees along with the ellipsoid heights for both stations, or 2) rectangular coordinates (X, Y, Z in the Conventional Terrestrial Reference System) for each station. The program works exclusively on the GRS80 ellipsoid and the units are meters. Both types of coordinates may be used in the same computation. The program reads input geodetic positions with the default hemispheres for latitude and longitude set at North and West.

Respondido 31 Jul 12, 21:07

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