# [Proj] Geodesic distances away from the ellipsoid

support.mn at elisanet.fi support.mn at elisanet.fi
Sat Mar 21 08:35:25 EST 2009

```Hello,

I think one method is to convert all coordinates to Cartesian
using Helmert's equations and forget the earth shape, since you
are more or less in the free space now... where the satellites rule.
The earth reference ellipsoid just adds complexity there.

Now you have vectors (x, y and z) and can calculate anything
using simple vector arithmetic.

A "laser line" distance is now very easy to calculate:

dist=sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

if your path is a set of 3D-curves, just calculate the perimeters
and add them together. This is more efficient especially for
space travellers (?)

regards: Janne.

----------------------------------------------------------

Jay Hollingsworth [jhollingsworth at houston.oilfield.slb.com] kirjoitti:
> At the risk of asking a dumb question, do any of the geodesic
> algorithms allow calculation of the geodesic distance if the path is
> not on the ellipsoid? Like in an airplane or satellite whose path
> could be assumed to be a constant height above the ellipsoid?
>
> Or do you have to define an ellipsoid matching the satellite orbit
> and use the normal equations on that ellipsoid? If so, how would you
> define an ellipsoid for a long airplane flight?
>
> I've poked around and nothing has jumped out at me. I assume
> aero-engineers guys figured this out long ago....
>
>
> Jay Hollingsworth
>
> Seabed Portfolio Manager and
> Principal Data Architect
> Schlumberger Information Solutions
> phone: 713 513 8854 fax: 713 513 2093
>
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```