# [Proj] Geodesic distances away from the ellipsoid

Gerald I. Evenden geraldi.evenden at gmail.com
Fri Mar 20 12:24:43 EST 2009

```On Friday 20 March 2009 12:56:53 pm Jay Hollingsworth wrote:
> 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....

I think the solution is fairly simple: just scale you path by the ratio:

R = approximate radius of the Earth over flights path
h = flight height

geodesic length * (R+h)/R

There is also the 3D geodesic at the NGS site which might apply and give a
better answer.  But I think the above would be good enough for most purposes.
Try both and see what happens.

PS: I did not convert the NGS 3D because it was hard-wired for WGS84 and the
description was confusing enough that I decided against bothering for the
time being.  Also, I could not get a mental image of what was happening when
there was a difference of altitude at the two end points.

> Jay Hollingsworth
>
> Seabed Portfolio Manager and
> Principal Data Architect
> Schlumberger Information Solutions
> phone: 713 513 8854 fax: 713 513 2093
>
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--
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist
```