### A man with two watches #MarsWalk

So I have, I think, accurate coordinates for Viking 2 and Mars Science Laboratory, but the Terrestrial Planet Mileage Calculator and Google Earth calculate different values for the distance between the two: 3095.3 and 3055 km respectively. Can I replicate one or the other?

I found a C++ implementation of the Vincenty algorithm for distances on an ellipsoid toward the bottom of this page. Plugging in values for the equatorial and polar radii of Mars, 3396.2 and 3376.2 km respectively (from here) and the above coordinates, it gives me a distance of…

3074.6 km. Almost exactly the mean value of the TPMC and Google Earth values.

Great. Now I know even less than when I started.

But… if I plug in 3389.5 km (the volumetric mean radius) for both radii, I get 3094.8 km. Close to the TPMC value. Is TPMC using a spherical distance formula?

Why, yes. It is. I tried entering two points 90° apart on a meridian and on the equator into TPMC and I got the same distance for both.

Probing Google Earth’s behavior is harder, though, nor do I have a good way to check the correctness of the Vincenty algorithm code especially for a non Earth application. My feeling at this point is it’s probably more accurate than Google Earth… though up until now I felt the same way about TPMC, and that turns out to be wrong.

But for now that’s my official estimate:

Distance is (?) 3075 km

At least this is probably no more than about 20 km off.