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It is not possible to determine longitude from the distance
between Mars and Mercury with an ordinary sextant with
reasonable accuracy.

Here is a very crude estimate.
Mercury has period about 88 days.
And the maximum elongation from the Sun is about 20 degrees in the
average. Which means that Mercury moves less than 1/4 degree per day.
While the Moon moves roughly 12 degrees per day.
Thus determination of the longitude from the Mercury distance
to anything will be
about 50 times less accurate than from the Moon distance.

Definitely out of the limit of the Longitude prize:-)

I am not even mentioning the difficulty if seeing Mercury
through the sextant telescope.

Alex.

On Sat, 2 Feb 2013, Brad Morris wrote:

>
> Coming up this week, Mars and Mercury will be in close angular proximity to 
each other.  Mercury, of course, is one of the swiftest moving planets in the 
solar system.   Both Mercury and Mars are in the ecliptic plane.
>
> The question is basic.  Can we tell our longitude by the angular separation 
of the two bodies, similar to a lunar?  Can we do this with a sextant?  We 
might be able to tell our longitude using this method, but its below the 
measurement sensitivity of a sextant.
>
> Just asking!
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