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The procedure I posted March 30, for calculating altitudes when both GMT and
longitude are wildly uncertain, works fine.

It's the same system navigators from James Cook to Joshua Slocum used to find
local hour angles. The only difference is it uses sidereal hour angle instead
of right ascension, so things are measured from east to west.

I've found it's less confusing if I first take only the GHAs of Aries and the
sun from the Almanac with the guessed-at GMT. That way, fewer numbers are
lying around to stumble over. Only after finding SHA meridian do I take the
other numbers from the Almanac, with the same guessed-at GMT of course.

The acid test for the method was the lunar Chuck Griffiths posted March 21.
Here both bodies are near prime vertical, so change in hour angle affects the
altitudes nearly 100%. What makes it exceptional is that the moon, Venus, and
the observer are all in nearly the same plane, so the distance is affected
nearly 100% by refraction and parallax. Total correction in altitude for
parallax and refraction was 45.'6, of which 44.'9 showed up in the difference
between the apparent and cleared distances. It would be hard to find a
situation where the distance could be more sensitive to changes in the GMT
used to calculate the altitudes. It couldn't happen except in low latitudes.

Since Chuck neglected to take an observation for local apparent time I did,
in this case, have to know his longitude and accurate GMT to get his LAT. I
did so by applying the equation of time to GMT to get GAT, and his longitude
to GAT to get LAT. LAT was March 18th, 18:36:35. That's 6:36:35 past noon.

I pretended Chuck had found his LAT by observation before the sun went down.
I also pretended he'd so egregiously screwed up his dead reckoning that it
put him seven and a half degrees, nearly 400 nautical miles at his latitude,
east of where he was. This made his estimated GMT half an hour less than the
true.

The first try got a GMT of 00:20:19, March 19th.

That's nearly half an hour from the GMT used to calculate the altitudes, so a
repeat was called for.

The second try got GMT of 00:18:33.

Obviously nothing much to be gained by going further. Half an hour off in the
GMT used to calculate the altitudes affected the result less than two
minutes. Two minutes off can be ignored. This may ease George's concerns
about the use of calculated altitudes for clearing distances.

Bruce

   

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