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Using calculated altitudes
From: Bruce Stark
Date: 2002 Mar 25, 16:50 EST

```In a message dated 3/24/02 4:30:58 PM, george{at}HUXTABLE.U-NET.COM writes:

<< Well, I don't see that the change from Right-ascension to GHA made any
difference to the difficulty of working lunars from calculated (as opposed
to measured) altitudes. The altitude of the Moon (and therefore its
contribution to lunar parallax) changed just as fast, no matter how it was
tabulated in the almanac. Perhaps Bruce will explain this "old system" for
us. >>

Response from Bruce

Where the change to GHA makes a difference is in the calculated altitude.
Whichever system is used, you need the local hour angle of the moon to
calculate her altitude. Using our present system, an hour off in Greenwich
time throws that local hour angle off about fourteen and a half degrees. That
can have quite an effect on the altitude you get.

Using the old nautical astronomy, an hour off in Greenwich time throws the
local hour angle off about half a degree. That's only about one-thirtieth as
much as with the GHA system, but still quite a lot. It's one of the reasons
the old navigators preferred to measure their altitudes (at least the
altitude of the moon) if it was at all convenient to do so. The other reason
was that the Almanac gave the moon's RA and declination only for noon and
midnight. Proportioning was no fun.

In the old system the word "time" meant local apparent time. Navigators
"regulated" their watches by time sight, then allowed for change of longitude
since the last regulation. To get Greenwich time to enter the Almanac they
converted dead reckoning longitude to time and applied that to local time.

Since the time their watches kept was the local hour angle of the sun, a
fifteen degree error in dead reckoning longitude (and thus an hour in the
supposed Greenwich time) would have zero effect on the hour angle they used
to calculate the sun's altitude. The effect on declination could be no more
than 1'.

With our present system the error in declination could still be no more than
1'. But the error in local hour angle would not be zero. It would be fifteen
degrees.

As for Lewis and Clark, the captains had three different arificial horizons,
and made good use of them. But I don't believe they ever used them when
observing a lunar distance. In working their lunars I've nearly always
started with a longitude (and thus a Greenwich time) pretty near the truth.
The exception was the lunar they took at Bald-pated Prairie. I calculated the
altitudes with a Greenwich time that was wrong by about half an hour. A
repeat changed the moon's altitude slightly, but not the cleared distance.

Generally, though, it was thought wise to repeat the calculation if the
Greenwich time found differed more than four of five minutes from that used
in the first calculation.

Bruce

```
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