Re: Haversines with Logarithms
From: Frank Reed
Date: 2020 Oct 20, 13:36 -0700
David C, you wrote:
"Remember that the time sight formula does not give LHA. It gives the meridian angle"
The so-called meridian angle is also known simply as "hour angle". That's what astronomers call it. And if you're working with this time sight approach, you don't need to know anything about the narrowly-defined "LHA" which is an element of late 20th century sight reduction methods. In short, you calculate HA, and then you have to make a decision, which is part of the sight-taking and analysis process, which I call the "lunch test". If you have had lunch, then the hour angle of the Sun is added onto 12:00:00. Otherwise you subtract the hour angle from 12:00:00. You never need so-called LHA. Just set that narrow bit of jargon aside. Or if you're working with the GHA of some body (Sun, star, whatever), you simply ask if that body is already past your meridian. If so then, the GHA (longitude) of the body must be past your longitude and the amount is equal to the hour angle in degrees. The hour angle calculated from the observed altitude is no more and no less than the difference in longitude between the observer and the subSun (or subStar) point. And the longitude of the subSun/subStar point is exactly identical to the GHA. GHA is longitude. Thus in west longitude, your longitude is the body's GHA minus the HA if the body has already gone past your meridian. Other cases follow easily. It really is just as easy as that.
"Before the introduction of the GHA almanac in the early 1950s the almanac gave RA and EOT. For one or two decades (1930/40s ??) the almnac gave instead factors R and E which were RA and EOT with +- 12 hours added. The GHA almanac makes things very easy."
I meant to mention this after an earlier message you wrote. You have a little problem here. You refer to "the" almanac. There was no such thing in the era you are trying to describe. There were a variety of almanacs both official and commercial. Indeed those R and E factors which you mention were utterly unknown to American navigators in this period. Most importantly The Nautical Almanac, was not a nautical almanac at all before 1958/60. Instead it was an astronomers' almanac --the volume which was finally renamed as "The Astronomical Almanac".