A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Samuel L
Date: 2015 Nov 19, 04:59 -0800
'Am a bit confused here. I see that the Hc formula will provide a value of zero after adjusting LHA up or down to obtain and Hc of 0 and using the first example's declination and AP Lat the LHA of 119 works. One of the problems is I don't understand is this equation- cos(t) = -tan(Dec)·tan(Lat)
In using the first example below my calculator gives the result of 73d 55'.
Any idea what I'm doing wrong?
Is this correct? Use Pub. 249 (understanding the declination limits) to locate the declination and Ap. Lat. of the body. Find when Hc is zero (or close enough). Locate the LHA of the body. Add Ap longitude to the LHA to obtain GHA Aries. Subtract body SHA to obtain GHA Aries and then convert that to time. Does that sound right?
Re: Calculate star rise or set time?
From: Frank Reed
Date: 2015 Nov 18, 20:42 -0800
When you do what Gary described, you'll discover a big simplification. Given the assumption that the true altitude is zero, the equation simplifies as follows:
0 = sin(Dec)·sin(Lat) + cos(Dec)·cos(Lat)·cos(t),
cos(t) = -tan(Dec)·tan(Lat),
where t is the time of starrise or starset measured from the time of the star's transit, and of course Dec and Lat are the declination and latitude. This assumes a few things: you can work out the time of transit separately, you're not worried about a minute or two here and there, and (related to that) you're willing to ignore refraction right at the horizon which slightly delays setting times and advances rising times. Since you can't see stars right near the horizon in almost all cases, these are reasonable assumptions.
Here's a couple of examples:
I. Star's dec is 30° N, observer's latitude is 40° N. Mean time of star's transit is 10:30pm. By the calculation above, t is 119.0°. We divide that by 15 to get hours: 7.93h which is 7h 56m. Add to or subtract that from the transit time to get set and rise times: 6:26am and 2:34pm.
II. Star's dec is 35° S, latitude is 40° N. Star transits at 5 minutes past midnight: 00:05. By the calculation, t is 54.0°. Convert to hours and minutes: 3.6h or 3h 36m. Therefore the star sets at 03:41am, and it rises at 8:29pm.
Note that the times are nearly correct for any longitude so long as we recognize that this is LMT or Local Mean Time. In other words, if Capella rises at 10:30pm in Boston, it also rises at nearly 10:30pm in Seattle.