Author

Topic: meridian transit

John R

posted June 22, 2010 06:47 PM
Hi celestial navigation gurus,
I'm new to all this, but with my limited knowledge, I've been trying to deduce the meridian transit of the stars so as to easily deduce longitude a la noon sight, but at night. I believe when GHA Aries = Longitude  SHA of the star. Since time is distance we just deduce the longitude we need (Long=GHA Aries+SHA Star) and convert to hours:minutes:seconds. So here goes. Using the long term almanac, I try to obtain meridian passage for Acamar on July 1, 2010: GHA Aries for a 2 year: 278d 52.5' GHA Aries for a=2: 3.7' yields a GHA Aries of 278d 56.2'
SHA for Acamar on July 1, 200: 315d 25.8' SHA for Acamar on July 1, 2010: 0.573'*10 yields a SHA Acamar of 315d 20.7'
So Long = 278d+315d 56.2+20.7' = 234d 16.27'
Which converts to HH:MM:SS according to the Tables of GHA increments on page 63 as 15:34:31.
So would I be correct is staying Acamar will be at meridian transit on July 1, 2010 at 3:34:31pm?
Also, any place on the web I can check my future calculations?
Thanks in advance.
John R
From: Philadelphia


David Burch

posted June 22, 2010 08:53 PM
we need to know your longitude to predict the time a body will cross it.
then we can track this down, but frankly, the 2102D star finder is the easiest way to solve this type of problem... but it can be done numerically as well, of course.
From: Starpath, Seattle, WA


John R

posted June 23, 2010 04:28 AM
Hi again,
Thanks for the quick reply. I'm trying to solve for UTC. If I have the GMT meridian passage of a star, I can deduce my longitude from that.
I just found the following website that will verify these calculations:
http://norfolkastronomical.org/calculators/TransitTime.html
It looks like 15:34 is the Hour Angle, which, if positive, you subtract from 24 to obtain the time. i.e. 8:25am is the hour of Meridian Transit for Acamar on July 1, 2010 according to my calculations. If negative, just use the time given.
The above website gives an answer of 8:22am. Why the difference? Is there a solar day/sidereal day multiplication I should be doing? Or taking into effect the equation of time?
On a related note. I found Taylor's Modern Navigation on the web and he states: "subtract the Sidereal Time, which is the Right Ascension of the mean sun, from the star's Right Ascension.... This will give the mean time of the Star's Meridian Passage, sufficiently near for the practice of ordinary navigation." (p74)
He then gives an example for Fomalhaut on Jan 1, 1894. He subtracts the Right ascension of the mean sun (18h 44m 29s) from the Right ascension of the star (22h 51m 48s), applies the equation of time and comes up with the apparent time of star passing meridian (4h 3m 26s).
Really simple. Any idea how I could accomplish the same task given the GHAs, declinations, and SHAs as provided by Geoffrey Kolbe in the Long Term Almanac?
Thanks again.
John R.
From: Philadelphia


David Burch

posted June 23, 2010 08:41 AM
I apologize that i am not following your question.
If you want to know what time a star or any other body crosses your meridian, you need to know your longitude.
On the other hand, if you know the GMT (same as UTC) that any body crosses your meridian, then you can figure your longitude from that. Your longitude is the GHA of the body at the time you observed. This can be looked up in Kolbe tables between 2000 and 2050.
Can you please clarify which if either of these two cases you wish to do and present the actual problem at hand and we can address that.
From: Starpath, Seattle, WA


John R

posted June 25, 2010 04:38 AM
Hello,
One way to calculate longitude is to note the time of upper transit of a celestial object (i.e. the sun). If we have a watch set to UTC, and we know noon occurs at 12:02:30, but we get 17:02:30, we deduce we're at 75d W.
So a watch and the knowledge of upper transit of an object gives us our longitude.
My question is how to calculate the upper transit of a star on a given date? If I had a table with these times for all the navigation stars, I could follow a star as it approaches upper transit just like a noon sight, and with my UTC watch, I could deduce my longitude, no?
Like I said in my above post, I'm close to calculating the time of that meridian passage, but I might be off by a day  hence the 4 minute error. Or am I missing something else? Or something easier?
From: Philadelphia


David Burch

posted June 25, 2010 05:03 AM
procedure: measure the GMT of the meridian passage of a star.
use nautical almanac to find the GHA of Aries at the time of mer pass of the star
add to that the sha of the star, also in the nautical almanac
your lon = gha * = gha aries + sha *
From: Starpath, Seattle, WA


David Burch

posted June 25, 2010 05:31 AM
for analogy, in the sun example you gave, the better way to find your longitude would have been to look up the GHA of the sun at 17:02:30 GMT on the day you saw it cross your meridian at that time. That would have given a more accurate result.... it is only a good approximation to scale if from the equation of time as done in your example.
From: Starpath, Seattle, WA


David Burch

posted June 25, 2010 05:41 AM
put another way, if your goal is to calculate from first principles the stellar equivalent of the equation of time, then you would have to refer to a book like Meeus on astronomical principles...
or you can look these up as well in the nautical almanac. they are presented in a diagram of star mer pass times for various sha...
... but if you have an almanac, you can do what was outlined above, which is the right way to do it.
In short the goal in mind is still not clear to me. david
From: Starpath, Seattle, WA


John R

posted June 25, 2010 02:16 PM
Hi David,
Thanks so much for taking time to understand and answer my questions. You state "use nautical almanac to find the GHA of Aries at the time of mer pass of the star." To me it's not obvious that I can calculate the time of meridian passage of a star at Longitude 0 for a given day.
And, based on your responses so far, I'm not convinced that if I'm sailing to Bermuda on that day, I can observe a star's meridian passage, look up the Longitude 0 time, and with a quick glance at my UTC watch, know my longitude.
??
John R.
From: Philadelphia


David Burch

posted June 25, 2010 02:31 PM
Please state what date you care about, and what star you care about and we will show how to figure the time it crosses Lon=0°.
For your second point, please note we have attempted to answer your questions, but have not ever suggested this is a good method.
it is not very practical and therefore not part of the routine cel nav procedures. You must catch the star crossing due N or S right at twilight and this is pure luck.
we do cover this method in the Emergency Navigation book, as it might be doable when you do not have sight reduction tables, and if the star is low you can get a good measure with just a ruler for a sextant.
We also have an online course on emergency navigation.
From: Starpath, Seattle, WA


John R

posted June 26, 2010 09:32 AM
Hi David,
You're right. It may not be too useful, but the old navigators mention it (see Taylor's Modern Navigation for instance) so I was curious if I could calculate it with Kolbe's Long Term Almanac.
Hour Angle = GHA Aries + SHA *. Hour Angle is converted to arc minutes, then time minutes, then subtracted from 24 hours to arrive at the time of upper transit:
For July 1, 2010 & July 2, 2010:
Deneb 02:06:04, 02:02:07 Dubhe 16:28:34, 16:24:37 Kochab 20:14:57, 20:11:00 Schedar 06:05:22, 06:01:26
So if I was somewhere between Philadelphia (75W) and Bermuda (65W), at 20:30 after sunset, I might see Kochab approaching its upper transit. If I don't have time to catch it on its ascent, the night watch could check on Deneb around 02:30 or so.
Are my numbers accurate or off by a day?
Once again, thanks so much for your books and your time. I keep the Long Term Almanac and Emergency Navigation on my boat. Star watching was always a hobby for me. Now, as a sailor, I realize it can be practical as well.
John R.
From: Philadelphia


David Burch

posted June 26, 2010 10:24 AM
Very good. Let us pursue this a bit.
First an important point. (I am sure you are aware of this, but we may have readers who are not.)
In modern cel nav we do not have any term called "hour angle." So this should be avoided.
We have GHA and LHA only. To use any other terminology risks, even invites, confusion. Thus we would have phrases such as "the GHA of Aries is..." "the LHA of Deneb is..." "the GHA of Deneb is.." and so on. We must always be clear and precise in these phrases.
Furthermore, LHA and GHA ALWAYS apply to a specific time and date, so when that time is not given, we do not know at all what is meant by the terms and phrases.

I will try to answer the specific question posed, but must stress again, that this is not required at all for the task originally proposed, namely how to find lon from mer pass of a star. You do that just as explained earlier. Nothing more is needed and it is quite simple and very fast analysis.
To go beyond that is some how mixing up how cel nav might have been done long ago with some modern task at hand.
There is much we can learn from old books on navigation, but cel nav techniques in use before folks were accustomed to using GMT is not one of them. This is often a nightmare of unwinding apparent times (relative to LAN) with the actual time systems we use today. It can lead to very convoluted approaches to extremely simple problems.
With that said, i believe you are asking:
What is the GMT that the star Deneb crosses Lon = 0° on July 1, 2010.
Again, this is a perfectly fair question to ask our almanacs to tell us, but it is not needed for any application in modern celestial navigation.
We can look this up for you as a check.... and then explain simple ways to prove that you have it right.
 let me come back to this after i get to the office today where we have a copy of Kolbe's Long Term Almanac.
==============================
A related question that has a similar remote application is to ask what time does the planet Venus rise on a particular day at a particular DR position. This too is not needed for any routine cel nav application, but is interesting to know when it is happening on a clear night, as it will appear as a oneeyed ship sailing straight toward you as it rises and gets strikingly brighter in the process. To predict this and alert the helm is a nice touch from a caring navigator.
From: Starpath, Seattle, WA


David Burch

posted June 26, 2010 10:40 AM
I just recalled that Chapter 11 of the Emergency Navigation book discusses in great detail the use of mer pass of stars for lat. It lists all the candidates for doing this with low stars and the dates possible. It also gives the formula for finding lat from the height at mer pass of a star.
It does not do much with Lon this way, but the sight times are the same, you would just need sights before and after mer pass to get the time of the peak.... again, you will see from the data given there that there are not too many opportunities.
There are much more if you include higher sights, the book only uses low ones (2° to 12°) that can be measured without a sextant. The high ones would actually be better for longitude as you could measure the mid point of their path more accurately than you can for the low ones.
It is just like a noon sight with the sun — the very thing that makes the Lat accurate (peak height insensitive to time), makes the Lon inaccurate.
From: Starpath, Seattle, WA


David Burch

posted June 26, 2010 04:12 PM
I have added a note to our online course on how to find the mer pass time of a star, and will make it available here so you can see the process.
See how to predict mer pass of stars.
The answer for Deneb on july 1, 2010 is 02h 05m 43s. You can use that example to track down errors or approximations that might have entered your solution.
As noted in the article, however, i want to stress once again that you never need to do this. This process of predicting the mer pass time of a star at Greenwich is not needed for anything we would ever do in routine or emergency navigation.
The star finder is the easiest (non electronic) way to predict what stars and planets are in the sky and how they move and when they cross your meridian, and if you did then happen to do a mer pass sight of a star, then you could get your lat from it as explained in the Emergency Nav book and you could get an approximation to your lon from it by simply looking up the GHA of the star at your best guess of its time of mer pass.
I hope that resolves this topic. Thanks for bringing it up.
From: Starpath, Seattle, WA


John R

posted June 27, 2010 07:48 PM
Your "note" is very useful. Thanks for putting it together.
As David says, everything we've mentioned isn't necessary for navigation, but is true  and fun?  for astronomy. David's pdf uses the 2010 Nautical Almanac, for anyone else wondering how to calculate meridian transit using the Long Term Almanac, here's how to.
Deneb, July 1, 2010. Look for Deneb's July SHA and add 10* the annual correction: 49d 32.82' The GHA of Aries for 2 years + the a=2 increment of 3.7: 278d 56.2' Add together (subtract 360 if necessary): 327d 89.02' Convert to decimal: 328.4836 Subtract from 360: 31.5163 Divide by 15.0417: 2.0952 Convert to HH:MM:SS: 2h & 0.0952*60 min = 2 & 5.72 min = 2 & 5 & 0.72*60 sec = 02:05:43
Wonderful!
From: Philadelphia


