Precession & Nutation

[Mike1956]

Trying to sort this out in my mind.

Studying Celestial from a little book that uses the Nautical Almanac and AP3270 for its examples.

When I realised the Earth is wobbling about all over the place it became clear this wobble would need to be considered for all celestial navigation either by factoring in the wobble when we work out the GP of the HB.

OR

Adjusting the resulting LOP or Fix

OR

a mixture of the two

I made the following ASSUMPTIONS

For Sun, Moon & Planets all is taken care of in the Ephemerides.

For Polaris I see there is a Polaris table in the Nautical Almanac

For star sights I see there is a final correction to be applied in AP3270 Vol 1 Table 5 either to the final fix or to any LOP of a star if it is to be used in conjunction with any LOP not derived from a star eg Planet, Moon or Polaris

If any of the above is rubbish I will be pleased to be corrected but now to the bit I do not understand

I ASSUME again that the Polaris tables in the NA and the final correction for stars in AP3270 Vol1 Table 5 perform the same correction ie for Precession and Nutation but it is the entering arguments that are confusing me

For Polaris the entering argument LHA, Latitude and Month

For Table 5 the entering argument is Year. LHA Aries & Latitude

I am wondering why one of the entering arguments is for Month and one for Year.

I accept "they just are" but I would like to understand why

Thanks

Mike

[Kelkara]

Mike,

Everything you know about where the sun, moon, stars, and planets are comes from the nautical almanac. Astronomers are well aware of the effects of the earth's precession etc, and so it will be built into the tables. The ephemeris for the stars is that of Aries.

From your previous thread, you should understand that the stars won't move relative to each other due to minor variations in the earth's orbit, but Aries will move relative to the stars.

For the position of the stars you have the value for the GHA of Aries in the first column of the almanac, and you have the SHA and Dec of the star in the sixth column. If you look at the SHA and Dec for a star on Jan-1st, and compare it to the SHA and Dec on Dec-31 one year later, you will see that it has moved by about one minute of arc ... That is the effect of precession (and other changes in earth's rotation) built into the tables for the stars.

Hope that helps.

Your celestial nav is now about as good as mine, since I never actually spent time putting it into practise. I wasn't taught using AP3270, so I can't help you with that.

[Mike1956]

Thank you Kelkara,

When I posted I realised in all probability I would not be able to understand the answer to my querie. However you have mentioned something that I have not considered, namely that precession & nutation will be included in the ephemerides for Aries which in turn effects the GP of the star.

I think in future I should try and stick to learning the application than trying to comprehend the compilation of the tables

Thanks

Mike

[Kelkara]

The precession and nutation are not actually included in the Ephemeris for Aries since it will be different for each star, but in the change in SHA and Dec (position of star relative to Aries) for the stars throughout the year - look at how the column labled "Stars" in the NA changes very slowly through the year - that is the precession and nutation in the tables.

But I think AP3270 is the same as Ho249 (Which was part of the course I did), like I said I'm super rusty on the details, but I think this method ignores this change during calculation of the GP, and calculates plotting parameters for stars directly from Aries (without using the SHA and Dec of the star) - which is why they add tables for the precession and nutation correction to the LOP afterwards (and because it is such a small correction, using the year is accurate enough).

Other methods will apply the SHA and Dec of the star from the NA into the calculation of the GP, and then the correction for nutation and precession is already built in, so not needed for the LOP.

So it depends on the methods by which the calculations have been simplified into tables as to when and how corrections like this are applied (or ignored) - and how calculations are tuned into tables isn't always explained to us in the books.


To try and answer your question about Polaris...

Tables like the Polaris table in the nautical almanac are designed to simplify the trigonometric calculations into a few additions and subtractions. So the question is: why is the month an important part of that calculation. I have never seen this calculation fully explained, so I might be wrong on this ...

but I think that the month is important, because what this table does is use the LHA of Aries as an input and not the LHA of Polaris, which is what you really want, and there will be a correction depending on the time of year because the ecliptic and the equator are not parallel. Using just the month is clearly considered accurate enough not to have to use a precision of day/hour/minute/second.

But basically this is just a black-box calculation that the boffins have turned into simple tables to make it easy for you - there isn't really any physical meaning to the values a0, a1 and a2. But what is important is that the variables that affect the result are the LHA of Aries, your latitude and the time of year. Variations for precession through the year are I think ignored because the effect is less than 0.1' which is as precise as the NA goes.

You will notice that the correction for Polaris in Ho249 (AP3270) is just a single value Q, and completely ignores the effect of both latitude and month because they are very small corrections, since these tables were designed to be even simpler at the cost of a little accuracy.

I'm prepared for an expert come join in and correct me if I've got it a bit wrong, but it's good that you've got me thinking about this again.

[Mike1956]

Thanks Kelkara,

You dont sound TOO rusty to me!

You will understand the reason I indicated which publications my little book is using for examples is because I anticipated as you have confirmed different methods/tables will deal with the corrections differently.

Thanks for your informative post, I will attempt to absorb it over the next day or so.

Mike

[Kelkara]

Originally Posted by Mike1956

Thanks Kelkara,

You dont sound TOO rusty to me!

You're welcome Mike. I did have to get the books off the shelf to remind myself what the tables look like. Like I said I'm not an expert ... just someone who took a course that went through all the theory. My practical celestial nav experience has been limited to a few practise sights on land without a proper horizon, and a couple of noon-sights on the one "offshore passage" that I have done.

There are some folk on here who really do know what they're doing - hopefully they will correct me if I'm wrong.

good luck.

[Adelie]

If you want the real experts to weigh in join NavList and post the question there: http://www.fer3.com/arc/

[double u]

why would precession & nutation be different for each star???

[Kelkara]

Originally Posted by double u

why would precession & nutation be different for each star???

It isn't different for each star if you think of it as a fixed rotation based on the movement of Aries. If the movement of Aries were to be parallel to the Celestial equator the correction would be a simple change in the SHA of each star with no change in Dec. But since the movement of Aries is not constrained to be along the equator both the SHA and Dec will change, and an artefact of the coordinate system is that the change in SHA and Dec will be different for each star, even though it is the same rotation for all stars.

[double u]

what I find here in my tattered "selected stars" from the 90ies: correction for precession & nutation: given for every 30° of LHA aries & 0, 20, 40, 50, 60, 70 & 80° of Lat: distance & direction the LOP or the fix has to be moved, the same for all stars...
what do I get wrong?

[Kelkara]

Originally Posted by double u

what do I get wrong?

What you got wrong was misunderstanding what I wrote. I said that you couldn't apply a uniform correction to the ephemeris of Aries to get the correction for the ephemeris of a star. I did not say that the correction for the LOP would be different for each star.

As an example using my(2011) nautical almanac.

Between Jan-1 and Dec-31:
Regulus has moved 0.7' in SHA and DEcreased 0.3' in Dec
but in the other side of the sky:
Alpheratz has moved a very similar 0.8' in SHA, but INcreased 0.4' in Dec

These two corrections are different.

But, if you plot this for all the stars in the northern hemisphere (extrapolated for 200 years, so that the difference is visible - red point=1/1/2011, blue point=1/1/2211) you can see that this is in fact the result of a simple rotation of the stars in the sky ... which is probably why the correction for the LOP is a simple offset for all stars (but I'm guessing at that, I really can't remember how that calculation is performed)

edit: ignore the N, S E and W on the plot that should be SHA from 0 to 360.

[double u]

I see! (While having done umpteen 100eds of starsights in my time, & pre_gps at that & in “dangerous waters“ too, all of them were done with “selected stars“, so this “precession & nutation detail“ never came up)
Well done & explained kelkara!

[PDA1]

Originally Posted by Mike1956

Trying to sort this out in my mind.

Studying Celestial from a little book that uses the Nautical Almanac and AP3270 for its examples.

When I realised the Earth is wobbling about all over the place it became clear this wobble would need to be considered for all celestial navigation either by factoring in the wobble when we work out the GP of the HB.

OR

Adjusting the resulting LOP or Fix

OR

a mixture of the two

I made the following ASSUMPTIONS

For Sun, Moon & Planets all is taken care of in the Ephemerides.

For Polaris I see there is a Polaris table in the Nautical Almanac

For star sights I see there is a final correction to be applied in AP3270 Vol 1 Table 5 either to the final fix or to any LOP of a star if it is to be used in conjunction with any LOP not derived from a star eg Planet, Moon or Polaris

If any of the above is rubbish I will be pleased to be corrected but now to the bit I do not understand

I ASSUME again that the Polaris tables in the NA and the final correction for stars in AP3270 Vol1 Table 5 perform the same correction ie for Precession and Nutation but it is the entering arguments that are confusing me

For Polaris the entering argument LHA, Latitude and Month

For Table 5 the entering argument is Year. LHA Aries & Latitude

I am wondering why one of the entering arguments is for Month and one for Year.

I accept "they just are" but I would like to understand why

Thanks

Mike

Mike,

This probably wont answer your question directly.

If you're trying to do a sight reduction using Polaris I assume you're doing it to determine latitude. Whether you carry out a star sight reduction for Polaris or use Polaris just to get latitude the result will still be an LOP plotted in the 090° direction. A more or less horizontal line.

Pub. No. 249 Vol. 1 (AP 3270 for UK) is fine if you're interested in performing a star sight reduction using selected stars but why not make it easy on yourself and use Polaris for Latitude? If just for latitude you only need Ho and LHA ♈ and The Air Almanac 2017 POLARIS(POLE STAR) TABLE, 2017 on page A157 or get it here;

https://thenauticalalmanac.com/Polar...%282017%29.pdf

Or you can use Pub. No. 249 Vol. 1 (epoch 2015- by Celestaire) has Table 6 Q correction found on page 353 which is equivalent to The Air Almanac's Polaris table. Table 6 is easy to find- it's the last page of Volume 1. Here-

https://www.thenauticalalmanac.com/P...No.%20249.html

I do understand precession and nutation and Table 5 but the amount of LOP adjustment isn't that much until around 2019 and even then it's not much. Of course, there's curiosity and enjoyment of "getting it just right" and understanding why you do need to adjust the LOP. However, keep in mind that your pencil width and accuracy in plotting a celestial LOP will introduce enough errors to negate the necessity of using Table 5.

You can get Pub. No. 249- Vol-1, 2, 3 (or any 10° portion here);

https://www.thenauticalalmanac.com/Pub.%20No.%20249.html

If you need sight reduction forms and methods, get them here;

https://www.thenauticalalmanac.com/Methods.html

As to your query relative to the month and year arguments I can only suggest that the declination of the stars change each month and year....even though it's very small.

Oh, we show our age by calling it Ho-249. In this wicked world there's got to be a Pub called "249".

PDA1