Formula for true lunar node

[Shriramana Sharma]

Jean Meeus in his Astronomical Algorithms (second edition) page 344 gives  
some terms to be calculated to obtain the correction to the mean lunar node
to obtain the longitude of the true lunar node. However, he specifies that
there are only principal terms, indicating that there are other terms as
well. Meeus mentions that the full terms are available in:

M. Chapront-Touze and J. Chapront, Lunar Tables and Programs from 4000 BC to
AD 8000, Willmann-Bell 1991.

So if anyone has access to this book, perhaps via a library, and also the
kindness and time to help me out here, I would be much grateful.

Thanks.

--

Shriramana Sharma            dives into Sanskrit, swims in Linux and astronomy
http://samvit.org            In India, today is CCE +2006-Mar-31, W13-Fri
Sun in:   Miina              Season:   Vasanta
Moon in:  Ashvinii           Tithi:    Chaitra Shukla Dvitiiyaa

[Tom Peters-2]

Op 31-mrt-2006, om 4:28 heeft Shriramana Sharma het volgende geschreven:

> Jean Meeus in his Astronomical Algorithms (second edition) page 344  
> gives
> some terms to be calculated to obtain the correction to the mean  
> lunar node
> to obtain the longitude of the true lunar node. However, he  
> specifies that
> there are only principal terms, indicating that there are other  
> terms as
> well. Meeus mentions that the full terms are available in:
>
> M. Chapront-Touze and J. Chapront, Lunar Tables and Programs from  
> 4000 BC to
> AD 8000, Willmann-Bell 1991.
>
> So if anyone has access to this book, perhaps via a library, and  
> also the
> kindness and time to help me out here, I would be much grateful.

I do have that book.
There are several ways to represent ephemerides.  One is to develop  
series for the positions and velocities in 3 spatial coordinates.  
Another is to develop series that will give six independent  
"osculating" orbital elements valid for a specific moment in time:  
the position at that instant can then be computed from the orbital  
elements using Kepler's formulae.

So for the longitude of the ascending lunar node on the mean ecliptic  
of the date (their p.27 and p.82):
Omega = 125.0446 - 1934.13618*t + 20.76210E-4*t**2 +2.139E-6*t**3  
-1.650E-8*t**4 +
        -1.4979*sin( 49.1562 -75869.8120*t +35.458E-4*t**2 +4.231E-6*t**3  
-2.001E-8*t**4) [2D-2F]
        -0.1500*sin(357.5291 +35999.0503*t -1.536E-4*t**2 +0.041E-6*t**3 ) [l']
        -0.1226*sin( ... ) [2D]
        +0.1176*sin( ... ) [2F]
        etc.

(all angles in decimal degrees)
        HTH,
--
        Tom Peters

[Shriramana Sharma]

Tuesday, 04 April 2006 04:40 samaye, Tom Peters alekhiit:

> So for the longitude of the ascending lunar node on the mean ecliptic
> of the date (their p.27 and p.82):

What is "their p 27 and p 82"?

Can you please send me a scan of those pages -- I will not trouble you to type
the full series in, but if you can send me a scan of the full formula for the
osculating lunar node, and the pages that describe it and its implementation,
I would be most grateful! Size of the scanned file is not an issue. I have
unlimited download credit.

Thanks, Tom, and hoping you can respond positively...

--

Shriramana Sharma            dives into Sanskrit, swims in Linux and astronomy
http://samvit.org            In India, today is CCE +2006-Apr-05, W14-Wed
Sun in:   Miina              Season:   Vasanta
Moon in:  Aardraa            Tithi:    Chaitra Shukla Ashtamii

[Tom Peters-2]

Op 5-apr-2006, om 7:10 heeft Shriramana Sharma het volgende geschreven:

> Tuesday, 04 April 2006 04:40 samaye, Tom Peters alekhiit:
>
>> So for the longitude of the ascending lunar node on the mean ecliptic
>> of the date (their p.27 and p.82):
>
> What is "their p 27 and p 82"?
>
> Can you please send me a scan of those pages -- I will not trouble  
> you to type
> the full series in, but if you can send me a scan of the full  
> formula for the
> osculating lunar node, and the pages that describe it and its  
> implementation,
> I would be most grateful! Size of the scanned file is not an issue.  
> I have
> unlimited download credit.
>
> Thanks, Tom, and hoping you can respond positively...

I can't get my PC get to recognise the scanner.  I can make a few  
photocopies and send them to you by snail mail, if you send me your  
post address.

--
        Tom Peters

[Shriramana Sharma]

Thursday, 06 April 2006 23:25 samaye, Tom Peters alekhiit:

> I can't get my PC get to recognise the scanner.  I can make a few  
> photocopies and send them to you by snail mail, if you send me your  
> post address.

Tom, thanks for the offer. I'll get back to you on this!

--

Shriramana Sharma            dives into Sanskrit, swims in Linux and astronomy
http://samvit.org            In India, today is CCE +2006-Apr-07, W14-Fri
Sun in:   Miina              Season:   Vasanta
Moon in:  Pushya             Tithi:    Chaitra Shukla Navamii

[Shriramana Sharma]

Thursday, 06 April 2006 23:25 samaye, Tom Peters alekhiit:

> I can't get my PC get to recognise the scanner.  I can make a few  
> photocopies and send them to you by snail mail, if you send me your  
> post address.

Are you sure? I hope it will not cost you too much. If it is not too costly, I
would very much indeed appreciate the help!

My postal address is:

Shriramana Sharma
Flat No 7, Old Door No 15,
Sai Kanthi Apartments,
Third Main Road,
R.A.Puram, Chennai - 600028
Tamil Nadu, INDIA.

--

Shriramana Sharma            dives into Sanskrit, swims in Linux and astronomy
http://samvit.org            In India, today is CCE +2006-Apr-08, W14-Sat
Sun in:   Miina              Season:   Vasanta
Moon in:  Aashreshaa         Tithi:    Chaitra Shukla Ekaadashii

[scott colmes]

So, did you get the answer? Did it help?

>From: Shriramana Sharma <jamadagni@...>
>Reply-To: East Carolina University Calendar discussion List              
><CALNDR-L@...>
>To: CALNDR-L@...
>Subject: Re: Formula for true lunar node
>Date: Sat, 8 Apr 2006 21:38:29 +0530
>
>Thursday, 06 April 2006 23:25 samaye, Tom Peters alekhiit:
>
> > I can't get my PC get to recognise the scanner.  I can make a few  
> > photocopies and send them to you by snail mail, if you send me your  
> > post address.
>
>Are you sure? I hope it will not cost you too much. If it is not too
>costly, I
>would very much indeed appreciate the help!
>
>My postal address is:
>
>Shriramana Sharma
>Flat No 7, Old Door No 15,
>Sai Kanthi Apartments,
>Third Main Road,
>R.A.Puram, Chennai - 600028
>Tamil Nadu, INDIA.
>
>--
>
>Shriramana Sharma            dives into Sanskrit, swims in Linux and
>astronomy
>http://samvit.org            In India, today is CCE +2006-Apr-08, W14-Sat
>Sun in:   Miina              Season:   Vasanta
>Moon in:  Aashreshaa         Tithi:    Chaitra Shukla Ekaadashii

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[scott colmes]

Tom Peters and Shriramana Sharma, please discount my previous mail on this
thread  if you saw, it was something else mis-sent to the list address.

>From: Shriramana Sharma <jamadagni@...>
>Reply-To: East Carolina University Calendar discussion List              
><CALNDR-L@...>
>To: CALNDR-L@...
>Subject: Re: Formula for true lunar node
>Date: Sat, 8 Apr 2006 21:38:29 +0530
>
>Thursday, 06 April 2006 23:25 samaye, Tom Peters alekhiit:
>
> > I can't get my PC get to recognise the scanner.  I can make a few  
> > photocopies and send them to you by snail mail, if you send me your  
> > post address.
>
>Are you sure? I hope it will not cost you too much. If it is not too
>costly, I
>would very much indeed appreciate the help!
>
>My postal address is:
>
>Shriramana Sharma
>Flat No 7, Old Door No 15,
>Sai Kanthi Apartments,
>Third Main Road,
>R.A.Puram, Chennai - 600028
>Tamil Nadu, INDIA.
>
>--
>
>Shriramana Sharma            dives into Sanskrit, swims in Linux and
>astronomy
>http://samvit.org            In India, today is CCE +2006-Apr-08, W14-Sat
>Sun in:   Miina              Season:   Vasanta
>Moon in:  Aashreshaa         Tithi:    Chaitra Shukla Ekaadashii

_________________________________________________________________
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[Shahid Qureshi]

I am also working on the Chapront-Touze Formulae. It is basically time series representation both in theory and in tables. One would have to make a computer program to implement it.

[bhanuparis]

Hello,

I am interested in this formula too.
Do you have this coded or do you have in electronically,

will it be possible to send me a copy.

Thank you for your help
Bhanu

Tom Peters-2 wrote:

Op 5-apr-2006, om 7:10 heeft Shriramana Sharma het volgende geschreven:

> Tuesday, 04 April 2006 04:40 samaye, Tom Peters alekhiit:
>
>> So for the longitude of the ascending lunar node on the mean ecliptic
>> of the date (their p.27 and p.82):
>
> What is "their p 27 and p 82"?
>
> Can you please send me a scan of those pages -- I will not trouble  
> you to type
> the full series in, but if you can send me a scan of the full  
> formula for the
> osculating lunar node, and the pages that describe it and its  
> implementation,
> I would be most grateful! Size of the scanned file is not an issue.  
> I have
> unlimited download credit.
>
> Thanks, Tom, and hoping you can respond positively...

I can't get my PC get to recognise the scanner.  I can make a few  
photocopies and send them to you by snail mail, if you send me your  
post address.

--
        Tom Peters

[Tom Peters-6]

Op 23-nov-2008, om 7:07 heeft bhanuparis het volgende geschreven:

> Hello,
>
> I am interested in this formula too.
> Do you have this coded or do you have in electronically,
>
> will it be possible to send me a copy.

That is from an old thread!  It referred to Lunar Tables and Programs  
by the Chapronts.  You can buy their book from Willmann Bell.  In my  
first response I gave the main terms down to 1/10th of a degree:

"
So for the longitude of the ascending lunar node on the mean ecliptic  
of the date (their p.27 and p.82):
Omega = 125.0446 - 1934.13618*t + 20.76210E-4*t**2 +2.139E-6*t**3  
-1.650E-8*t**4 +
        -1.4979*sin( 49.1562 -75869.8120*t +35.458E-4*t**2 +4.231E-6*t**3  
-2.001E-8*t**4) [2D-2F]
        -0.1500*sin(357.5291 +35999.0503*t -1.536E-4*t**2 +0.041E-6*t**3 ) [l']
        -0.1226*sin( ... ) [2D]
        +0.1176*sin( ... ) [2F]
"

More accurate expressions for the main arguments you will find in  
their 2002 paper in Astronomy and Astrophysics:
http://www.aanda.org/index.php?
option=article&access=standard&Itemid=129&url=/articles/aa/abs/
2002/20/aa2201/aa2201.html

HTH,
--
Tom Peters