Formula for converting Epoch 1950 RA/DEC to Epoch 2000

Could someone please post the formula for converting Epoch 1950 right
ascension and declination coordinates to Epoch 2000? Thanks in
advance.

-Paul W.
----------
Remove 'Z' to reply by email.

Paul Winalski wrote:
Could someone please post the formula for converting Epoch 1950 right
ascension and declination coordinates to Epoch 2000? Thanks in
advance.

It's fairly involved and not amenable to newsgroup posting. See low
precision precession model without aberration and nutation per:

Meeus, J. 1998. Astronomical Algorithms. 2nd ed.
Willmann-Bell. p. 132-133.

See also Duffett-Smith, P. 1988. Practical Astronomy with your
calculator. 3rd ed. Cambridge Univ. Press. p. 56.

Maybe others will have a link or short version. Contact me via email
and I will send you what code snippet I put together for Meeus.

- Canopus56

Paul Winalski wrote:
Could someone please post the formula for converting Epoch 1950 right
ascension and declination coordinates to Epoch 2000? Thanks in
advance.

Just multiply the proper motion by the number of years and add/subtract
it to/from the starting position. But, alas, I presume you really meant
Equinox, not Epoch, right?

In that case see the references already posted; it's more than just a
short formula.

--
Greg Crinklaw
Astronomical Software Developer
Cloudcroft, New Mexico, USA (33N, 106W, 2700m)

SkyTools: http://www.skyhound.com/cs.html
Observing: http://www.skyhound.com/sh/skyhound.html
Comets: http://www.skyhound.com/sh/comets.html

To reply have a physician remove your spleen

On Fri, 04 Nov 2005 22:22:07 GMT, Paul Winalski
wrote:

Could someone please post the formula for converting Epoch 1950 right
ascension and declination coordinates to Epoch 2000? Thanks in
advance.

It is painful to write formulas in pure ascii. Here is the C function I
use for this- you can probably pull what you need from it. This converts
from any date to any other; for 1950.0 to 2000.0 just set dDeltaYear to
50. Also, note that all the units are in degrees.


/************************************************** *
*
* Precess - precess an object (in place)
*
* input: dpRA - ptr to object RA in degrees
* dDec - ptr to object dec in degrees
* dFromJD - starting JD
* dToJD - ending JD
*
* return: none (precessed in place)
*
************************************************** */

void Precess(double *dpRA, double *dpDec, double dFromJD, double dToJD)
{
double dDeltaRA, dDeltaDec, dDeltaYear;
double dM = 2.2354759e-4;
double dN = 9.7156662e-5;

dDeltaYear = (dToJD - dFromJD) / 365.25;

*dpRA /= 57.29577951;
*dpDec /= 57.29577951; // convert to radians

dDeltaRA = dM + dN * sin(*dpRA) * tan(*dpDec);
dDeltaRA *= dDeltaYear;

dDeltaDec = dN * cos(*dpRA);
dDeltaDec *= dDeltaYear;

*dpRA = (*dpRA + dDeltaRA) * 57.29577951;
*dpDec = (*dpDec + dDeltaDec) * 57.29577951;

return;
}

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

"Chris L Peterson" wrote in message
...
On Fri, 04 Nov 2005 22:22:07 GMT, Paul Winalski
wrote:

Could someone please post the formula for converting Epoch 1950 right
ascension and declination coordinates to Epoch 2000? Thanks in
advance.

It is painful to write formulas in pure ascii. Here is the C function I
use for this- you can probably pull what you need from it. This converts
from any date to any other; for 1950.0 to 2000.0 just set dDeltaYear to
50. Also, note that all the units are in degrees.


/************************************************** *
*
* Precess - precess an object (in place)
*
* input: dpRA - ptr to object RA in degrees
* dDec - ptr to object dec in degrees
* dFromJD - starting JD
* dToJD - ending JD
*
* return: none (precessed in place)
*
************************************************** */

void Precess(double *dpRA, double *dpDec, double dFromJD, double dToJD)
{
double dDeltaRA, dDeltaDec, dDeltaYear;
double dM = 2.2354759e-4;
double dN = 9.7156662e-5;

dDeltaYear = (dToJD - dFromJD) / 365.25;

*dpRA /= 57.29577951;
*dpDec /= 57.29577951; // convert to radians

dDeltaRA = dM + dN * sin(*dpRA) * tan(*dpDec);
dDeltaRA *= dDeltaYear;

dDeltaDec = dN * cos(*dpRA);
dDeltaDec *= dDeltaYear;

*dpRA = (*dpRA + dDeltaRA) * 57.29577951;
*dpDec = (*dpDec + dDeltaDec) * 57.29577951;

return;
}

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

It has been awhile since I have seen any C code... Can anyone pass me a
pointer please.

-p

On Fri, 4 Nov 2005 17:51:58 -0700, "Pippen" wrote:

It has been awhile since I have seen any C code... Can anyone pass me a
pointer please.

*pointer

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

The formulae below are only approximations. dM and dN in the code,
usually called m and n in the literature, are instantaneous rates.
They're OK for short time intervals and for objects not too close to
the poles. Otherwise you'll have to use the high-octane stuff.

The _Astronomical Almanac_ has a few pages in section B ... tough
reading, but it's really the only way to go.

-- Bill Owen

Pippen wrote:
"Chris L Peterson" wrote in message
...

On Fri, 04 Nov 2005 22:22:07 GMT, Paul Winalski
wrote:


Could someone please post the formula for converting Epoch 1950 right
ascension and declination coordinates to Epoch 2000? Thanks in
advance.

It is painful to write formulas in pure ascii. Here is the C function I
use for this- you can probably pull what you need from it. This converts
from any date to any other; for 1950.0 to 2000.0 just set dDeltaYear to
50. Also, note that all the units are in degrees.


/************************************************** *
*
* Precess - precess an object (in place)
*
* input: dpRA - ptr to object RA in degrees
* dDec - ptr to object dec in degrees
* dFromJD - starting JD
* dToJD - ending JD
*
* return: none (precessed in place)
*
************************************************ ***/

void Precess(double *dpRA, double *dpDec, double dFromJD, double dToJD)
{
double dDeltaRA, dDeltaDec, dDeltaYear;
double dM = 2.2354759e-4;
double dN = 9.7156662e-5;

dDeltaYear = (dToJD - dFromJD) / 365.25;

*dpRA /= 57.29577951;
*dpDec /= 57.29577951; // convert to radians

dDeltaRA = dM + dN * sin(*dpRA) * tan(*dpDec);
dDeltaRA *= dDeltaYear;

dDeltaDec = dN * cos(*dpRA);
dDeltaDec *= dDeltaYear;

*dpRA = (*dpRA + dDeltaRA) * 57.29577951;
*dpDec = (*dpDec + dDeltaDec) * 57.29577951;

return;
}

________________________________________________ _

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com


It has been awhile since I have seen any C code... Can anyone pass me a
pointer please.

-p

Bill Owen wrote:
The formulae below are only approximations. dM and dN in the code,
usually called m and n in the literature, are instantaneous rates.
They're OK for short time intervals and for objects not too close to
the poles. Otherwise you'll have to use the high-octane stuff.

Yup. I borrowed Chris's code at first for precessing coordinates back
to 1875 (in order to identify which constellation the coordinates were
in), and encountered a few snags near the pole. Since I didn't need
the precision, just freedom from snags, I just wrote in a few boundary
conditions.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Chris L Peterson wrote:
snip
dDeltaRA = dM + dN * sin(*dpRA) * tan(*dpDec);
dDeltaRA *= dDeltaYear;

dDeltaDec = dN * cos(*dpRA);
dDeltaDec *= dDeltaYear;

*dpRA = (*dpRA + dDeltaRA) * 57.29577951;
*dpDec = (*dpDec + dDeltaDec) * 57.29577951;

To Paul,

Duffet-Smith's low precision formula to precess B1950 is -

a1 = a0 + (3.07327" + 1.33617" * sin(a0) * tan(d0) * N
d1 = d0 + (20.0426" * cos(a0) * N

a0,d0 - Starting B1950 RA, Dec
a1,d1 - Precessed coordinates
N - Number of years since 1950.0

Once precessed, add N years of proper motion in RA and declination.

This formula is valid only for B1950 coordinates. Other variations
apply for other major epochs. See Duffett-Smith at Sec. 34, p. 56-57.

In form, this appears similar to Chris's C code snippet. I have not
looked at the units to see if they convert to Chris's constants.

This method provides a low precision astrometric position of the star.
It does not include the effects of nutation, abberation and atmospheric
refraction.

Both Duffett-Smith and Meeus provide more rigorious methods. Meeus's,
for example, is based on Julian Days, that is the period between the
current Julian Day and the Julian Day on the old Besselian year. E.g.
-

B1950.0 = JDE 2433282.4235
J2000.0 = JDE 2451545.0000

Use of Julian Days instead of fractional years is the foundation of
more precise and rigorous alogrithms. Those methods are more difficult
to reduce and code. I have not implemented Duffett's low precision
method and do not have a code snippet for it. I have implemented a
variant of Meeus's moderate precision method.

Whatever method you decide to implement, you can check its accuracy
using the CDS Simbad web application at:

http://simbad.u-strasbg.fr/sim-fid.pl

You can put an astronomical object, like M57 or alf Per (Mirfak), in
the web applet. Options allow you to display the object's coordinates
in B1950 or J2000. For Mirfak, Simbad gives:

FK5 2000.0/2000.0 coordinates
03 24 19.37 +49 51 40.2

FK4 1950.0/1950.0 coordinates
03 20 44.44 +49 41 06.0


Proper motion (mas/yr)
24.11 -26.01

Regards - Canopus56

On Fri, 04 Nov 2005 17:55:39 -0800, Bill Owen wrote:

The formulae below are only approximations. dM and dN in the code,
usually called m and n in the literature, are instantaneous rates.
They're OK for short time intervals and for objects not too close to
the poles. Otherwise you'll have to use the high-octane stuff.

True- the function is intended for practical use. It isn't what you'd
want, say, for a general purpose planetarium program. I use it for
telescope pointing- one of the equinoxes is always current, the other is
no more than 1950, and it only needs to be good to a large fraction of
an arcsecond. Perfectly good for that.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com