## Astrometry: Looking for Pascal/Delphi functions

### Re: Astrometry: Looking for Pascal/Delphi functions

My program reports for that date, time and position an altitude of 11.1 degrees without any atmospheric refraction. The best is to check a few examples in one of the Meeus books. For planetary ephemerides you could use JPL https://ssd.jpl.nasa.gov/horizons.cgi?s_target=1#top

### Re: Astrometry: Looking for Pascal/Delphi functions

DEC {(epoch T)} := (DECU -90/360000 + pmDE * (epoch2 - 2000.0)/10.0)*((pi/180)/(3600*1000))-pi/2; {DEC first}

RA {(epoch T)} := (RAU + pmRA / cos(dec)*(epoch2 - 2000.0)/10.0)*((pi/180)/(3600*1000));

DECU -90/360000 ... is the Dec value in degrees from the catalogue corrected with a constant value of -900 mas ??? Is this constant value specific to the USNO catalogue?

The -90/360000 doesn't belong there. I will remove it. Looks like a leftover from previous modified routine. I have been sloppy there. The DEC is stored in south pole distance and that's corrected by the -pi/2. In my program all calculations result in radians.

Luckily it didn't really do harm. The distance in the USNO4 is stored in distance from the celestial south pole in milli arc seconds. So -90/360000 is only 0.00025 milli arcseconds.

The UCAC4 code is now:

DEC {(epoch T)} := (DECU + pmDE * (epoch2 - 2000.0)/10.0)*((pi/180)/(3600*1000))-pi/2; {DEC first}

RA {(epoch T)} := (RAU + pmRA * (epoch2 - 2000.0)/(10.0* cos(dec)) )*((pi/180)/(3600*1000));

I added some test star values in the code taken from Simbad like

{capella, ICRS coord. (ep=J2000, eqJ2000) 05 16 41.35871 +45 59 52.7693 }

{capella, ICRS coord. (ep=J2016, eqJ2000) 05 16 41.47425 +45 59 45.9390 }

{capella, ICRS coord. (ep=J2100, eqJ2000) 05 16 42.08070 +45 59 10.0801 }

{capella, ICRS coord. (ep=J2250, eqJ2000) 05 16 43.16312 +45 58 06.0459 }

RAU is the RA value in degrees from the catalogue

It is from the catalog but in milliarcseconds from the celestial south pole.

pmDE and pmRA ... proper motion in mas/10yr ???

Yes. See below

DEC first ... because DEC calculated from DECU is required for calculating RA.

The proper motion is in mas/10yr but the influence on the RA value increases near the celestial poles where the RA lines come together. So divide by the cos(dec)

DEC and RA are in radians.

Yes

Is distance and radial velocity not used?

Only proper motion in ra and dec.

So this has positive result, one small correction. Patrick will most likely not react. He is much too busy with his own programs and bug tracker.

Regards, Han

From UACA$doc.txt:

RA {(epoch T)} := (RAU + pmRA / cos(dec)*(epoch2 - 2000.0)/10.0)*((pi/180)/(3600*1000));

DECU -90/360000 ... is the Dec value in degrees from the catalogue corrected with a constant value of -900 mas ??? Is this constant value specific to the USNO catalogue?

The -90/360000 doesn't belong there. I will remove it. Looks like a leftover from previous modified routine. I have been sloppy there. The DEC is stored in south pole distance and that's corrected by the -pi/2. In my program all calculations result in radians.

Luckily it didn't really do harm. The distance in the USNO4 is stored in distance from the celestial south pole in milli arc seconds. So -90/360000 is only 0.00025 milli arcseconds.

The UCAC4 code is now:

DEC {(epoch T)} := (DECU + pmDE * (epoch2 - 2000.0)/10.0)*((pi/180)/(3600*1000))-pi/2; {DEC first}

RA {(epoch T)} := (RAU + pmRA * (epoch2 - 2000.0)/(10.0* cos(dec)) )*((pi/180)/(3600*1000));

I added some test star values in the code taken from Simbad like

{capella, ICRS coord. (ep=J2000, eqJ2000) 05 16 41.35871 +45 59 52.7693 }

{capella, ICRS coord. (ep=J2016, eqJ2000) 05 16 41.47425 +45 59 45.9390 }

{capella, ICRS coord. (ep=J2100, eqJ2000) 05 16 42.08070 +45 59 10.0801 }

{capella, ICRS coord. (ep=J2250, eqJ2000) 05 16 43.16312 +45 58 06.0459 }

RAU is the RA value in degrees from the catalogue

It is from the catalog but in milliarcseconds from the celestial south pole.

pmDE and pmRA ... proper motion in mas/10yr ???

Yes. See below

DEC first ... because DEC calculated from DECU is required for calculating RA.

The proper motion is in mas/10yr but the influence on the RA value increases near the celestial poles where the RA lines come together. So divide by the cos(dec)

DEC and RA are in radians.

Yes

Is distance and radial velocity not used?

Only proper motion in ra and dec.

So this has positive result, one small correction. Patrick will most likely not react. He is much too busy with his own programs and bug tracker.

Regards, Han

From UACA$doc.txt:

col byte item fmt unit explanation notes

---------------------------------------------------------------------------

1 1- 3 ra I*4 mas right ascension at epoch J2000.0 (ICRS) (1)

2 5- 8 spd I*4 mas south pole distance epoch J2000.0 (ICRS) (1)

3 9-10 magm I*2 millimag UCAC fit model magnitude (2)

4 11-12 maga I*2 millimag UCAC aperture magnitude (2)

5 13 sigmag I*1 1/100 mag error of UCAC magnitude (3)

6 14 objt I*1 object type (4)

7 15 cdf I*1 combined double star flag (5)

15 bytes

8 16 sigra I*1 mas s.e. at central epoch in RA (*cos Dec) (6)

9 17 sigdc I*1 mas s.e. at central epoch in Dec (6)

10 18 na1 I*1 total # of CCD images of this star

11 19 nu1 I*1 # of CCD images used for this star (7)

12 20 cu1 I*1 # catalogs (epochs) used for proper motions

5 bytes

13 21-22 cepra I*2 0.01 yr central epoch for mean RA, minus 1900

14 23-24 cepdc I*2 0.01 yr central epoch for mean Dec,minus 1900

15 25-26 pmrac I*2 0.1 mas/yr proper motion in RA*cos(Dec) (8)

16 27-28 pmdc I*2 0.1 mas/yr proper motion in Dec

17 29 sigpmr I*1 0.1 mas/yr s.e. of pmRA * cos Dec (9)

18 30 sigpmd I*1 0.1 mas/yr s.e. of pmDec (9)

### Re: Astrometry: Looking for Pascal/Delphi functions

Han, it looks like your result is more off than mine. In the book from Montenbruck and Pfleger they forgot to divide by cos(Dec) when correcting proper motion for RA. With this correction my new result is Htrue=8.4979711212 deg which agrees to 4 mas with the results some one else obtained using full SOFA. I am however not yet there; despite noticable improvements there is an other bench mark case which differs more than half an arcsec. As I mentioned before, once the star results are sufficently accurate, only then I will start implementing JPL DE. I can imagine I might have in this context one or the other question to get it going. BTW: I know JPL Horizon. For a previous study I did run there a batch of solar data.han.k wrote: ↑15 Jun 2019, 16:05My program reports for that date, time and position an altitude of 11.1 degrees without any atmospheric refraction. The best is to check a few examples in one of the Meeus books. For planetary ephemerides you could use JPL https://ssd.jpl.nasa.gov/horizons.cgi?s_target=1#top

Thank you for all your explanations regarding your code!

Best wishes,

Marcel

P.S: Please let me know if you would like to see my intermediate values for this case.

### Re: Astrometry: Looking for Pascal/Delphi functions

You make me a little worried, so I entered the data again in HNSKY and get the same result an altitude of 11.1. Delta_T on/off is only 3 seconds and did not make a difference. The UCAC4 doesn't include Arcturus, so I can't calculate the position in 1867 using proper motion.

As a test , I also entered it in CDC:

Arcturus

Universal Time: 1867-08-15T21:21:28 JD=2403194.38991

Local sidereal time: 20h58m04s

Hour angle: 06h48m28s

Azimuth: 290°23'13"

Altitude: +11°17'22.8"

Geometric altitude: +11°12'39.0"

Airmass: 5.0

Rise:06h55m51s Azimuth:46°10'

This makes me comfortable again. CDC and HNSKY are totally independent developed and they agree in the altitude. The only common part is the long term precession.

So you result doesn't match. I hope you can find out where it goes wrong or if my calculation is wrong.

Where in Montebruck & Pfleger does it go wrong?

As a test , I also entered it in CDC:

Arcturus

Universal Time: 1867-08-15T21:21:28 JD=2403194.38991

Local sidereal time: 20h58m04s

Hour angle: 06h48m28s

Azimuth: 290°23'13"

Altitude: +11°17'22.8"

Geometric altitude: +11°12'39.0"

Airmass: 5.0

Rise:06h55m51s Azimuth:46°10'

This makes me comfortable again. CDC and HNSKY are totally independent developed and they agree in the altitude. The only common part is the long term precession.

So you result doesn't match. I hope you can find out where it goes wrong or if my calculation is wrong.

Where in Montebruck & Pfleger does it go wrong?

### Re: Astrometry: Looking for Pascal/Delphi functions

And this is TheSkyX reporting:

Object Name: Arcturus

Name 2: HIP 69673

Object Type: Star

RA (Topocentric): 14h 09m 26.2801s

Dec (Topocentric): +19° 48' 17.062"

RA (2000.0): 14h 15m 49.3220s

Dec (2000.0): +19° 15' 21.354"

Azimuth: 290° 22' 16"

Altitude: +11° 08' 08"

Proper Motion RA: -1,093.45

Proper Motion Dec: -1,999.40

Position Error RA: 0.9200

Position Error Dec: 0.4200

Sidereal Time: 20:58

Julian Date: 2403194.38991000

Object Name: Arcturus

Name 2: HIP 69673

Object Type: Star

RA (Topocentric): 14h 09m 26.2801s

Dec (Topocentric): +19° 48' 17.062"

RA (2000.0): 14h 15m 49.3220s

Dec (2000.0): +19° 15' 21.354"

Azimuth: 290° 22' 16"

Altitude: +11° 08' 08"

Proper Motion RA: -1,093.45

Proper Motion Dec: -1,999.40

Position Error RA: 0.9200

Position Error Dec: 0.4200

Sidereal Time: 20:58

Julian Date: 2403194.38991000

### Re: Astrometry: Looking for Pascal/Delphi functions

Han, you mixed-up the times.

Recordet time of observation was 21:21:27.9 local sideral time (LAST)

The result consists in finding first the corresponding UT1 which was found to be 21.747813289 (or 21:44:52.1)

My result relates to this time.

Recordet time of observation was 21:21:27.9 local sideral time (LAST)

The result consists in finding first the corresponding UT1 which was found to be 21.747813289 (or 21:44:52.1)

My result relates to this time.

### Re: Astrometry: Looking for Pascal/Delphi functions

With 21:44:52.1 I get 8.4 degrees altitude. I'm not aware of anybody is using sidereal time. Maybe in 1867. Now it is UTC or Julian Day.

### Re: Astrometry: Looking for Pascal/Delphi functions

"I'm not aware of anybody is using sidereal time. Maybe in 1867. Now it is UTC or Julian" Sorry, Han, but that is how these historical observations are documented.

Before closing down here also the other one.

Thanks and regards,

Marcel

Can you notice why the following case seems to produce a less accurate result?

Reference: #316

Loc."E" Lat N: 59.77263889

Loc."E" Lon E: 30.33027778

Star catalogue:

HIP: 72105

RA(J2000): 221.2467394

Dec(J2000): 27.07422497

PM_RA [mas/yr] -50.95

PM_Dec [mas/yr] -21.07

Observation Date/Time:

Date: 1868.02.05

LAST Hr: 05:38:48.7 (observed time)

Calculation with corresponding UT1

Time UT1: 18.611627558

dCyJ2000: -1.3190068305 centuries from J2000

after applying proper motion:

RA(date): 221.24883589

Dec(date): 27.073452985

Precession Matrix T0->T:

T0: 0

T: -1.3190068305 centuries from J2000

A[1,1]: 0.99948322253

A[1,2]: 0.029478403824

A[1,3]: 0.01281840786

A[2,1]: -0.029478404373

A[2,2]: 0.99956539955

A[2,3]: 0.00018893908104

A[3,1]: -0.012818406597

A[3,2]: -0.00018902476874

A[3,3]: 0.99991782298

after Nutation:

A[1,1]: 0.99948234635

A[1,2]: 0.029503395975

A[1,3]: 0.012829252162

A[2,1]: -0.029503927087

A[2,2]: 0.99956465462

A[2,3]: -0.00014787204991

A[3,1]: -0.012828030768

A[3,2]: -0.00023071757616

A[3,3]: 0.99991769173

RA, Dec -> Cartesian:

X: -0.66946797007

Y: -0.58708358979

Z: 0.45513239354

multiplying with Precession/Nutation-Matrix and

adding Aberration:

VX: -7.0032342811e-05

VY: -6.4720410462e-05

VZ: -2.8031318128e-05

results in Cartesian:

X: -0.68067340125

Y: -0.56720809325

Z: 0.46379030728

and converting back to

Polar:

RA: 219.8045904

Dec: 27.629820296

and converting further to

Horizon:

Htrue: 4.8620883086

Before closing down here also the other one.

Thanks and regards,

Marcel

Can you notice why the following case seems to produce a less accurate result?

Reference: #316

Loc."E" Lat N: 59.77263889

Loc."E" Lon E: 30.33027778

Star catalogue:

HIP: 72105

RA(J2000): 221.2467394

Dec(J2000): 27.07422497

PM_RA [mas/yr] -50.95

PM_Dec [mas/yr] -21.07

Observation Date/Time:

Date: 1868.02.05

LAST Hr: 05:38:48.7 (observed time)

Calculation with corresponding UT1

Time UT1: 18.611627558

dCyJ2000: -1.3190068305 centuries from J2000

after applying proper motion:

RA(date): 221.24883589

Dec(date): 27.073452985

Precession Matrix T0->T:

T0: 0

T: -1.3190068305 centuries from J2000

A[1,1]: 0.99948322253

A[1,2]: 0.029478403824

A[1,3]: 0.01281840786

A[2,1]: -0.029478404373

A[2,2]: 0.99956539955

A[2,3]: 0.00018893908104

A[3,1]: -0.012818406597

A[3,2]: -0.00018902476874

A[3,3]: 0.99991782298

after Nutation:

A[1,1]: 0.99948234635

A[1,2]: 0.029503395975

A[1,3]: 0.012829252162

A[2,1]: -0.029503927087

A[2,2]: 0.99956465462

A[2,3]: -0.00014787204991

A[3,1]: -0.012828030768

A[3,2]: -0.00023071757616

A[3,3]: 0.99991769173

RA, Dec -> Cartesian:

X: -0.66946797007

Y: -0.58708358979

Z: 0.45513239354

multiplying with Precession/Nutation-Matrix and

adding Aberration:

VX: -7.0032342811e-05

VY: -6.4720410462e-05

VZ: -2.8031318128e-05

results in Cartesian:

X: -0.68067340125

Y: -0.56720809325

Z: 0.46379030728

and converting back to

Polar:

RA: 219.8045904

Dec: 27.629820296

and converting further to

Horizon:

Htrue: 4.8620883086

### Re: Astrometry: Looking for Pascal/Delphi functions

Okay I can understand sidereal time is the only way in 1867.

Tomorrow I will have a look to this last observation. Time to shutdown the computer.

Han

Tomorrow I will have a look to this last observation. Time to shutdown the computer.

Han

### Re: Astrometry: Looking for Pascal/Delphi functions

My program reports an altitude of 5.0. I do not include observatory height nor the pear shape of the Earth. The altitude measurements are for me of less interest.

Best regard, Han

Best regard, Han