Anna CastelazSummer 2003

Introduction

Why do we need pointing models?

Which models did I develop?• East, 1420 MHz• East, 4.8 GHz• West, 4.8 GHz• Revisions on 1420 MHz for West

There were several calculations necessary to make the data easier to work with. I precessed the coordinates to the current catalog positions, using the site http://fuse.pha.jhu.edu/support/tools/precess.html to do so.

Then these coordinates and the peaked coordinates, in RA and DEC, were changed into decimal notation.

2003.5 RA 2003.5 DEC 2003.5 RA 2003.5 DEC peak RA peak DEC HA

04 37 18 29 40 14.9 4.62167 29.67081 4.65075 30.41222 -3.27544

SAMPLE POINT:

DEC degreemin

60

sec

3600RA HA hr

min

60

sec

3600

Procedure

To make a model, I would first have to point the telescope at point sources throughout the sky.

SAMPLE POINT: 0022+5544

date object z dist start X start Y peak X peak Y Epoch catalog RA catalog DEC peaked RA peaked DEC Hour Angle

6/13/03 0433+2933 43.26 42.855 5.209 41.08 5.155 1950 04 33 55.6 29 33 49 04 39 02.7 30 24 44 -03 16 31.6

The coordinates had to be changed into degrees:

x cos DEC

180 cos HA 15

180

y cos DEC

180 sin HA 15

180

z sin DEC

180

X1 x cos latitude( ) z sin latitude( )

Z1 x sin latitude( ) z cos latitude( )

The formulae on the left changed the data into unit vectors and the ones on the right compensate for latitude

•the latittute at PARI is 35.2049 degrees, or .6144 radians.

After taking latitude into account, I could finish converting into degrees:

SAMPLE POINT:

MAJ180

atan

y

X1 MIN

180

atan

Z1

X12 y2

2003.5x 2003.5y 2003.5z 2003.5 X1 2003.5 Z1 2 003.5 SMAJ 2003.5 SMIN

0.56853 -0.65706 0.49502 0.74992 0.61310 41.22418 31.58797

peakx peaky peakz peakX1 peakZ1 peak TMAJ peak TMIN

0.56429 -0.65216 0.50622 0.75291 0.61711 40.89875 31.77976

Now I could calculate errors. The EMAJ and EMIN errors and the total error:

EMAJ TMAJ SMAJ( )EMIN TMIN SMIN( ) ETOT EMAJ2 EMIN2

EMAJ EMIN ETOT

-0.32543 0.19179 0.37774SAMPLE POINT:

I collected approximately 35 points for the models for 26 East at 1420 MHz and 26 West at 4.8 GHz.. There were 51 points from the model for West in 1420 last year, and I was only able to collect 15 points for East at 4.8. I ran all of the points through the calculations.

For each model there were four graphs. They were combinations of either the observed positions and the difference between the catalog and observed positions; or TMAJ vs. EMAJ, TMAJ vs. EMIN, TMIN vs. EMAJ, and TMIN vs. EMIN.

To save space, I have plotted all four on the same graph for each model

Results

East 1420 all points

y = 9E-05x2 - 0.0003x + 0.1418R2 = 0.5315

y = -0.0001x2 - 0.0164x + 0.099R2 = 0.8369

y = 0.0002x2 - 0.034x + 1.1293R2 = 0.7723

y = 0.002x2 - 0.1444x + 2.9615R2 = 0.1244

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-80 -60 -40 -20 0 20 40 60

MAJ or MIN coordinate

erro

r

TMAJ, EMAJ

TMAJ, EMIN

TMIN, EMAJ

TMIN, EMIN

Poly. (TMAJ, EMIN)

Poly. (TMAJ, EMAJ)

Poly. (TMIN, EMIN)

Poly. (TMIN, EMAJ)

Graph for 1420 MHz on 26 East

West 4.8 All Points

y = -0.0001x2 - 0.0011x + 0.2773

R2 = 0.7389

y = 5E-05x2 + 0.0003x - 0.0003

R2 = 0.7573

y = -2E-05x2 - 0.0012x - 0.0074

R2 = 0.8713

y = -0.0002x2 + 0.0203x - 0.5017

R2 = 0.8393

-0.2

-0.2

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

0.3

-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

MAJ or MIN observed position

erro

r

TMAJ, EMAJTMAJ, EMINTMIN, EMAJTMIN, EMINPoly. (TMIN, EMAJ)Poly. (TMAJ, EMAJ)Poly. (TMAJ, EMIN)Poly. (TMAJ, EMAJ)Poly. (TMIN, EMIN)

Graph for 4.8 GHz on 26 West

Graph for east 4.8 on this page!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

West revised at 1420

y = 2E-05x2 - 0.0026x - 0.6265

R2 = 0.2223

y = -5E-05x2 + 0.003x - 0.5584

R2 = 0.251

y = 2E-05x2 + 0.0069x + 0.0019

R2 = 0.9244

y = -2E-05x2 - 0.0007x - 0.0081

R2 = 0.0054

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-80 -60 -40 -20 0 20 40 60

MIN or MAJ position

erro

r

TMAJ, EMAJ

TMAJ, EMIN

TMIN, EMAJ

TMIN, EMIN

Poly. (TMAJ, EMIN)

Poly. (TMIN, EMIN)

Poly. (TMAJ, EMAJ)

Poly. (TMIN, EMAJ)

Graph for 1420 MHz on 26 West

These graphs are important because their slopes and curvatures are used as constants in the pointing model formulas.

MajorError SCLMAJMAJ

cos MIN( ) CH

cos MIN( )NP tan MIN( ) ME sin MAJ( ) tan MIN( ) MAJECC cos MAJ MINOFF( )

180

TFLX sin MAJ( )

EMAJ vs. TMAJCurve = TFLX = tube flexure for major axisSlope = SCLMIN = major scale factor

EMIN vs. TMAJCurve = ME = elevation misalignment in arc secSlope = MA = azimuth misalignment in arc sec

EMIN vs. TMINCurve = TFLX = tube flexure for minor axisSlope = SCLMIN = minor scale factor

EMAJ vs. TMIN Curve = CH = collimationSlope = NP = non- perpendicularity

ME sin MAJ( ) tan MIN( ) MAJECC cos MAJ MINOFF( )

180 TFLX sin MAJ( )

MinorError SCLMINMIN ME cos MAJ( ) MA sin MAJ( ) TFLX sin MIN( )

Constants not previously mentioned:MAJECC = eccentricity error amplitudeMINOFF = eccentricity offset

The Pointing Model Program

To run my data in the pointing model program, I created a *.pat file of the data. This was essentially a long column of entries including the current catalog RA and DEC, the observed RA and DEC, and the HA.

The program shows graphs and a list of the constants. It corrects its pointing by looping through the EMIN and EMAJ equations and the MajorEorror and MInorError equations. (For the EMIN and EMAJ equations, it uses:

and EMAJ TMAJ SMAJ( ) MajorErrorEMIN TMIN SMIN( ) MinorError

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