Telescope ASPH 611 Term Project
A University of Calgary Department of Physics and Astronomy
Graduate Course in Radio Astronomy

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ASPH 611 Team

Telescope Pointing & Coordinate Systems

Nicole Kaiser, December 12, 2005

Pointing the Telescope

In order to determine exactly where the telescope is pointing, it is easiest to align the telescope based on horizon coordinates (azimuth and altitude), and later convert this to right ascension (RA) and declination (DEC). To determine the pointing of the dish, an alignment was performed during the transit of the Sun. A transit, or culmination, is when a celestial body reaches its greatest altitude above the horizon. This occurs when the body crosses the meridian, which is an imaginary line that runs from north to south in the sky. So if the telescope is pointed directly at the Sun while it transits, we know the telescope is pointing due south.

This alignment was performed on November 23, 2005. On this day, the Sun transited at 12:22 pm. Before the actual transit, some leveling of the dish was done. The dish was pointed straight up at the zenith, and the struts were adjusted until the dish lay flat (see figure 1). It was then necessary to get the dish pointed at the right altitude to observe the Sun. This was done by pointing the dish in the direction of the Sun and observing the shadow the feed horn made on the center of the dish. If aligned correctly, the shadow should be evenly distributed across the center. At exactly 12:22pm, we ensured the shadow was perfectly aligned (see figure 2). This verified we were pointing directly at the Sun, and therefore directly due south. A measurement of 17.5 degrees was taken on the altitude indicator, and the actual altitude of the Sun at transit that day was 18 degrees. This assured our confidence that the telescope’s altitude indicator gave an accurate reading.

level_dish

Figure 1: Leveling the dish while pointed at the zenith

sun_shadow

Figure 2: Aligning the center of the dish with the shadow of the Sun at its transit

With the telescope properly aligned, it is possible to observe any object at its transit by simply changing the altitude of the telescope (provided the azimuth is at 180 degrees, and altitude above ~17 degrees).

Transit times were found using the following software:

  • The Sky6 Astronomy Software
  • Professional Edition version 6.0.0.32
  • © 2005 Software Bisque
  • http://www.bisque.com/

Pointing Errors

Aligning the telescope with the Sun at its time of transit ensured that we had a correct azimuth value of 180o at an altitude of 18o. However, if the alignment of the telescope is slightly off (due to a slight tilt of the dish), as we increase the altitude of the telescope, an error in azimuth will occur. We were not able to fully investigate this, but judging from the fact that we received no apparent signal from the observation of CasA, one of the strongest radio sources in the sky (see section on 'HI Observations' and 'Radio Sources of Interest'), we assume that we did indeed have an error in our alignment.

If the telescope is not properly aligned (in both altitude and azimuth), then the source we were trying to observe may not pass directly through the beam, but instead may graze the edges of our field of view, or be missed entirely. If the source does not pass through the center of the beam, the total power we receive from it will be significantly lower.

Coordinate Systems

To convert from azimuth and altitude to RA and DEC, a transformation must be applied. The following are the equations required for this transformation:

  • dec = declination
  • az = azimuth
  • alt = altitude
  • lat = latitude
  • ha = hour angle

(1) dec = sin-1[cos(az)*cos(lat)*cos(alt) + sin(lat)*sin(alt)]

(2) ha = cos-1[(sin(alt)-sin(dec)*sin(lat))/cos(dec)*cos(lat)]

where the hour angle is the difference between an object’s right ascension and the local sidereal time (LST) (i.e. an object on the meridian will have an hour angle of 0h). RA can be found using:

(3) RA = LST - ha

If the azimuth of the object being observed is between 0 and 180, it has not yet crossed the meridian, thus hour angle must be negative. This is important in obtaining the correct value for the right ascension.

The sidereal time is the time that has elapsed since the vernal equinox last crossed the meridian. The local sidereal time is equal to the right ascension of a star that is on the meridian. To calculate this, a formula for the Greenwich mean sidereal time (GMST) is used, then adjusted to account for our difference in longitude from Greenwich.

(4) GMST = 18.697374558 + 24.06571*JD

where JD is the Julian Date from J2000. The format of the answer to equation (4) is in hours, and it must be factored by 24h until an answer is reached within the range of 0-24h. The Julian Date (J2000) is calculated using:

(5) JD = INT(367*y) - INT(7*(y+INT(m+9)/12))/4) + INT(275*m/9) + d - 730531.5 + (ut/24)

where y = year, m = month, d = day, ut = universal time, and INT refers to taking only the whole number part inside the brackets. (Note: Calgary is 6h behind universal time during daylight savings time, and 7 hours behind during the rest of the year).

To find the local mean sidereal time (LMST), the longitude of the observing station must be taken into account. Calgary is at a longitude of ~114o W of Greenwich. Since the beam size if ~4o on the sky, this longitude measure is sufficiently accurate. When measuring longitude, east is positive, and west is negative. Thus 114o (divide by 15 to convert to hours) must be subtracted from the GMST:

(6) LMST = GMST - (longitude/15)

The answer to equation (6) is in hours, and if the answer is negative, 24 hours must be added to obtain a positive time. This value can then be plugged into equation (3) to solve for the RA.

  1. Astro Java http://www.roman-britain.org/astronomy/astro.htm
  2. Positional Astronomy http://www.astunit.com/tutorials/positional.htm
  3. Positional Astronomy http://star-www.st-and.ac.uk/~fv/webnotes/index.html
  4. Ridpath, Ian. Norton’s Star Atlas and Reference Handbook, 19th Edition. Addison Wesley Longman Limited, England, 1998.

Last modified: 10:22 am July 17, 2014

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