Astrometry Method of Measurement

The position angle and separation are calculated from the measured right ascension and declination positions of the star pair.3 The following equations define the relationship between the pair separation (p) and the position angle (0):

where aa is the right ascension of the brighter star and ab is the right ascension of the dimmer star in the pair, Sa is the declination of the brighter star and S is the declination of the fainter star.

To illustrate this method, an example is in order. Figure 16.4 is a negative CCD image of the field of the quadruple system WDS 07131 + 1433. This is a routine system with only three of the four stars visible in the figure. The separation of the B and D star is below the

Figure 16.4.

Negative CCD image of the field of the quadruple system WDS 07131+1433.

resolution of the CCD frame and they appear as one star. Table 16.1 gives the measurements from the WDS Catalog.

The first step in the process is to determine the right ascension and declination of at least three stars in the field. These stars are used to define the positions of the remainder of the stars in the field of view. A variety of software packages are readily available to perform the required astrometry calculations. Some examples of software that performs astrometric measurements are: Axiom Research's MIRA, Herbert Raab's Astrometrica, John Rogers' CCD Astrometry, Project Pluto's Charon, Bob Denny's Pinpoint, and BdW Publishing's Canopus. These software packages typically use the Guide Star Catalog, Tycho, and the USAO 1.0 catalogs.

The author used the MIRA software and the positions from the Tycho catalog, which are labelled 1-4 in Figure 16.4, to determine the positions of the stars labelled A, B, and C in the same figure. The positions of

Figure 16.4.

Negative CCD image of the field of the quadruple system WDS 07131+1433.

Table 16.1. WDS data for WDS 07131+1433










9.1, 11.1





11.1, 11.9





11.1, 11.0

Table 16.2. Position of reference stars

Star Tycho


2 774 1053 1

3 774 535 1

4 774 821 1

07h 12m 54s.64 07h 12m 48s.97 07h 13m 20s.19 07h 12m 19s.88

+ 14 24' 33'.'2 + 14 36' 03'.'5 +14 48' 07'.'7 + 14 40' 36'.'3

Table 16.3. Measured positions for WDS 07131+1433

Star RA(2000)


A 07h 13m 05s.05 BD 07h 13m 05s.12 C 07h 13m 04s.46

+ 14° 32' 57'.'85 + 14° 34' 01'.'42 + 14° 34' 09'.'10

the reference stars are listed in Table 16.2. It is best if catalog positions for any of the stars in a double star system are not used as a reference star, the reason being that the measurement process tends to introduce systematic errors in positions. Calculating the position angle and separation effectively removes the effects of the systematic error.

The closest pairs that can be measured with certainty using the 8-inch are about 3'' (providing the difference in magnitude is 2 or less). This is limited by the pixel size and the seeing.

Using the four reference stars in Table 16.2, the three visible stars in WDS 07131 + 1422 are measured. Table 16.3 gives the positions of the stars in the quadruple system.

With the positions known for the three stars in the system and equations (16.1) and (16.2), the position angle and separation are now calculated. Comparing Tables 16.1 and 16.4 you see a difference in the separations and position angles. These differences are due to the errors in both previous and current (Epoch 2000.787) measurements and the actual position changes of the stars due to their proper motions.

Table 16.4. Measured PA and separations Pair (2000) (2000)

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