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2016-12-08

How to align polar axis in the southern hemisphere


この記事は南半球での極軸の合わせ方を、職場の同僚向けに英語で説明したものです。南半球での合わせ方を説明していますので、北半球では逆センスになります。日本語での説明はこちらの記事をご覧下さい。

f:id:kamenoseiji:20161209032101p:image
Figure 1, click to enlarge

There is no bright 'polaris' around the celestial south pole. Instead of a polar finder, here I introduce the procedure to align the polar axis of an equatorial tracker.

Principle

If the polar axis is misaligned, we'll meet tracking errors. Figure 1-1 shows the case when the polar axis is misaligned to the west of the true south pole. The misalignment causes tracking error for a star near the meridian. Similarly when the polar axis is misaligned below the true polar axis (figure 1-2), it causes tracking error for a star just ascending in the east.
The rate of the tracking error, ω, is given by the equation:
¥frac{¥omega}{1^{¥prime ¥prime} {¥rm sec}^{-1}} = ¥frac{¥Delta ¥theta}{3^{¥circ}.8} ¥cos ¥delta
Here, Δθ is the amount of polar axis misalignment and δ is the declination of the star.

Procedure

  1. Align the polar axis coarsely.
  2. Point to a star near the equator at meridian.
  3. Take 2 shots (each 10-sec exposure) with the interval of 60 sec.
  4. Compare two frames and measure the displacement, W [arcmin] to the north, of the star.
  5. Adjust the polar axis to the west by ¥frac{3.8^{¥circ}}{¥cos ¥delta} W. If the displacement is to the south (i.e.  W < 0), adjust the polar axis to the east.
  6. Point to a star rising from the east.
  7. Take 2 shots (each 10-sec exposure) with the interval of 60 sec.
  8. Compare two frames and measure the displacement, W [arcmin] to the north, of the star.
  9. Adjust the polar axis upward by ¥frac{3.8^{¥circ}}{¥cos ¥delta} W. If the displacement is to the south (i.e.  W < 0), adjust the polar axis downword.

Tips

It is better to recognize the FoV (Field of View). The measurement of tracking error displacement refers to the FoV. And when you adjust the polar axis by given amount, camera live-view of the tracking star guides you.
An APS-C sensor has the format of 16.7 mm × 23.4 mm and the FoV is given by ¥frac{16.7 {¥rm mm}}{f} ¥times ¥frac{23.4 {¥rm mm}}{f}, where  f is the focal length of the optics. In the case  f = 400 mm, for instane, the FoV will be  0.0278 {¥rm rad} ¥times  0.0585 {¥rm rad} or  2^{¥circ}.39 ¥times  3^{¥circ}.35.

トラックバック - http://d.hatena.ne.jp/kamenoseiji/20161208/1481223914