Astronomical Society of Coonabarabran

The Sun and the Moon: measuring things

by Harry Roberts

Perhaps the two most interesting objects in the sky, and also the most neglected, are the Moon, and its antithesis, the Sun.

Both objects are huge, subtending half a degree in diameter. And both objects are roughly one hundred times their own diameter away from us, and so the Moon can exactly eclipse the Sun: a remarkable thing that made the early discovery of the solar corona, prominences (and even CME's) possible.

The Moon is a good example of a medium sized rocky planet, smaller than Mercury, but bigger than down-rated Pluto. Members will know that the Moon's creation was a very unusual event that resulted in Earth's only moon being much larger than is normal.

The Sun is a good example of a medium sized star, one close enough to see real detail with the smallest 'scopes, yet far enough away not to fry us! We are greatly blessed. And yet the Sun hardly rates a mention in those "marketing catalogues", the amateur periodicals. The Moon is attracting much more interest largely due to Charles Wood's efforts. The Sun needs another "Chuck" Wood to raise its profile.

Measuring the size of things on the Moon and Sun is a (daily) revelation, and if you have a stopwatch you can get velocities for events on the Sun; be prepared for some gigantic numbers! Solar escape velocity is 618km.s^-1! Surges will shoot across 100,000km of the Sun's surface (at 1000km.s^-1), then pause for a while, before shooting back to their starting point, sometimes around a right angle turn. A flare can light up along a 150,000km front in half a minute.

How is distance measured? I will describe the process for the Sun, and the same method is used for the Moon. You will need an orthoscopic cross-hair eye-piece (try e-bay) giving about 80 magnification, that will show the whole solar disc; Naglers won't work. Your telescope must be protected with a full aperture solar filter to protect both your eyesight and the 'scopes optics. The 'scope must be rigidly mounted on either an alt-az or equatorial mount.

Firstly, align one of the cross-hair's with the direction of drift of a sunspot when the drive is OFF. This cross-hair gives celestial E-W, and the Sun drifts westwards. The other cross-hair gives N-S. The eye-piece is now aligned with Declination and Right Ascension, just like in the star atlases.

Now time a transit of the Sun at its widest point (repeat and average). This with give a result of ~2m10s (130s) depending on the season. Since the Sun is 1392530 km in diameter, then for each second of its journey across the solar disc the cross-hair travelled 10,700 km at the solar distance (= diameter divided by time.) Because the Sun is round this number can be used to measure sunspot sizes only when they are near the Sun's central meridian (CM).

If you are recording a spot more than say ±20º from the CM you should multiply your timing by a factor based on the spot's angular distance from the CM. If your spot is 30º from the CM, take the cosine of 30º (=.866) and convert to its reciprocal (=1.15). Now multiply your timing by 1.15. The result can now be multiplied by 10,700 to get the spot length in km, as before, and you have compensated for the Sun's curvature.

For the Moon this method gives a distance of about 27 km for each second of drift. Again you must apply the correction for landforms more than 20º from the CM. It's a very useful measuring stick. Notice that the ratio between 10,700 and 27 is about 400, telling us that the Sun is only 400 times further away than the Moon! Or, the Sun is 8 light minutes away, while the Moon is 1.3 light seconds distant.

On the Sun in H-alpha any prominence that rises higher than 50,000 km "will erupt within 48 hours" (see Zirin, "Astrophysics"). Because prominences mostly rise vertically above the limb it's safe to assume they lie "normal" (at 90º) to our line of sight, and the height in seconds of transit time, multiplied by 10,700km gives their actual height. Any prominence higher than 4.5 s (~50,000km) needs to be watched very closely. An erupting prominence may travel at only 20km.s^-1, or over 600 km.s^-1. I promise you will be impressed when you see one! But note, if you have no method of calculating height you can't tell if the prominence is erupting, it may not show any visually obvious motion, because Space is bigger than we think. Regular measurements with the cross-hairs will detect the motion. Events may unfold over 7 hours, or be all over in 40 minutes! During solar maximum my logs showed that I needed to observe for about 40 hours to see one decent flare. We must observe a lot. The figure shows a typical sunspot drawing made using the cross-hair method, and a sequence of four views of a prominence eruption from 2004 July 22^nd.

In a companion piece on cross-hair astronomy I described how I use "Helio" freeware to derive accurate solar coordinates for events on the Sun, and I can provide a copy to interested readers; hopefully you are many.

Dust off those Ortho's, and perfect your transit technique while solar activity is still low; believe me, when the Sun gets active events move at an amazing pace.