The Official Publication of the Bucks-Mont Astronomical Association, Inc ________________________________________________________________________________________________________________________________________

VOL XV, NO 9w                                                   SEPTEMBER                                                    Scott Petersen, Editor
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It is time, once again, to elect next year's BMAA officers. Of the current Executive Committee, only President Ed Murray is eligible to run again. Club by-laws state that any one person may only be in office for three consecutive years, and then must step down for at least one year.

We have some club members interested in the various officers' positions - their names and bios (as available) are listed elsewhere in this issue. Vice-President Peter van der Spek has said that nominations will be accepted until the October General Meeting, although the by-laws also state that the nominees are to be published in the CONSTELLATION one month prior to the election.

Marian Shearer will host this session.

Submission deadline for articles is the 15th of the month prior to publication.

SCOTT PETERSEN
CONSTELLATION EDITOR
WYCOMBE PA 18980-0333
TEL: 215/598-8447
FAX: 215/598-8446

BMAA WEB SITE: bmaa.freeyellow.com/

bmaa@ixc.net

2000 Calendar Of Events

StarWatch Chairman: Ed Radomski - 215/822-8312, ejrado@prodigy.net

So, big telescopes yield higher resolution images than smaller telescopes. Well, we all know this is not true. Let's explore some aspects related to this issue.

Assume we have two telescopes, each of very high quality- say a 4" and, what the heck, one the size of Pennsylvania! It is easy to see the larger instrument will see through a greater variety of air temperatures and will encounter more moving, mixing air. This mixing air will retard and advance the wave front and render the image quality very poor. On the other hand, the 4" scope may reside in a given column of air longer. Recall how Jupiter or Mars behaves in a telescope of this aperture. It wonders about the field BUT RETAINS IMAGE INTEGRITY. As single cells of mixing air move over the aperture the entire image will shift about with details intact. The image in the larger telescope will jiggle about and show less surface detail. On page 218 of the second printing of Telescope Optics by Harrie Rutten and Martin van Venrooij (1989 Willmann-Bell), we find a diagram relating magnification, seeing and aperture. On a night of moderate to poor seeing (common conditions for our area) a power of 173 X can be used with an aperture of 334mm (13in). Still pretty big, but at 90% of this power (160 X) an 8in. does as well! Atmospheric turbulence is the great equalizer. For years I have used three or more telescopes of different aperture on any given night. Rarely (maybe two nights of the year) would there be evident difference between the image from a 10in f/8 and my 8in f/8 Newtonians, even though the 10in is fully baffled and the 8in not. For a really excellent review of tube currents, something particular to open tubes, see Understanding Thermal Behavior in Newtonian Reflectors, Bryan Greer, Sky and Telescope September 2000.

In the next Constellation I will give directions on building and using a knife edge eyepiece on the stars to further explore tube and atmospheric currents.

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Having just finished a series on eyepieces, and being at a loss for words, I'll talk on a topic mentioned by Brad Miller.

He recommended a series of formulas for various telescope applications, so here goes. Some of these are easily tracked down, some not. I won't give the proof of these, just the formulas. All can be located in the literature, though some may require searching.

The FOCAL RATIO of the scope is.....

* FOCAL RATIO = FOCAL LENGTH / DIAMETER (OBJECTIVE)

FOCAL RATIO is usually abbreviated f/- or f-.

MAGNIFICATION, the end all for some buyers, is easily calculated by dividing the eyepiece FOCAL LENGTH into the scope FOCAL LENGTH..

* MAGNIFICATION = FL (SCOPE) / FL (EYEPIECE)

Magnification can also be calculated by dividing the OBJECTIVE DIAMETER by the EXIT PUPIL diameter, but only if the aperture is not constricted..

* MAGNIFICATION = DIAMETER (OBJECTIVE) / DIAMETER (EXIT PUPIL)

Obviously the EXIT PUPIL diameter can be calculated ...

* DIAMETER (EXIT PUPIL) = DIAMETER (OBJECTIVE) / MAGNIFICATION

By manipulating these formulas, one can find the power (FL) of an eyepiece.

* FL (EYEPIECE) = FOCAL RATIO X EXIT PUPIL

Manipulating the numbers....

* EXIT PUPIL = FL (EYEPIECE) / FOCAL RATIO

FIELD OF VIEW in a scope is simply the eyepiece field of view (manufacturers state this) divided by the MAGNIFICATION.

* FOV (ACTUAL) = FOV (EYEPIECE) / MAGNIFICATION

The real field can be found by allowing a star on the celestial equator (a star having a declination of 0v) to drift across the center of the field of the eyepiece. The stars there move at a rate of 1 degree in 4 minutes, thusly 15 arcminutes in 1 minute, or 15 arcseconds in 1 second.

* FOV (ACTUAL, IN ARCMINUTES) = SECONDS (DRIFT TIME) x FOUR

The size in INCHES PER DEGREE OF SKY of the real field at the focal plane can be found by...

* DIAMETER (REAL SIZE INCHES/DEGREE) = 57.3 / FOCAL LENGTH

* DIAMETER (REAL SIZE MM/DEGREE) = 1445 / FOCAL LENGTH (IN MM)

Multiplication factors for BARLOW LENSES are given by the manufacturer, and are multiplied by the magnification of the scope/ eyepiece combination. THESE ARE NOT EXACT, as the amplification factor is dependent on the distance the Barlow is placed inside the focal plane and the focal length of the negative lens in the Barlow. since eyepieces do not all focus at the same distance from the focal plane when inserted to the shoulder in the focuser, it follows the magnification will vary accordingly.

The Barlow also increases the FOCAL RATIO of the scope, and the REAL FIELD will change along in ratio.

TRANSMITTANCE is beyond your control other than for cleanliness of optics, but is the ratio of incoming light to light at the focal plane. It is dependent on lens absorption, lens reflections, and reflectivity of mirrors. Mirrors can vary from about 88 percent reflectivity in standard coatings to 98 or more in multilayer coatings. Light absorption in small lenses is minimal, including objectives to about 10 inches or so. However, each surface will reflect some of the incoming light, and the low reflectivity coatings can make a considerable difference.

If each surface in an eyepiece is uncoated, and their are two elements (four surfaces) and each reflects about 5 percent, that's a loss of about 19 percent (.95 X .95 X .95 x .95). If you have a mirror and a diagonal reflecting 88 percent each, there's another loss of 23 percent (.88 X .88). Your total transmittance is down to 63 percent. And that's if all is clean and new. Obviously, coated lenses in eyepieces are a thing. All that reflected light will also cause ghosting and loss of contrast. A three element eyepiece with 98 percent coatings will transmit 88 percent compared to the 81 percent in the two element uncoated.

LIGHT GATHERING POWER is just a a ratio of one optic to another. It is the determined by the square of the ratios of the diameters.

* LGP = (DIAMETER (OPTIC A) / DIAMETER (OPTIC B)) SQUARED

To illustrate, the eye in round numbers is about 1/3" fully opened. A 6 inch telescope will gather (6 divided by 1/3) squared, or 18 squared or about 324 times as much light as the eye.

MAGNITUDES, by convention, is a factor of the fifth root of 100. Rounded off to about 2.5 times per magnitude, this yields..

1 mag = 2.514

2 mags = about 6.3

3 mags = about 16

4 mags = about 40

5 mags = 100

6 mags = about 250 etc etc etc

Obviously 10 mags is a factor of 10,000, and 15 mags is 1,000,000.

Our six inch scope will see to about 12.5 mag (6.5 mags fainter than an unaided eye) on a night when 6th mag stars are visible. This ratio is very much a point of contention, and the factor is more like 1000 in reality. This is about 7.5 mags fainter than the eye can see. I have easily seen beyond mag 13 stars with a 4.5 refractor.

RESOLVING POWER is the ability to perceive close objects as separate entities, and is usually given in seconds of arc. The empirically derived formula is

* RESOLVING POWER (IN ARCSECONDS) = 4.5 / DIAMETER (OBJECTIVE)

* RESOLVING POWER (IN ARCSECONDS) = 115 / DIAMETER (MM)

THE MOON, relative to the stars, moves (on average) just over 12 degrees a day, or 1/2 degree in 60 minutes of time. Since the moon is about 1/2 degree (30 minutes of arc) in diameter, it moves it's diameter in 1 hour. This is about 30 seconds of arc per minute.

THE PLANETS move at all kinds of different speeds due to the earth catching up or dropping behind, and the angle of each. Jupiter moves about 30 degrees per year, and Saturn about 12. Figure out the rest from the orbital period and the Earth's motion.

I'm tired of this for now. More next time.

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