Chapter 9 – Further Programs (Telescope)

The Messier List, check out the fake comets
Telescope, the facts about telescopes, binoculars, cameras and astronomy
Star Tester, a quiz
Ellipses, various ellipses
Spectrum World Map, a map of the world in CHR$ CODE.


This program sets out to answer the following questions:

  1. What is the faintest star visible in a 6 cm or a 6 m telescope?
  2. What is the maximum and minimum useful power eyepiece to use?
  3. Why is the Hale 5 m telescope not suitable visually?
  4. What sort of area in degrees will a 35 mm camera lens cover?
  5. What is the photographic and visual resolution of a 15 cm telescope?
  6. What astronomical performance can I expect from my telescope/camera?

The last question summarizes most of the previous questions.

The answers
There is nothing particularly special about this program other than the fact that it brings together all the facts and figures pertinent to telescopes, binoculars and cameras, when used for astronomy. Only two items have to be INPUT — the aperture of the instrument in millimetres and the f/ratio as it is called. The latter is the ratio of the diameter of the lens (of the camera, for example) against the focal length and this in turn is the distance from the lens to the image the lens forms. From these two INPUTs a lot of data can be computed in just one second that would need a library of books to reference. Just key in the program and RUN it.

The program
The program is based on my own many years of practical experience at the telescope. Only one item — the visual or Dawes resolving power of a telescope — assumes a perfect instrument, perfectly aligned on a perfect night free from atmospheric turbulence (twinkling stars) and an experienced eye. The balance of the items is either reasonably indisputable (like the power of a given eyepiece) or not too contentious (like the limiting visual magnitude attainable on a clear night away from town lights).

Figure 9.3 shows a screen COPY for an f/4 120 mm focal length camera lens and Figure 9.4 a screen COPY for my own telescope. It may be useful to go through each sample and the relevant program lines to explain the significance of the data.

Figure 9.3
Astro performance of f/4: 120 mm fl lens.

Figure 9.4
Astro performance of a 44.4 cm (17.5 inch) aperture telescope.

The first two lines of the printout are the INPUT of aperture and f/ratio and these, multiplied together, produce the third line — focal length. The next two lines are the maximum and minimum power eyepieces for the system and their respective focal lengths. It will be noted that the next line in Figure 9.3 for the camera lens comments: “This lens not suitable visually”

This is worked out by slicing the A$ and T$ in Line 20 according to the conditional Lines 170 and 180. In this case the focal length is less than 300 mm and therefore not identified as a telescope.

The next group of four items specifically refers to the photographic performance of the instrument. The items are, in order, the ‘plate scale’ or number of seconds of arc per mm of film, the area in degrees for a 35 mm format camera, the resolving power of TRI-X film in seconds of arc and, finally, the faintest star normally recorded in a guided exposure before skyfogging (stray light) sets in. The next group of two items refers to the visual resolving power (to Dawes formula) in seconds of arc and the limiting visual magnitude the instrument will show. Notice how a given lens or telescope will record stars on film to 1.5 magnitude less than the eye will record at the same instrument. This is because the eye (when fully adapted to dark conditions) sees no more after about quarter of a second, however much you peer through the eyepiece, whereas the photographic film slowly builds up an image over seconds, minutes and even hours in perfect conditions. The human eye’s sensitivity is much superior to the fastest 1000 ASA film but tires easily. Also the eye’s resolving power — pixel for pixel — is again superior to all but the slowest film, say 20 ASA.

The final section of the printout gives some typical focal length eyepieces and notes the effective powers with the lens concerned. This is done by the FOR/NEXT loop in Lines 250 to 270. An option to COPY the screen is included on Line 290.

Interpreting results
Practical experience would indicate that any telescope magnifying more than x 500 is pointless. The Earth’s atmosphere is never steady enough to support such a magnification and remain sharp and clear. Line 100 sets this upper limit: otherwise Line 90 assumes that the aperture (in mm) x 2 is the upper limit. The lowest useful power eyepiece is set by the maximum diameter of the human pupil, 7 mm when adapted to dark. I have adopted a diameter of 6 mm from practical experience of numerous tests. Effectively, if the eyepiece power is too low, not all the light entering the telescope reaches the retina because of the physical limit to the diameter of the eye’s iris.

In the case of the Hale 200-inch telescope at Mt Palomar with a clear aperture exceeding 5000 mm, a minimum power eyepiece exceeding x 750 would be necessary for all the light to enter the eye for the reason mentioned above. This giant telescope is not for looking through but is a huge camera for peering into the most remote regions of the cosmos.

The following variables carry the various formulae used in the program:

A = the clear aperture in mm
F = the focal ratio of system
FL = the focal length of system in mm
L = lowest useful power eyepiece
H = highest useful power eyepiece
V = limiting visual stellar magnitude P = plate scale in ” arc/mm

The two last variables are also used for the following:

P/100 = field width in degrees
P/50 = TRI-X film resolving power in ” arc/mm
V + 1.5 = limiting photo magnitude 114/A = Dawes visual resolution

5 REM Telescope Performance
15 PLOT 0,167: DRAW 255,0
20 LET a$=”not suitable visually”: LET t$=”Telescope This lens ”
30 PRINT “Aperture (mm) =”,
40 INPUT a: IF a500 THEN LET h=500
110 LET v=1.9+INT (LN (a*a)*11)/10
120 LET p=INT (206264/fl)
130 PRINT “Focal Length =”,fl;” mm”
139 PAPER 6
140 PRINT INT (fl/l+.5);”mm fl ep =”,”x”;l;” min power”,
150 PRINT INT (fl/h*10)/10;”mm fl ep =”,”x”;h;” max power”,
160 IF l>=h THEN PRINT FLASH 1;t$( TO 10);a$,
170 IF l=25 AND fl>=300 THEN PRINT FLASH 1;t$( TO 10);a$(5 TO ),
180 IF l<h AND (a<25 OR fl<300) THEN PRINT FLASH 1;t$(11 TO );a$,
190 PAPER 5: PRINT ,,”Plate scale”,p;” “”arc/mm”,
200 PRINT “Field (26x24mm)”,INT p/100;”[G]2 x “;INT (p*2/3)/100;”[G]2 “,
210 PRINT “Res photo Tri-X”,INT (p*2)/100;” “”arc”,
220 PRINT “Limit photo mag”,”+”;v+1.5,
229 PAPER 6
230 PRINT ,,”Res(Dawes)visual”;INT (11400/a)/100;” “”arc”,
240 PRINT “Limit vis mag”,”+”;v,,,
250 FOR n=1 TO 6 STEP 1.5
260 PRINT PAPER 6;”Eyepiece fl = “,(” ” AND n=1);6*n;”mm = x”;INT (fl/6/n),
270 NEXT n: PAPER 7
280 PRINT #0;”Press ‘z’ to COPY, ‘r’ to RUN”: PAUSE 0
300 RUN

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