# Chapter 6 – The Planets (Saturn Draw)

## Saturn Draw

For the dedicated Saturn observer it is usual to prepare an outline of the planet and ring system for use at the telescope. The most difficult aspect in sketching the planet is getting the ring geometry correct. Much precious telescope time can be wasted in attempting to draw these subtle ellipses — a test for the most skilled draughtsman. In case those unfamiliar with planetary observation suspect that the following program will obviate the need to go to the telescope at all, this is not so. There are many subtle shadows and shadings and divisions in the rings to be recorded — the program is merely an aid, and great fun even if you are not a telescope enthusiast.

This short program, based on the Saturn Rings routine, is designed for use with the ZX printer by drawing standard outlines measuring 100 mm across the ring system major axis for subsequent tracing. Because the ZX printer cannot cope with this full width, the left hand edge of the ring system has been folded.

The planet can be tilted up to 27.22° and the program accepts 0° to 28° for INPUT. Negative values cannot be entered and in any case are unnecessary as the globe is transparent. Correction for globe oblateness according to the tilt has been carefully applied and the ring systems represent the outer edge of ring A (largest ellipse) and inner edge of ring B (smallest ellipse) respectively. Figure 6.9 is a typical COPY from the program.

Figure 6.9
Copy from the ZX printer as a standard outline for sketching Saturn through a telescope.

Computer Aided Design
If you wish to have a permanent record of the appearance of Saturn through every possible phase over a 29½-year orbital period, covering the axial tilt from 0° to 28°, make the following minor modifications to the program so that the Spectrum with printer does it automatically. You will need about 2 m (6½ ft) of ZX printer paper for the 29½ COPYs. Amend Line 170 to read:

170 NEXT f: NEXT n: COPY: CLS: LET z = z+ 1: GOTO 40

Now press

RUN ENTER 0 ENTER

and your Spectrum will make a fine and effortless job of Computer Aided Design (CAD). The computer is best left to its own devices as it takes about 5 minutes to PLOT each image before it is COPYed. The PLOT time can be reduced to about 90 seconds per image if only the outer and inner rings are drawn, with wider spacing between the PLOT positions. For this, the STEPs in the two FOR/NEXT loops in Lines 120 and 130 need modification as follows:

120… STEP .5 130… STEP .04

If you are unhappy with the left portion of the ring system being folded, then the whole image can be rescaled so that it is contained on the screen, by changing the variables in lines 80 and 90:

x = 255/2
r = 60*.9
h = 140*.9

10 PRINT “Saturn Draw “;
30 INPUT “Tilt (0” CHR\$ 130; “to 28″; CHR\$ 130;”)”,z
40 IF z>28 THEN GO TO 30
50 LET ob=1.1*z/100
60 PRINT “Tilt=”;z;CHR\$ 130
70 LET e=1/SIN ((.1+z)/180*PI)
80 LET x=115: LET y=88
90 LET r=60: LET h=140
100 GO SUB 190
120 FOR n=1 TO 1.6 STEP .1
130 FOR f=0 TO PI*2 STEP .02
140 LET sx=INT (SIN f*h)
150 LET cy=INT (COS f*h/e)
160 PLOT x+sx/n,y+cy/n
170 NEXT f: NEXT n: STOP
190 PLOT 0,y: DRAW 255,0
200 PLOT x,10: DRAW 0,155
210 FOR f=0 TO PI*2 STEP .02
220 PLOT INT (x+SIN f*r),INT (y+COS f*r*(.89+.11*ob)): NEXT f
240 FOR f=PI*.5 TO PI*1.5 STEP .1: PLOT x+SIN f*r,y+COS f*r/e
250 NEXT f: RETURN