Chapter 6 – The Planets (The Moons of Mars)

Solar System Trek, view the solar system from the skies of any planet on any date
Planetary Ephemeris, trace the planets in the sky for any date
The Moons of Mars, animated presentation of Mars and its moons
Jupiter’s Satellites, identify and name the positions of Jupiter’s four moons on any date
The Rings of Saturn, simulation of Saturn and its rings
Saturn’s Rings, brief outline only
Saturn Draw, a Computer Aided Design
Planets through a Telescope, relative sizes of the planets
Globe-pixel, plots a globe divided at 10° intervals of latitude and longitude
Globe Projection, as before, using lines.

The Moons of Mars

In Gulliver’s Travels, published in 1735, satirical writer Jonathan Swift poked fun at contemporary astronomers by attributing superior instrumentation and discoveries to the mythical people of Laputa. At the same time Swift proved that he was no mean mathematician.

The Laputans discovered (amongst other things) ‘two lesser stars or satellites… revolving about Mars… at a distance of three times and five times the planet’s diameter.. .from the primary’s centre.. .in periods of 10 and 21 hours respectively….’

As the length of the Martian ‘day’ (24hr 37m) was first deduced by Cassini in 1666, Swift was probably fully aware that his fictional nearer moon to Mars would, as seen from the Martian surface, rise in the west and set in the east a few hours later. The second fictional moon would remain virtually fixed in the Martian skies, because the orbital period nearly matched the planet’s rotation period.

142 years later, in 1877, Professor Asaph Hall, using the 26-inch Naval Observatory refractor in Washington DC, turned Swift’s fiction into fact.

He discovered two moons of Mars, the inner moon indeed orbiting the planet faster than the planet’s axial rotation and the outer moon remaining above a given landscape for nearly three Martian days — passing through all its phases from new moon through full moon twice over. The currently recognised synodic orbital period (new moon to new moon) is 7hr 39m for Phobos and 30hr 21m for Deimos.

The screen display
The following program shows most of these factual features in an animated presentation, correct in both scale and relative motion of the three bodies. Incorporated into the display is a unique projection showing the skies as seen from the Red Planet’s surface, together with the changing phases of each moon as they orbit the planet. See Figure 6.4 for a typical display.

Figure 6.4
The positions of Phobos and Deimos are revealed by their shadows as they orbit Mars. Inset is the view from the Martian surface at local noon with the sun due south. Deimos is in the western sky. As in many of the programs in this book, they can only be fully appreciated in animation and colour.

Moons_of_Mars

The viewpoint is from space looking down on the north polar ice cap of Mars. Sunlight shines from the bottom of the screen with the shadow of the globe cast upwards into space. The planet is slowly rotating on its axis as indicated by a flickering line of longitude — the location of our observation post on the surface. Phobos and Deimos orbit the planet and their shadows in turn are cast up the screen into space.

At the bottom right of the screen is the mini-sky projection of the scene from the planet’s surface. The view covers the southern horizon from east to west and the Sun and moons as they pass across the sky, all synchronised to the main display. Inset into the mini-sky projection is the current phase of each moon, marked ‘p’ for Phobos and’d’ for Deimos. Immediately above is indicated the elapse time since the animation started, marked in days and hours.

Phobos and Deimos
The animation starts at a colourful sunset on the first day — Phobos and Deimos are due south and therefore centred in the mini-sky projection. Phobos moves rapidly to the left in overhauling the planet’s rotation and soon sets on the eastern horizon. In contrast, Deimos moves very slowly westwards, remaining in the sky for over 30 Martian hours before setting, being overtaken by the Sun in the process. Phobos will arc across the skies from west to east many times in the days that follow — Deimos only putting in an appearance again at the end of the program RUN.

It is advisable to reRUN the program several times, preferably in colour, to glean the most from the various interacting displays. The following pointers may be of interest.

When an orbiting moon is at the top of the screen, it appears as a fully illuminated disc or full moon. When at the bottom of the screen, between the Sun and Mars, it is said to be a new moon and, because it is effectively unilluminated as seen from Mars, it disappears briefly. If new moon occurs during the Martian daytime then the moon in question will pass briefly near the Sun, as shown on the mini-sky projection. The UDG CHR$ set from CHR$ 144 to CHR$ 159 is defined in the program to show the moons’ phases in 16 steps.

The program RUN time is controlled by the FOR/NEXT n loop in Line 280 and RUNs for 5 days where PI* 10 equals 10 semicircular arcs of planetary rotation STEPped at half hour intervals by STEP PI/24. Test the program with different values instead of 10 and 24 in this line. A RUN longer than 5 days lacks synchronisation for Phobos.

It is also possible to change the size of Mars and the two orbits with the variable scale in Line 110. Currently it is set so as to contain Deimos’s orbit on the Spectrum screen. The variables ‘mars’, ‘ph’ and ‘de’ are the diameter of Mars and the orbital radii of Phobos and Deimos respectively in kilometres, and should not be changed.

10 REM Moons of Mars
20 RESTORE : GO SUB 2000
40 DIM a$(3): DIM d$(13)
50 LET m$=” martian ”
60 LET n$=”Mars Phobos Deimos”
70 LET x=83: LET y=92: LET d=0: LET p=0: LET sky=0: LET sk=1
80 LET h=0
90 LET dd=4.7: LET pp=4.7
100 LET m1=4: LET m2=4
110 LET q=203: LET scale=290
120 LET mars=6790/2/scale
130 LET m=mars-1
140 LET ph=9350/scale
150 LET de=23487/scale
170 BORDER 0: PAPER 0: CLS
180 PRINT AT 12,9;n$;AT 15,22; INK 4;”hour=”;AT 14,22; INK 6;”day =”
190 PRINT PAPER 6; INK 9;AT 16,19;m$+”day “””'”sunlight ^ ^ ^ ^ ^ “; PAPER 2; INK 5;”e–+–s–+–w”
200 LET pa=5: GO SUB 740
220 FOR n=0 TO 9: PRINT PAPER 1;AT n,9;a$: NEXT n
230 OVER 0: CIRCLE x,y,mars
240 FOR n=0 TO PI*2 STEP PI/24
250 PLOT x,y: DRAW INK 2;COS n*m,SIN n*m: NEXT n: PRINT AT 12,5;d$+d$; BRIGHT 1; PAPER 7;AT 10,10;” ”
260 PRINT AT 0,13;n$;CHR$ 127
280 FOR n=0 TO PI*10 STEP PI/24
290 IF h>24 THEN LET h=h-24
300 PRINT AT 15,28;h;” ”
310 BEEP .01,40: LET h=h+.5
320 PRINT AT 14,28;sk-.5;” ”
340 LET cn=COS n: LET cm=cn*m
350 LET sn=SIN n: LET sm=sn*m
360 IF sky/24=INT (sky/24) THEN LET pa=3: GO SUB 740: GO SUB 690
370 GO SUB 850
390 LET dc=COS d: LET ds=SIN d
400 LET pc=COS p: LET ps=SIN p
420 OVER 1: LET ddc=COS dd: LET dds=SIN dd: LET ppc=COS pp: LET pps=SIN pp: LET sky=sky+1
440 LET dx=x+dc*de
450 LET dy=y+ds*de
460 LET px=x+pc*ph
470 LET py=y+ps*ph
490 FOR f=0 TO 1: PLOT x,y: DRAW INK 2;cm,sm: GO SUB 780
500 INK 9
520 PLOT dx,dy
530 DRAW 0,175-dy-(96 AND dyx-13 AND dx<x+13)
540 PLOT px,py
550 DRAW 0,175-py-(96 AND pyx-13 AND px15 THEN LET m1=m1-16
640 IF m2>15 THEN LET m2=0
650 OVER 0: NEXT n
660 PRINT #0; FLASH 1;” Press any key to run again “: PAUSE 0: GO TO 30
690 PRINT AT 16,19;
700 IF skINT sk THEN PRINT PAPER 6; INK 9;m$+”day “: LET pa=5
710 IF sk=INT sk THEN PRINT PAPER 5; INK 9;m$+”nght”: LET pa=1
720 LET sk=sk+.5
740 FOR k=17 TO 20: PRINT PAPER pa;AT k,19;d$: NEXT k
750 INK 9: PLOT 154,9: DRAW 100,0: DRAW 0,30: DRAW -100,0: DRAW 0,-30
760 PRINT BRIGHT 1; PAPER 0; INK 7;AT 20,23;”p d”
770 RETURN
790 INK 9: IF sm<0 THEN PLOT q+cm*4.2,10+ABS sm*2.4: DRAW 0,1
810 IF dds<0 THEN PLOT q+ddc*50,12+ABS dds*20: DRAW 0,1
820 IF pps<0 THEN PLOT q+ppc*50,10+ABS pps*20: DRAW 0,1
830 INK 0: RETURN
850 PRINT PAPER 0; INK 7; BRIGHT 1;AT 20,24;CHR$ (144+ABS m1)+” “+CHR$ (144+m2): RETURN
2010 DATA 0,0,0,12,2,1,12,6,3,12,6,7,12,14,15,12,30,31,28,62,63
2020 DATA 60,126,127,60,126,255,60,126,254,56,124,252,48,120,248
2030 DATA 48,112,240,48,96,224,48,96,192,48,64,128
2050 FOR n=0 TO 15: FOR f=0 TO 1
2060 READ p
2070 POKE USR CHR$ (144+n)+f,p
2080 POKE USR CHR$ (144+n)+7-f,p
2090 NEXT f
2100 READ c: FOR x=2 TO 5
2110 POKE USR CHR$ (144+n)+x,c
2120 NEXT x: NEXT n: RETURN



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