Chapter 6 – The Planets (Jupiter’s Satellites)

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.

Jupiter’s Satellites

In 1609, Galilei Galileo in Italy applied his newly-constructed telescope (invented by Han Lippershey in Holland the previous year) to the study of the heavens. His announcements astounded the civilised world but dismayed the Church.

One discovery in particular caused the gravest consternation with the authorities: ‘the planet Jupiter had four attendant moons orbiting it…’ — proof that not all heavenly bodies encircled the Earth and that the Earth (and especially the Vatican) was not the centre of the universe. At a time when science had reached a high pinnacle in Europe, Italy became isolated from the discussions for many decades thereafter. Today everyone can enjoy the thrill of discovering the moons of Jupiter with a modest pair of binoculars, and this program will help you do so.

Despite the modest length of this ephemeris-type program, it is accurate enough for you to identify and name the four moons for whatever date and hour you choose. The predictions prove virtually identical to those published in Sky & Telescope and the BAA Handbook, both authorities on this type of work.

Plotting the moons
The program has a good display and screen layout, best seen in colour. Once the program has been keyed in and RUN, the chosen date is requested of you for INPUT. You then have the option of computing and displaying the position of the moons for that date at two-hour intervals or for each day at midnight (0 hours universal time) for a period of twelve days. The layout (see Figures 6.5 and 6.6) is such that you can see the various moons ‘swaying’ back and forth across the planet Jupiter, fixed in the centre line of the screen display.

The bi-hourly motion of the moons is quite small but noticeable, particularly for the inner moons Io and Europa. The daily motion of the moons (with an INPUT of’d’) is very marked in comparison and to help you identify each moon the ‘configuration’ as it is called, is displayed against each prediction as a series of numbers plus the letter ‘J’ for Jupiter. The numbers represent the order of the moons from Jupiter, 1 = Io, 2 = Europa, etc. Of course from Earth, for which this program computes the apparent position of each moon, the order of the configuration may seem jumbled, 132J4, caused by viewing the Jovian system edge-on. A bird’s-eye view would show all the moons following neat circles about Jupiter and maintaining their order of 1, 2, 3, 4 from the planet.

Finding Jupiter in the sky
The planet Jupiter is currently visible low in the south-west skies from Britain and the rest of the northern hemisphere, after dusk and can be seen each summer and autumn night for some years to come low in the southern aspect. (The prospect for the southern hemisphere is even more favourable.) It is the brightest ‘star’ in that region of the sky — a powerful pair of binoculars or a small telescope will show the planet as a tiny disc and the moons in attendance as points of light shifting hourly and daily in time with your program. If the evening you choose to use this program is cloudy and you have a ZX printer why not make a COPY — the program contains this option — against INPUT’d’ and save it for when skies clear.

Figure 6.5
The positions of Jupiter’s moons for one selected day at 2-hour intervals

Jupiters_Satellites_110585

Figure 6.6
This plots the moons for a 12-day period. The daily motion of the moon is much more pronounced.

Jupiters_Satellites_070684

10 REM Jupiter’s Satellites
20 BORDER 0: PAPER 0: INK 9: CLS
30 DIM x(5): DIM t$(5): DIM x$(30)
40 DEF FN z(i)=i-360*INT (i/360)
50 LET t$=”1234J”: LET s$=””
60 LET r1=PI/180
70 LET m$=”JanFebMarAprMayJunJulAugSepOctNovDec”
90 PRINT PAPER 5;AT 1,1;”Galilean Satellites of Jupiter”
100 INPUT “Year: “;yr
110 PRINT ‘” Year = “;yr
120 LET d$=STR$ yr
130 INPUT “Month (1-12): “;mh: IF mh12 THEN GO TO 130
140 LET m$=m$(mh*3-2 TO mh*3)
150 PRINT ” Month= “;m$
160 LET d$=d$+” “+m$
170 INPUT “Day: “;dy: IF dy31 THEN GO TO 170
180 PRINT ” Day = “;dy
190 PRINT ” Interval period=”;
200 INPUT “Hours or days (h/d)? “; LINE a$
210 IF a$=”h” THEN PRINT “2 hrs”
220 IF a$”h” THEN PRINT “daily”
230 PRINT #0; FLASH 1;” Date OK (y/n)?”: PAUSE 0: IF INKEY$=”n” THEN GO TO 10
240 LET d$=d$+” “+STR$ dy
260 CLS
270 PRINT PAPER 5;AT 1,1;”Galilean Satellites of Jupiter”
280 PRINT INK 4;AT 3,1;”Configuration key:”,” 1:Io 3:Ganymede”,” 2:Europa 4:Callisto”
290 PRINT PAPER 5; INK 1;AT 3,20;d$+(” ” AND LEN d$<11)
300 INK 6: PRINT AT 7,1;”Confg”
310 PRINT AT 7,27;(“UThr” AND a$=”h”)+(” day” AND a$”h”): INK 9
320 PRINT INK 3;AT 7,14;”South”;AT 14,0;”W”;AT 14,31;”E”;AT 21,14;”North”
340 LET m=mh: LET y=yr
350 IF mh>=3 THEN GO TO 370
360 LET m=m+12: LET y=y-1
370 LET f=INT (y/100)-INT (y/400)
390 LET a=INT (365.25*(y+4712))-2415020
400 LET b=INT ((367*(m-1)+5)/12)
420 LET hr=0: FOR c=0 TO 12
430 LET d=dy+hr/24+a+b-f-.5
450 LET m=FN z(358.476+.9856003*d)
460 LET n=FN z(225.328+.0830853*d)
470 LET j=FN z(221.647+.9025179*d)
480 LET aa=1.92*SIN (m*r1)+.02*SIN (2*m*r1)
490 LET bb=5.537*SIN (n*r1)+.167*SIN (2*n*r1)
500 LET k=j+aa-bb
510 LET delta=SQR (28.07-10.406*COS (k*r1))
520 LET psi=ASN (SIN (k*r1)/delta)/r1
530 LET u1=FN z(84.5506+203.405862*(d-delta/173)+psi-bb)
540 LET u2=FN z(41.5015+101.291632*(d-delta/173)+psi-bb)
550 LET u3=FN z(109.977+50.2345169*(d-delta/173)+psi-bb)
560 LET u4=FN z(176.3586+21.4879802*(d-delta/173)+psi-bb)
570 LET x(1)=5.906*SIN (u1*r1)
580 LET x(2)=9.397*SIN (u2*r1)
590 LET x(3)=14.989*SIN (u3*r1)
600 LET x(4)=26.364*SIN (u4*r1)
610 LET x(5)=0
630 PAPER 1
640 PRINT AT c+8,1;x$;AT c+8,16; INK 6;”o”
650 PRINT AT c+8,28;
660 IF a$=”h” THEN PRINT (” ” AND hr<10);hr
670 IF a$”h” THEN PRINT (” ” AND dymax THEN LET max=x(n): LET t=n
730 NEXT n
740 LET s$=s$+t$(t): LET x(t)=-50
750 NEXT o
760 PRINT PAPER 1;AT c+8,1;s$: LET s$=””
770 PLOT 8,104-c*8: DRAW 239,0
780 IF a$”h” THEN LET dy=dy+1
790 IF a$=”h” THEN LET hr=hr+2
800 BEEP .1,30: NEXT c
820 PRINT #0;” Press c to COPY, r to RUN”: PAUSE 0
830 IF INKEY$=”c” THEN LPRINT : COPY : INPUT “”: GO TO 820
840 RUN



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