Chapter 5 – Solar System Orbits (Halley’s Comet)

Orrery, simulates the scale and relative movement of the planets about the Sun
Bode’s Law
Kepler’s Orbits, demonstrates the first two of Kepler’s Laws
Orbit Foci, plotting the second focus
Comet Orbit, eccentric orbits
Halley’s Comet, depicts one complete orbit, 1948-2023
Pluto’s Orbit, plots the relative positions of Pluto and Neptune from 1880-2128, one complete orbit for Pluto
Solar Apex, corkscrew motion of a planet towards the Solar Apex.

Halley’s Comet

Halley’s Comet is without doubt the most famous comet of all time and, as a visit to our part of the solar system is due shortly, a program would not be inappropriate.

1066 and all that
Edmund Halley (1656 – 1742) did not discover this comet but was the first to notice that the bright comets seen in 1531,1607 and 1682 had practically identical orbital data and were one and the same object reappearing in the skies about every 75 years.

Halley’s Comet can now be traced back to 611 BC, via Chinese records, but perhaps the most famous reference of all in European history is its depiction in the Bayeux Tapestry of 1066 with the inscription of INTIMIRANT STELLA. Every return of the Comet since King Harold’s reign has been recorded and this is most unusual as the longevity of comets is measured in hundreds rather than thousands of years. This indicates that Halley’s Comet is a substantial body able to survive repeated visits to the inner solar system and the relatively great heat radiated upon it from the Sun.

You should be asking the question: How do comets survive repeated crossings of all the planets without collison? Well, comets (or rather, the survivors after over 5000 million years) have learned to avoid the orbital plane which all planets occupy with highly-inclined orbits. The comet crosses this danger zone for only a few days each perihelion passage.

The program
The program depicts one complete orbit of Halley’s Comet beginning in 1948 _ the year the Comet started its current journey towards both Earth and Sun from beyond the orbit of Neptune. The Comet will return to this aphelion position again in about 2023. The perihelion passage occurs on 10th February 1986 and the program PAUSEs briefly at this point. (See Figure 5.11.) During mid-November 1985 the comet is a binocular object below the Pleiades.

This program is a variation of the Comet Orbit program, but uses one specific orbit produced by the line LET w = 4.5. Again, only one half of the orbit is computed and PLOTted — the inward journey — but each x and y coordinate position is entered into two arrays, x(t) and y(t). These are then used in a second FOR/NEXT loop to PLOT the Comet’s journey back into deep space.

It is necessary to add PAUSE 10 to this second FOR/NEXT loop to slow the PLOTting down to the same speed as the first loop. This indicates the rapidity with which the Spectrum can PLOT pixel positions once the actual position has been computed and SAVEd in an array. Try pressing any key to cancel the PAUSE statement to see what happens.

Screen display
At the top of the screen is denoted the current year against the Comet’s progress — the Comet itself is PLOTted in a different coloured pixel for the inward and outward journeys (for clarity) using inverse graphics on a black screen (BORDER 0: PAPER 0: INK 9).

Figure 5.11
The path of Halley’s comet over a 75-period. Closest approach to the Sun occurs in February 1986.

Halleys_Comet

10 REM Halley’s Comet
20 BORDER 0: PAPER 0: INK 7: CLS : PAPER 5: INK 9
30 PRINT ” Halley’s Comet year= “; FLASH 1;” ”
40 PAPER 1
50 PRINT AT 11,1;”Sun”
60 PLOT 40,80: GO SUB 390
70 PAPER 5
80 LET w=4.5
90 DIM x(170): DIM y(170)
100 LET h=.212: LET g=1e6
110 LET x=g/1e3: LET y=0
120 LET i=h/4: LET v=0
130 LET r=x: LET s=y: LET z=0
140 LET x=x+i*v: LET y=y+i*w
150 GO SUB 230
160 FOR t=1 TO 170
170 LET yr=1948+INT (t/4.5)
180 PRINT AT 0,26;yr
190 LET x=x+h*v: LET y=y+h*w
200 GO SUB 230
210 LET v=v+h*b: LET w=w+h*c
220 GO SUB 260: NEXT t: STOP
230 LET e=x*x+y*y: LET d=SQR e
240 LET a=-g/e: LET b=a*x/d
250 LET c=a*y/d: RETURN
260 PLOT INK 4;40+x/5,y/5+80
270 LET x(t)=x/5: LET y(t)=y/5
280 IF y<0 THEN GO TO 300
290 RETURN
300 PLOT OVER 1;40+x/5,y/5+80
310 PRINT #0; FLASH 1;” Comet at perihelion passage ”
320 PAUSE 300: INPUT “”
330 FOR t=169 TO 1 STEP -1
340 LET yr=2023+INT (-t/4.5)
350 PRINT AT 0,26;yr
360 PLOT INK 6;40+x(t),-y(t)+80
370 PAUSE 10: NEXT t: STOP
390 CIRCLE 40,80,8
400 CIRCLE 40,80,40
410 FOR n=1 TO 3: READ a,b: PLOT 40+a,20: DRAW 0,120,b: NEXT n
420 PRINT AT 13,1;”Earth”
430 PRINT AT 18,1;”Jupiter Saturn Uranus Neptune”: RETURN
440 DATA 40,2,105,1.1,160,.9

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