Chapter 5 – Solar System Orbits (Pluto’s Orbit)

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.

Pluto’s Orbit

On 21st January 1979, Pluto relinquished to Neptune the dubious honour of being the most remote planet from the Sun by crossing within Neptune’s orbit. Pluto will regain the ‘title’ in March 1999 by once more crossing Neptune’s orbit — this time in an outward direction.

A collision between the two planets is unlikely as Pluto’s orbit is inclined 17° to the general plane of the planets including Neptune. During this twenty-year period, Pluto will pass up to 10 AU (10 astronomical units = 10 x Earth to Sun distance) above Neptune’s orbit — a gap almost big enough to contain the complete orbit of the giant planet Jupiter. The planets Pluto and Neptune are themselves well separated — Neptune last overtook Pluto in the 1890s as each moved ponderously along its orbital track in periods of 165 years and 248 years respectively.

Screen display
The following program PLOTs to scale the relative positions of Pluto and Neptune from the year 1880 to 2128 — one complete orbit for Pluto. Both a plan and a section are displayed of the overlapping orbits, with a tiny flashing CIRCLE in the centre representing the Earth’s orbit (at the very centre of which is, of course, the Sun). The passing years are recorded in the top right of the screen and Pluto is PLOTted in a green pixel (a darker shade in monochrome) on a black background (PAPER 0: BORDER 0:) for clarity. The display PAUSEs briefly to PRINT six significant comments against specific dates relevant to the progress of the two planets.

Pluto’s elliptical orbit
Neptune’s orbit has the lowest eccentricity of all the planets, being a near-perfect circle. Because of this, its program requirements are minimal — just Line 340 both to calculate and PLOT its orbit, where variable f is used to increment the PLOT position.

In contrast, the bulk of the program from Line 110 is used to calculate Pluto’s elliptical orbit, which has the highest eccentricity of the major planets with a value of 0.25. Pluto moves faster when closest to the Sun (by wider spacing of the PLOT positions) but, because this presentation is to scale and overlaps Neptune’s orbit, it may not be obvious at this time.

Lines 300 and 310, both of which PLOT Pluto’s orbital progress, appear almost identical except for the expression at the end of Line 310:

“…y/200 + 10 ”

where /200 effectively compresses the y or vertical axis by a factor of 200 so that, instead of a second full ellipse being PLOTted, it is reduced to a near edge-on view of the orbit as shown in the lower part of the display.

Experiments with Pluto display
Once the program has been RUN a few times, using the screen COPY (Figure 5.12) to check that it works correctly, SAVE the program on tape. Now try changing some of the variables to see what effect it has. (These amendments will invariably corrupt an accurate presentation which is why the program should be SAVEd first.)

Figure 5.12
The orbits of Pluto and Neptune from two viewpoints.

Plutos_Orbit

The following variables can be tested for effect:
xx   x coordinate (horizontal) of the Sun
yy   y coordinate (vertical) of the Sun
f     position and increment steps to PLOT Neptune (Lines 110 and 340)
h    STEP value to main FOR/NEXT loop
t     FOR/NEXT main loop starting at value 0 (3 o’clock start)
w    relative eccentricity of Pluto’s orbit

The value 13 (Lines 300 and 310) and the value 55 (Line 340) control the radius of each planet’s orbit.

10 REM Pluto’s Orbit
20 LET t=0: BORDER 0: PAPER 0: INK 7: CLS : GO SUB 400
30 PRINT INK 5;”Pluto’s Orbit”
40 PRINT AT 11,0;”plan”;TAB 16;”Sun”;TAB 25; INK 5;”Pluto”
50 PRINT AT 15,14;”Neptune”
60 PRINT ”””edge-on”‘” view”
70 LET xx=140: LET yy=92
80 PLOT xx-55,0: DRAW 110,20,.1: DRAW -110,-20,.1
90 CIRCLE FLASH 1;xx,yy,2
100 CIRCLE FLASH 1;xx,10,2
110 LET f=12.3: LET w=28.7
120 LET h=.8: LET g=1e6
130 LET x=g/1000: LET y=0
140 LET i=h/4: LET v=0
150 LET r=x: LET s=y
160 LET x=x+i*v: LET y=y+i*w
170 GO SUB 260
180 LET x=r: LET y=s: LET o=h/2
190 LET v=v+o*b: LET w=w+o*c
200 GO SUB 300
210 FOR t=0 TO 155 STEP h
220 LET x=x+h*v: LET y=y+h*w
230 GO SUB 260
240 LET v=v+h*b: LET w=w+h*c
250 GO SUB 300: NEXT t: STOP
260 LET e=x*x+y*y: LET d=SQR e
270 LET a=-g/e: LET b=a*x/d
280 LET c=a*y/d: RETURN
300 PLOT INK 4;x/13+xx,y/13+yy
310 PLOT INK 4;x/13+xx,y/200+10
320 LET tt=1880+INT (t*1.6): PRINT AT 0,20;”year=”;tt
340 PLOT BRIGHT 1;xx+COS f*55,yy+SIN f*55: LET f=f+.05
360 IF tt=1888 OR tt=1929 OR tt=1979 OR tt=1999 OR tt=2040 OR tt=2127 THEN GO SUB 500
370 RETURN
410 LET b$=”1889 – Neptune ‘overtakes’ Pluto”
420 LET c$=”1930 – Pluto discovered”
430 LET d$=”Pluto inside Neptune’s orbit Jan 1979″
440 LET e$=”Pluto outside Neptune’s orbit Mar 1999″
450 LET f$=”Neptune completes orbit: 164 yrs”
460 LET g$=”Pluto completes orbit: 248 yrs”
470 DIM a$(40): RETURN
500 PRINT BRIGHT 1;AT 1,0;(b$ AND tt=1888)+(c$ AND tt=1929)+
(d$ AND tt=1979)+(e$ AND tt=1999)+(f$ AND tt=2040)+
(g$ AND tt=2127)
510 PAUSE 250: PRINT AT 1,0;a$: RETURN

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