Chapter 6 – The Planets (Globe-pixel)Posted: March 29, 2013
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.
Since the invention of the telescope and the discovery that the planets are worlds similar in shape to our Earth, astronomers have sliced up each globe into the homely lines of latitude and longitude with a north and south pole and an equator. Of the giant gas planets Jupiter, Saturn, Uranus and Neptune, only Jupiter and, to a lesser extent, Saturn have such systems of any practical interest. No positive markings (other than banding of polar and equatorial regions) have been detected on Uranus and Neptune due to their extreme remoteness. Only rarely does Saturn reveal any identifiable markings that are carried across the disc by the planet’s rotation. This leaves the relatively close (typically four to six times the distance of the Sun) planet Jupiter. A wealth of detail is visible on the disc in amateur telescopes but there is a snag.
Jupiter, being a rapidly spinning gas world, has no fixed reference point — only the constantly shifting cloud top is revealed. Also the rotation of the equatorial cloud zone is faster than at higher latitudes, and the planet is distorted from a neat sphere to an oblate spheriod shape. Thus, although a grid system of latitude and longitude is possible via the Spectrum graphics which even accounts for the oblate shapes of Jupiter and Saturn, it was not quite what we had in mind. A journey closer to Earth is called for.
Mars, Mercury and the Moon
The four inner planets from Mercury to Mars (including Earth) all have rocky surfaces. Only Venus with her permanent cloak of dense cloud is unwilling to reveal all. To this foursome, the Moon should be added as Earth’s twin planet. All are ripe for dissection into neat parcels of latitude and longitude as a globe projection. The two that are of practical interest to amateur astronomers are the Moon, somewhat obviously, and Mars. Mars is the only planet apart from Earth where the changing seasons and rotation-carrying surface markings across the disc can be seen using a back-yard telescope. The two programs that follow are particularly useful in converting the normal flat Mercator-type projection of, say, Mars’s maps to that of a globe — making for easier recognition of features, especially when displayed in the limb regions, ie adjacent to the disc edge.
The short Globe-pixel routine can be used to PLOT a globe divided at 10° intervals of latitude and longitude. Figure 6.11 is a COPY from the screen. The scale of the COPY to the ZX printer gives a 5 cm diameter disc — the diameter recognised by amateur specialist observers of Mars and Venus for sketching these planets as basic outlines.
Globe accurately plotted at 10° intervals of latitude and longitude.
The program uses two FOR/NEXT loops to PLOT each pixel — the z loop for the lines of longitude (vertical lines) and the n loop for the lines of latitude (horizontal lines). The results are precise and accurate as presented to the screen and to the ZX printer. The separation of each pixel is controlled by the STEPs in the FOR/NEXT loops as follows:
FOR z= .001 TO 91 STEP 10
where STEP 10 is for each 10° of longitude. Note that although these STEPs are at precisely 10° intervals, the actual value returned has the sequential value of:
.001, 10.001, 20.001, 30.001, 40.001, etc.
Adding .001° (1/1000 degree or 3.6″ (seconds) arc) has no visible effect on the PLOTted positions but does ensure that the program will not crash trying to evaluate the SIN of 0° – an infinite number. The n loop takes the form:
FOR n = 0 TO PI*2 STEP 1 /r* 10 (latitude lines)
where PI*2 gives a full circle and STEP 1/r*10 equals a STEP interval of 0.175 from (1/(180/PI))*10 producing the required 10° spacing in latitude.
The lines of latitude are parallel to the equator whilst the curved lines of longitude originate from the poles. The latter PLOTting is controlled by the variable c in Line 60 to produce the curvature in Line 90.
With a very minor amendment to the program it is possible to simulate Jupiter’s oblate globe — in this case, expanding the equatorial regions and leaving the polar or vertical dimensions unchanged. Amend the following line:
90 LET b = COS n*80/c* 1.08
It is the last value in the expression, ie * 1.08, that does the necessary expansion. Figure 6.12 shows Jupiter’s shape.
The oblate figure of planet Jupiter shown by reducing the STEP value to 1 in the z FOR/NEXT loop.
3 REM Globe-pixel
10 BORDER 0: PAPER 0: INK 5: CLS
20 PRINT PAPER 1;”Globe-pixel at 10″; CHR$ 130;” intervals ”
30 LET r=180/PI
40 FOR z=.001 TO 91 STEP 10
50 PRINT INT z;CHR$ 130
60 LET c=1/SIN (z/r)
70 FOR n=0 TO PI*2 STEP 1/r*10
80 LET a=SIN n*80
90 LET b=COS n*80/c
100 PLOT INK 6;INT (137+b),INT (85+a)
110 NEXT n: NEXT z