# Chapter 2 – Spheres Within Spheres (Star Point)

The celestial sphere and coordinate positions
Celestial Sphere (3D images), reconstruct a 3D image via the Spectrum
Celestial Sphere (X-eyed 3D), 3D images via your ZX printer
Star Point, find out where a particular star or planet can be found in the sky
Star Tracker, plots a star or planet on a representation of the sky over a 24-hour period.

## Star Point

It is often of interest to know where a particular star or planet can be found in the sky, and this short program does just that. Because of its brevity, it does assume that the star coordinates in terms of Right Ascension and Declination are known beforehand. In the case of a star, a star atlas like Norton will give the information and for a planet reference can be made to Sky & Telescope or the BAA Handbook (see appendix). Alternatively, the planetary positions can be predicted by the Planetary Ephemeris program contained in Chapter 6.

Equatorial to horizon coordinate conversion
What the program does is convert the star or planet’s equatorial coordinate position (RA and Dec) to horizon coordinates in terms of the azimuth and the altitude above that horizon. Figure 2.2, earlier in this chapter, clarifies the inter-related spheres involved. Other relevant facts are the date and the time the observation is to be made and the latitude of the observer. This information is the initial INPUT at the beginning of the program.

The next section of the program, form Lines 80 to 120, works out the sidereal time prior to the INPUT of the star name, etc. The INPUT of the RA takes the form of, for example:

12.56 (12h 56m)

The decimal point must be included. In Line 300, this is converted to hours and decimal hours via the variable rh. The actual conversion to horizon coordinates is executed in Lines 410 and 390 via the variables az (azimuth) and al (altitude).

Using the results
The program results are PRINTed in the final section (Line 440) with the star name and coordinated position in RA and Dec highlighted with PAPER 5. If the star is below the observer’s horizon, then Line 445 FLASHes this information.

The program then provides an option to INPUT a new date or a new star for the existing date. If the latter option is taken, then the GOTO 130 command is effected and the new star’s data has to be INPUT afresh. You will usually require information on a number of stars, and perhaps planets, at a particular date and hour and this option speeds up the process – each successive result SCROLLing up the screen. See Figure 2.3.

Now the azimuth and altitude of perhaps a series of stars is at hand, being either noted or COPYed off the screen – how are they located in the sky? Some ‘field work’ is now essential from a convenient vantage point of perhaps garden or terrace with a fairly unobstructed skyline (see Figure 2.4).

If you choose bright stars for the program, then you should be able to identify them in the sky, with the help of a star atlas or a COPY from the Starmaps program.

Figure 2.3
The azimuth and altitude of Jupiter for the same time on the same day, but from different latitudes. In the upper example, for latitude 63.2N Jupiter has just set (-1°) but from latitude 32.7N it is still 23° above the horizon.

Elusive planet Mercury
Planet Mercury shows us why familiarity with the local horizons is essential. The planet is invariably only visible in a bright sky within a hour of sunset or sunrise, when the stars can give no guidance as to its location. So plotting its position on a star atlas may be pointless.

In the northern hemisphere, the most favourable time of year to find the planet is on a spring evening in the western sky and on an autumn morning before sunrise in the eastern sky.In the southern hemisphere, the favourable seasons for viewing are reversed, ie autumn for the evening appearance and spring for the morning. Mercury is never more than 20° from the Sun.

Mercury’s RA and Dec can be found in the BAA Handbook where the ‘elongation’, or distance from the Sun in degrees, provides useful guidance as to whether a search is likely to be fruitful. Alternatively the Planetary Ephemeris program (Chapter 6) can be used to predict RA and Dec of Mercury and the Solar System trek program (also in Chapter 6) for suitable elongation. Here it is advisable to INPUT a number of dates, say at three-day intervals, before they are transferred to our Star Point program (in case some prove unfavourable).

Note: The famous astronomer Copernicus (1473 – 1543) is reputed never to have seen Mercury despite several attempts to do so. Perhaps the mists that arose from the River Vistula in Thorn, Poland, where Copernicus resided, thwarted him. Using this program, you may have a better chance.

Figure 2.4 A Local Skyline about Midnight
The sketches show the Plough (Big Dipper) and Cassiopeia (the ‘W’) for each season with Polaris (P) midway between and fixed above the north point. The Pole Star’s altitude above the horizon is equal to the observer’s latitude (about 51° for London). Z marks the zenith – directly above the observer’s head.

The dotted line from the ‘Pointers’ should aid identification of Polaris. Suitable landmarks should then be found along the whole horizon for future reference using a fixed vantage point.

9 REM **********************
10 REM AltAz Star Point
11 REM **********************
30 RESTORE : DATA 0,16,16,124,16,16,0,124: FOR f=0 TO 7: READ d: POKE USR “a”+f,d: NEXT f
60 INPUT “Date yyyy,mm,dd”;TAB 5;y;TAB 10;mm;TAB 13;d: IF mm>12 OR d31 THEN GO TO 60
65 INPUT “Local time: hour (0-23) “;th;TAB 12;”min (0-59) “;mi: LET tt=th+mi/60
69 REM **********************
70 REM Julday/Sidereal Time
71 REM **********************
80 LET yy=y: LET m=mm
90 IF m>2 THEN LET m=m+1: GO TO 110
100 LET y=y-1: LET m=m+13
110 LET j=INT (365.25*y)+INT (30.6001*m)+d+1720982
120 LET g=6.63627+6.570982e-2*(j-2443144): LET ts=g-INT (g/24)*24
129 REM **********************
130 INPUT “Star/planet name”, LINE a\$
140 INPUT “Right Asn (hh.mm)”;TAB 11;ra
150 INPUT “Dec (\add.d)”;TAB 5; LINE d\$
160 LET dc=VAL d\$: IF ABS dc>=90 THEN LET dc=dc-.1
180 INPUT “Your lat (\all.l)”;TAB 10; LINE l\$
181 REM **********************
190 LET l=VAL l\$: IF ABS l>=90 THEN LET l=l-.1
280 PRINT PAPER 5;a\$;” RA=”;ra;” Dec=”;d\$
290 PRINT d;”/”;mm;”/”;yy;”:”;th;”h “;mi;”m lat=”;l\$;”\’ ”
300 LET c=360: LET r=180/PI: LET lr=l/r: LET f=100/60: LET dr=dc/r: LET rh=INT ra+(ra-INT ra)/f
310 LET t=tt
330 LET s=t+ts+t/1436*4
340 IF s>24 THEN LET s=s-24
350 IF s0 THEN LET az=c-az
440 PRINT “Sidereal time (LST) “;: LET h=st: GO SUB 530: PRINT PAPER 6;”Azimuth=”;INT (.5+az);”\’ “,”Altitude=”;INT (.5+al);”\’ ”
445 IF al<0 THEN PRINT FLASH 1;”Star below horizon”
469 REM **********************
470 REM select
471 REM **********************
480 PRINT #1;”Key C=copy D=new date S=new star L=new latitude”
485 PRINT “——————-”
490 PAUSE 0: LET b\$=INKEY\$
500 GO TO (b\$=”l”)*180+(b\$=”c”)*510+(b\$=”s”)*130+(b\$=”d”)*60
510 COPY : GO TO 490
519 REM **********************
520 REM decimal hrs=hr mn
521 REM **********************
530 PRINT INT h;”h”;INT ((h-INT h)*60+.5);”m”: RETURN
9900 REM **********************
9990 SAVE “starpoint” LINE 1