The ancients didn't use the stars much for time keeping because it's much more complicated than using
the sun or moon. Planets wander around, comets zip around. And, there are so many stars!
But, all those stars must mean something, so **...**

to start:

- Pick a bright star (one you can see). To resonate with the Ancient Mysteries Of The Pyramids, use Sirius, alpha Canis Majoris, the brightest star in the sky. The Old Kingdom Egyptians used it to predict when the Nile would flood (and probably to play Senet too).
- Then, learn the astronomical coordinate system so you can find Sirius, (For finding stars and planets, nothing beats an iPad - there's an app that uses the built-in hardware to show the sky where you point it, anywhere in the world.)
- get familiar with sidereal time - the crab-like rotation of the earth relative to the stars, and how to find it from the date or on line, and
- find your latitude and longitude, from a map or on line.

At this point, you can calculate a current star time-of-day. But, since the stars are forever, you should extend your calculation for more than a few mere centuries from the present. So, you really must

- read a bit about calendars, particularly the roots of our present one.

- learn about the non-spherical shape of the earth, and
- learn basic spherical trigonometry (cosine and sine rules) so you can
- calculate the precession of the earth's rotation about the pole of the ecliptic,
- calculate the proper motion of Sirius, and
- check out the PALEOMAP Project, to understand how much the earth's surface flows around. (The continental plate on which the pyramids sit is not perceptibly rotating, but your plate may be.)

Then, you have to choose your data. Here is where I got mine:

- station longitude and latitude: 1:50000 topographical map (Geological Survey of Canada)
- Sirius coordinates: on line
- Sirius proper motion: Hipparcos Catalogue Vol.1 Table 3.6.1
- precession eccentricity: Astronomie populaire Flammarion (1960)
- precession mean period: a value attributed to "Stockwell" in a reference I've misplaced
- sidereal time coefficients: Explanatory Supplement to the Astronomical Almanac p.50

Based on this data, it appears that the current Sirius year began approximately at 0540 UT 25 August 9967 BC Gregorian, and will have a length of about 9 327 011.52 Sirius days.

Further work is planned to refine these values and to organize this year into suitable subdivisions.

10 REM Calculate Sirius Time 20 REM The Sirius Calendar contains days and years. 30 REM The Sirius day is a bit less than 24 hours solar time, 40 REM the year a bit more than 25 000 solar years. 50 REM The data used are chosen to give optimal accuracy over the 60 REM year about Y2K (0000 UT 1 Jan 2000 AD Gregorian) 70 REM ----------------------------------------------------------- 80 DEFDBL A-Z :REM this sets QuickBasic to high precision (IEEE) mode 90 REM as does the # suffix on constants. 100 REM % suffix on variables sets integer type; non-# constants are integer. 110 REM The BASIC INT function returns the integer less than its argument 120 REM e.g. INT(3.1)=3; INT(-2.2)=-3 130 REM ***** data at IAU J2000.0 ***** 140 P0=75.621# :REM station longitude, degrees W of Greenwich 150 L0=45.43# :REM geodetic latitude, degrees N of equator 160 G0=5# :REM time zone, hours after UT 170 S1=6.7525# :REM Sirius RA 6h45m8.9s 180 S2=-16.716# :REM declination -16d42'58" 190 M1=-.54601# :REM proper motion RA as/yr 200 M2=-1.22308# :REM dec as/yr 210 R0=24110.54841# :REM sidereal offset seconds 220 R1=8640184.812866# :REM offset rate seconds/century 230 R9=.0027379094# :REM siderealday/solarday -1 240 Z0=-119.6510681407965# :REM start of Sirius year, Julian centuries 250 REM ***** get sidereal time offset at day start ***** 260 REM Seen from above the earth north pole, the rotation of the earth 270 REM about its axis is +ve (CCW) period 24- h. 280 REM Its orbit about the sun is +ve, period 365+ solar days, 290 REM so the Sirius day is shorter than the solar day. 300 REM Add 1 year to Gregorian dates if BC e.g. use Y%=-9 for 10 B.C. 310 REM there is no year 0 in the Gregorian system 320 D$=DATE$ :REM this is how Basic gets 330 Y%=VAL(MID$(D$,7)) :REM todays year YYYY 340 M%=VAL(MID$(D$,1,2)) :REM todays month (1:12) 350 D%=VAL(MID$(D$,4,2)) :REM and todays day (1:*) 360 PRINT "Gregorian date";Y%;"yr";M%;"mo";D%;"da" 370 REM find solar days from Y2K 380 Y1%=Y%-2000 :REM years since Y2K 390 J%=INT((Y1%+3#)/4#)-INT(Y1%/100#)+INT(Y1%/400#) 400 FOR I%=2 TO M% :REM add days in each complete month to date 410 J%=J%+VAL(MID$("3128313031303131303130",I%*2-3,2)) 420 NEXT I% 430 IF INT(Y%/4)*4<>Y% THEN 470 :REM this year not a leap year 440 IF INT(Y%/400)*400=Y% THEN 460 :REM this year is a leap year 450 IF INT(Y%/100)*100=Y% THEN 470 :REM this year not a leap year 460 IF M%>2 THEN J%=J%+1 470 J%=J%+D%-1 :REM add day of the month 480 J=J%+Y1%*365# :REM add year factor 490 REM The IAU sidereal equation includes terms for high powers of J. 500 REM These are a numerical fit to near-epoch precession effects, 510 REM and do not apply to long term time scales. 520 R=(R1*J/36525#+R0)/3600# 530 T=R: T$="sidereal offset": GOSUB 900 540 REM ***** get time of day (hr) ***** 550 D$=TIME$ :REM this is how Basic gets the time 560 H%=VAL(MID$(D$,1,2)) :REM hour (0:23) 570 M%=VAL(MID$(D$,4,2)) :REM minute (0:59) 580 S%=VAL(MID$(D$,7,2)) :REM and second (0:59) 590 G=((S%/60#)+M%)/60#+H% 600 T=G: T$="civil time": GOSUB 900 610 L=G+G0-P0/15# 620 T=L: T$= "local solar time": GOSUB 900 630 PRINT "solar days from local Y2K ";J+L/24# 640 T0=(J-.5#+(G+G0)/24#)/36525# :REM Julian centuries from J2000.0 650 REM ***** get position of Sirius ***** 660 REM spherical trigonometry is in radians and Julian centuries 670 P=3.1415926536# 680 REM proper motion of Sirius - change in RA affects time 690 REM because it is a movement relative to the average 700 REM star position used to determine IAU sidereal time. 710 REM change in dec affects cycle 720 REM A is epoch earth pole, B epoch star, C star 730 Z1=S1/12#*P :REM star RA at epoch 740 Z2=(90#-S2)/180#*P :REM polar angle c 750 Z3=M1*P/6480# :REM RA proper motion rate 760 Z4=M2*P/6480# :REM dec proper motion rate 770 Z5=SQR(Z3*Z3+Z4*Z4)*T0 :REM proper motion a 780 Z6=ATN(Z3/Z4) :REM B 790 Q=COS(Z2)*COS(Z5)+SIN(Z2)*SIN(Z5)*COS(Z6) 800 Z7=ATN(SQR(1-Q*Q)/ABS(Q)) :REM cosine rule b (new polar angle) 810 Q=SIN(Z6)/SIN(Z7)*SIN(Z5) 820 Z8=-SGN(T0)*ATN(ABS(Q)/SQR(1-Q*Q)) :REM sine rule A (change in RA) 830 S=(Z1+Z8)/P*12# :REM current star hour angle 840 T=R+(L+S)*(1#+R9) 850 T$="Sirius local time": GOSUB 900 860 J1=(J-.5#+L/24#-Z0*36525#)*(1#+R9) 870 PRINT "Sirius Day ";J1 880 IF LEN(INKEY$)=0 THEN 880 :REM wait until a key is hit 890 GOTO 980 900 REM output time T title T$ 910 IF T>=24# THEN T=T-24#: GOTO 910 920 IF T<0# THEN T=T+24#: GOTO 920 930 H%=INT(T) 940 M%=INT((T-H%)*60#) 950 S%=INT((T-H%-M%/60#)*3600#) 960 PRINT T$;H%;"h";M%;"m";S%;"s" 970 RETURN 980 END