Article View: comp.sources.hp48
Article #9v06i017: tyko_ks - Handheld Astronomy v3.0, Part01/03
From: Kati Sinenmaa
Date: Thu, 13 Aug 1992 01:44
Date: Thu, 13 Aug 1992 01:44
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33157 bytes
Checksum: 2979051011 (verify with brik -cv)
Submitted-by: Kati Sinenmaa <sinenmaa@cc.helsinki.fi>
Posting-number: Volume 6, Issue 17
Archive-name: tyko_ks/part01
BEGIN_DOC tyko.doc
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Version 3.0 1991-1992
by Kati Sinenmaa
HandHeld Astronomy for HP48SX
________________________________________________________
PREFACE
Tyko ( Tycho Tyco ) Brahe ( 1546-1601) was a famous medieval astronomer
who developed the observation methods in its top reaching incredible 1 arc
minute precision without any optical or electronical instruments.
I hope this program would be able to the same accuracy.
COPYRIGHT, WARRANTY
TYKO30 is a freeware program. But if you find this program to be usefull
to your purposes, you can support the author on a moderate sum of money.
You may distribute and modify it completely freely but you have NOT a
permission to change its name or its version number and you MUST NOT take
any charge distributing this program. All the taken payments must be
returned to the author. This program is without WARRANTY.
The author delegate the liability to the users.
The following files are to be found when distributing this program;
TYKO Executable programs for the HP48sx and all their sub-
programs. See below
TYKO30.DOC This file
INTRODUCTION
This program does the time changes both in the Julian Calendar and the
Gregorian Calendar. The date have to be later than March 1st 4712 BC.
or greater than Julian day 98 in the Gregorian calendar, Julian day 60
in the Julian calendar.The Calendar can be selected from the SETUP menus.
The other and perhaps the main part of this program contains the main
objects of our Solar system and 22 brightest stars of this corner.
Furthermore there is a simple calendar with almost unlimited time scale
to the both calendar form. And a lot other usefull tiny programs.
Executable files:
START main program
ASCAL a simple calendar
GSTR yields the Easter Sunday for Gregorian calendar
JSTR yields the Easter Sunday for Julian calendar
JDAY a fast way to get a Julian day number
CADA a fast way to convert JDAY to calendar date
EOFT yields the Ephemeris Transit (12-EOFT = Equation of the Time)
GWUT yields a mean Side real Time at Greenwich longitude
EQSO Equinoxes and Solstices
CONV Ecliptical coordinates to Equatorial coordinates
EQEC Equatorial coordinates to Ecliptical coordinates
SETUP a simple time application. Subprogs; JDAY, CADA, CHUT, NOVA.
SYSTEM REQUIREMENTS
Tyko v3.0 is purposed on the HP48SX-calculators. Tyko3.0 requires about
35000 bytes and about 10000 bytes free memory space.
All the following files must be found from the TYKO directory in order to
Tyko30 can be run;
{ start.,ascal,gstr,jstr,jday,cada,eoft,gwut,eqso,conv,eqec,setup,solar,
sudep,misc,crob,drav,pdrv,sdrv,chut,deep,aars,daes,geoc,calm,cals,cal1,cal2,
cal4,cal5,cal6,cal7,cal8,cal9,sdat,damo,nm,news,nova,wipe,zz,f24,f36,\GD\165,
\GD\Ge,\Glm,\O/.\Ge,jd0,jd,jg,ut,dt,lt,tz,dl }
HOW IT WORKS ?
48SX
__________________________
* Gregorian DST= 1 * Calendar and Daylight Saving Time
* TZ= 2 LT= 13 * Time Zone and Local Time
* JD0 = 2448839.5 * Julian Day at 0 UT
* JD = 2448839.91667 * Julian day related to the Universal Time
* UT= 10 today * Universal Time
* Wed Aug 5.1992 218 * Defined date and its year number
* \Gl = 25 \O/ = 60 * Geographical coordinates
[ab][cd][ef][gh][ij][kl]
This program doesn't contain any fancy things so I suppose one
is accustomed to use menu keys and other HP48's features so I
leave them to explain.
NOTE; UT = hh.mmss yesterday = defined date - 1
UT = hh.mmss today = defined date
UT = hh.mmss tomorrow = defined date + 1
SETUP: a simple time application program for the settings
DATE form is MM DD YYYY, the preceding zeros are not essential
TIME must be entered in the 24-hour system
LATIT latitude is between -90 and +90 degrees, must be as decimals
LONG longitude range is -180 to 180, westerns are negatives, as decimals
ZONE user's local time zone
BACK lets you to go back to the START-menu
DST Dayligth Saving Time-switch
CALE Calendar-switch
SETUP requirements for;
LT.ST Local Time to Sidereal Time : DATE TIME LONG ZONE DST CALE
ST.LT Sidereal Time to Local Time : DATE TIME LONG ZONE DST CALE
SPACE Sun Moon Planets Stars : DATE TIME LATIT LONG ZONE DST CALE
SETUP <ZONE>
Time Zone have to be entered in hours, as negative at western
longitudes otherwise positive.
Here is a few example; Longitudes around
Melbourne +10 +150
Delhi +5 +75
Moscow +3 +30
most West European countries +1 +15
Reykjavik -1 -15
In the North America and the Pasific Ocean;
Eastern Standard Time -5 -75
Central -6 -90
Mountain -7 -105
Pasific -8 -120
Alaska -9 -135
Havaii -10 -140
NOTE; Time zone related very closely to the longitude. If you change
either one of them then you must check also the other.
TEMPORARY MENU TREE
=================== see above
____________________________________________
DATE TIME LONG LATIT ZONE BACK DST CALE
--------------------------------------------
first page second page
A
================ A
Let's Begin Here A
=======V======== A
V A
V __A_____________________________________________
<< START >>>>>>>>>>>>>>>>> SETUP JULIA LT.ST ST.LT SPACE END
------------V--------V--------V--------V--------
V V V V
V V V V
see below V
V
JULIA an alternate time set, completely different than SETUP V
LT.ST Local Time to Sidereal Time, just press it V
ST.LT Sidereal Time to Local Time, just press it V
V
JULIA V
V
Allows you to put a Julian day number instead of the calendar V
date and time. This is a little bit confusing way to define a V
given moment because it related to the Universal Time and the V
current Time Zone can affect that date so much that it differ V
from the Julian day which has been typed in. V
V
EXAMPLE 1: V
TZ (time zone) = -8 and DST= 1 then by pressing JULIA V
and type number 2448942.7 <enter> yields following; V
V
LT= 21.48 V
JD0 = 2448941.5 V
JD = 2448942.7 V
UT= 4.48 tomorrow V
Sun Nov 15.1992 DN (tough JD 2448942.5 is V
at 0 UT in November 16.1992) V
V
You find that UT = fraction part of JD - 0.5 because the Julian V
day begins always at 12 UT in the calendar date and therefore at V
0 UT is the noon of Julian day and the fraction .7 .5 - = .2 V
represents the Universal Time. V
V
More confusing, if you then use the SETUP-menu and put the V
date 11 16 1992 to the DATE you will get the next things; V
V
LT= 21.48 V
JD0 = 2448942.5 V
JD = 2448943.7 V
UT= 4.48 tomorrow V
Mon Nov 16.1992 321 V
V
Again, JD and UT related together and LT, JD0 and current date V
should represent the same date if all values have been set V
correct. You can update the time e.g. by putting 13 to the V
TIME-menu and you will get; V
V
LT= 13 V
JD0 = 2448942.5 V
JD = 2448943.33333 V
UT= 20 today V
Mon Nov 16.1992 321 V
V
In general, to the West longitudes, if LT >= 24+(-TZ+DST) V
then UT is situated to the next day. V
To the East longitudes, If LT < +TZ+DST then the UT is V
situated the day before. V
V
NOTE; If you are using the JULIA-input then you MUST NOT V
change the DATE and TIME, because it contains both of them V
V
APPREVIATIONS of the main program V
V
GMST0: mean Sidereal Time at 0 UT at the longitude of Greenwich V
GMST: mean Sidereal Time at the defined time in Greenwich V
AST: local Apparent Sidereal Time V
MST: local Mean Sidereal Time at the defined time and longitude V
LT: mean sidereal time converted to the Local Time V
V
NOTE; For Apparent Sidereal Time you must execute the SPACE-menu V
first to get better accuracy. V
NOTE; You will get the Equation of Equinox to subract MST from AST V
(i.e. press [-]-button only). V
NOTE; if the GMST = 0 then the LT shows the Greenwich Transit of V
the Mean Equinox (when LT TZ and DST are all zero). V
NOTE; To convert sidereal time to the local time then the TIME V
represents the sidereal time. V
V
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
V
_____________________________V______________________________
SUN SOLAR STARS CALE BACK END
-V-----------V-----------V---------V-----------V----------V-
V V V V V V
Just press it V V show settings back to All ENDs
Remember; V V and change START are the same
SUN is a STAR ? V V calendar
>>>>>>>>>>>V>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
V V
<<<<<<<<<<<<<<<<<<< V
V V
V V
------------V------------ V
PICK CONT BACK END V
------------------------- V
V
PICK: pick a desired star to calculate. See TYKO30S.DAT below V
CONT: Calculates the picked star. As a result is a GROB. V
BACK: Back to the previous menu. V
END: All ENDs are the same. V
V
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
only one way to go V
__________________________V_____________________________
first page second page
________________________________________________________
MERC VENU MARS JUPIT SATUR URAN NEPT PLUTO MOON CALE
------------------------------------------------------V-
V V
V show settings and change
____________________V_____________________ calendar
PICT FILE DATA NEW END
------------------------------------------
PICT: A GROB-picture from the Heliocentric space. Selected object
plus Sun and Earth and their orbits. Not real scale.
FILE: Data for the selected object. Form is GROB.
DATA: More data for the selected object. Form is GROB.
NEW: Back to the previous menu.
END: All ENDs are the same.
OTHER EXECUTABLES file's input and output;
ASCAL it requires two number, you can't miss it. This calendar also
searchs your calculator's alarms. However, there is a tiny quirk.
If it finds the latest alarm then it reports all of them ??
GSTR a year number from stack, you will be see it.
JSTR a year number from stack.
JDAY three values, MM DD YYYY. results are Julian Day number and Day
of a year. Uses the selected calendar.
CADA Type Julian day to the stack, result is a string contains calendar
date. It check automatically the current calendar form.
EOFT Julian day number at 12 UT, ( i.e. no fraction part ). result is
Ephemeris Time. Takes Time Zone, Longitude and/or Dayligth Saving
Time from current SETUP-variables. Therefore it is more desirable
to beg it from the SUN-menu.
EQSO put month and year to the stack ( the months March, Jun, September
and December only ). Gives to the level 2 a tagged object which is
the time of the phenomenon at your local time. The accuracy is about
ten minutes. On the level 1 is a string containing that date.
GWUT Julian day with decimals; yields two numbers, level 2 is a tagged
object; GMST0: this is valid only if entered Julian day is at 0 UT,
otherwise it represents the mean Side real Time in the Greenwich at
decimal of the Julian day number. Both numbers are actually same;
the number level 2 is the form HH.MMSS and the other is in decimals.
CONV put ecliptical coordinates to stack. To level 2 ecliptical longitude
and level 1 latitude. Yields 2 tagged objects. Takes the current
Obliquity of the Ecliptic from somewhere. You can update it by
running the SUN-menu. Type both in as decimals; dd.fraction !!
EQEC type equatorial coordinates to the stack. To level 2 Right Ascension
and level 1 Declination. If you convert Apparrent coordinates then
use APPAR. If Equatorial coordinates are referred to the standard
equinox of J2000 then use MEAN.
Type RA. in the form hh.mmss and DECL. dd.mmss !!
NOTE; CONV and EQEC have not been purposed on reduction use, i.e. to reduce
coordinates from one date to another. It does the conversion at the
defined moment and before the conversion execution the SPACE must be
run at the same moment ( to update the Obliquity of the Ecliptic ).
GROB EXPLANATIONS
=================
GROB for SUN & STARS;
greek letter # lamda = Ecliptical longitude dd.mmss
# beta = Ecliptical latitude dd.mmss
# alfa = Right Ascension (R.A.) hh.mmss equatorial
# delta = Declination (DECL) dd.mmss coordinates
Azi = Azimuth dd.mmss horizon
Alt = Altitude dd.mmss coordinates
Rise = rising time hh.mm
Set = setting time hh.mm
ET = object's transit time over the South Meridian hh.mm
R = geocentric distance
UT = universal time hh.mmss
V = visual magnitude
B-V = color index
SD = Sun's SemiDiameter in arc minutes mm.ss
# epsilon = Obliquity of the Ecliptic dd.mmss
# delta # psi = Nutation in Longitude ss.fraction
# delta # epsilon = Nutation in Obliquity ss.fraction
EXAMPLE 2: Find the Sun's position and Equation of Equinox on December 25
1992 at 0 UT ( LONGitude is -75, TZ = -5, calendar is Gregorian ).
1. Start the program by pressing START. ( are you kidding )
2. Go to the SETUP-menu
3. Press DATE and type 12 25 1992 <enter>.
4. Press TIME and set time to be same as the sum of TZ+DST
e.g. TZ= -5 DST= 0, then type -5 <enter>
5. Press BACK
6. Press SPACE
7. Press SUN and wait ... ==>> GROB
8. Press ON
9. Press BACK
10. Press LT.ST
11. Press [-] ==>> Eguation of Equinox
12. Press END
To pass steps 2.- 5. press JULIA and type 2448981.5 <enter>.
This yields exactly the same ecliptical and equatorial coordinates
as steps 2.- 5. do. An other method to determine time at 0 UT is
to put TIME, ZONE, LONG and DST to zero.
Results as a GROB picture
Sun FRI DEC 25.1992
UT= 0 today Tyko v3.0 Astronomical Almanac 1992
Ecliptical long. (lambda) 273.270446 273 27 05.20
Ecliptical latit. (beta) -0.000009 +0".05
Apparent R.A (alfa) 18.150259 18 15 02.39
Apparent decl. (delta) -23.234062 -23 23 40.6
Distance R 0.983466 0.9835409
SemiDiameter SD 16.153 16'15".70
Ephemeris Transit ET 12.002 12 00 15.40
Visual magnitude V -26.780
Color index B-V 0.620
Obliquity of the Ecliptic 23.26226988 23 26'22".69
Nutation in Longitude 17.301 17".352
Nutation in Obliquity -2.045 -2".044
Mean Greenwich Sidereal Time 6.150086323 6 15 00.8632
Equation of Equinox .0001058205 +1.0613 sec.
Compare these results with each other and I bet you can find the Sun
from the sky by this program. This program ignore the dynamical time.
All calculation are made in the Universal time i.e. it is your clock
time at different time zones.
NOTE; When you have pressed the SPACE key you can check what date is it
in the other calendar by pressing CALE key -- before or after the
SUN executing. This is due to the fact that the Julian day is the
same for the both calendars.
GROBs for SOLAR; planets & Moon
PICT
The basic Crob-picture is created when you run PICT the first time. It
takes quite long time at this time but later it is much faster if you
do not purge it. To the Moon it always takes about one minute to
make it so be patient.
There are two eclipses representing the planets orbit. The Earth is
switched from one orbit to the other depending on the selected object.
In the case of the inner planets, Mercury, Venus and the Moon, the
Earth is located to the outer ring ( of course, the Earth and Mars
belong also to the inner solar system ). Calculating the outer planets
the inner ring is the Earth's orbit.
You can identify the Earth in that way there is a tiny circle in the
surface of the Earth. If you look at it on the HST you will find it is
an observer with handheld. That observer is bound to the local time
which has been displayed in the lower right corner and the local time
is bound to the things which have been expressed above.
In the lower left corner is object's heliocentric latitude converted
to the distance unit.
The half line should be the vernal equinox, i.e. when the Earth is on
that line then the Sun's longitude should be about zero.
The basic picture reserves 1106.5 bytes.
WEIRDS; The planets' size is changing with the time. I didn't
able to solve it and that's why the picture is sometimes
little bit messy. XRNG and YRNG are every time the same.
FILE
Object
CAL = Used calendar
date
greek letter # lambda = ecliptical longitude dd.mmss Heliocentric
# beta = ecliptical latitude dd.mmss Heliocentric
# alfa = right ascension hh.mmss Equatorial
# delta = declination dd.mmss Equatorial
R = heliocentric distance R*AU or AU/6378.14*r for Moon
# delta = Geocentric distance delta*AU or delta*6378.14 Moon
JDAY = Julian day representing the calculated moment
GMST0 = Greenwich mean sidereal time at 0 UT hh.mmss
LST = local mean sidereal time hh.mmss
AZ = azimuth dd.mmss Horizon
A = altitude dd.mmss Horizon
D = the planet's equatorial Diameter in arc seconds, or
the Moon's SemiDiameter in arc minutes
M = apparent magnitude
RISE = rising time hh.mms
ET = object's transit time over the South meridian
SET = setting time hh.mms
# tau = perihelion date
DATA
date LT
L = mean longitude dd.mmss
M = mean anomaly dd.mmss
# phi = longitude of the perihelion dd.mmss
# omega = longitude of the ascending node dd.mmss
T = the time measured in Julian centuries of 36525
ephemeris days from the epoch J2000 -67.12 ==>>
# epsilon = obliquity of the ecliptic dd.mmss
# delta # psi = nutation in longitude ss.fraction
# delta # epsilon = nutation in obliquity ss.fraction
L = ecliptical longitude dd.mmss Geocentric
B = ecliptical latitude dd.mmss Geocentric
# psi = elongation dd.mmss
# delta T = ligth time mm.ss
I = phase angle dd.mmss
K = phase 0-1
***
# delta # psi = the Moon's effect on the longitude
# delta # epsilon = the Moon's effect on the obliquity of the equator
# psi = angle Object Earth Sun
# delta T = light's travel time from the object to the Earth
I = angle Sun Object Earth
K = object's illuminated surface seen from the Earth;
1 = full object, 0 = new object
***
NOTE; For the Moon; there is not Heliocentric coordinates.
NOTE; To the Moon the values of the psi, delta T, I and K are absolutely
meaningless.
EXAMPLE 3: Search the mean orbital elements for the Mercury on
June 24 2065 at 0 UT ( in the Gregorian calendar ).
As in the example3 we are set the date and time so that UT= 0 or we are
found the Julian day by using JDAY; putting 6 24 2065 to the stack and
JDAY; we have; GreCal: 2475461. Because this number represents the noon
of that date we must subract .5 from it = 2475460.5. Typing this number
to the JULIA then we have the required date at 0 UT. Finally press menu
keys SPACE SOLAR MERC DATA, respectively.
Results as a GROB picture
Tyko30
Wed Jun 24.2065 LT
L = 203.293588 mean longitude
M = 125.010841 mean anomaly
# Phi = 78.282747 longitude of the perihelion
# Omega = 49.062765 longitude of the ascending node
T = 0.654771
# phi = Phi - Omega = 29.215982 argument of the perihelion
a = no
e = no
i = no
The reference elements at 0 TD* from the Astronomical Algorithms p. 199
L = 203.494702 = 203 29' 40".927
M = 125.019320 = 125 01' 09".552
# Phi = 78.475382 = 78 28' 31".375
# Omega = 49.107650 = 49 06' 27".54
T = +0.65477074997
# phi = 29.367732 = 29 22' 03".835
a = 0.387098310 semimajor axis of the orbit
e = 0.205645 eccentricity of the orbit
i = 7.006171 inclination on the plane of the ecliptic
* Dynamical Time TD is unpredictable creature
I think in the year 2065 exist lots of programs which give
much worse results than these two are !
ABOUT COORDINATES
In here the ecliptical coordinates' zero point is the Earth's center
(Geocentric) or the Sun's center (Heliocentric). Zero direction to the
longitude is vernal equinox growing counterclockwise from 0 to 360
degrees. Reference plane to the latitude is Earth's orbit plane,
is called the ecliptic.
The reference point of the right ascension is the direction of the vernal
equinox ( the first point of Aries ). This happens when the Sun is in this
direction ( about March 21st, you can check it by EQSO and then put the
given time and date to the SETUP-menu and run the SUN-menu. The both
coordinates, ecliptical longitude and Right Ascension, should be around
zero at vernal equinoxes. ).
R.A. gets all values counterclockwise from zero to 360 degrees but usually
the degrees are converted to the 24-hour system as this program does.
The reference plane of the declination is the Earth's equatorial plane.
This number can get values -90 to +90 degress (in the case of the Sun
this gets values about -23 to 23 ).
This program counts the Azimuth to the clockwise from the South on the
northern hemisphere and from the North on the Southern hemisphere and the
values are between 0 and 360 degrees. E.g. if Azi= 90 deg. then the Sun is
about in the West (if LATIT is positive).
Altitude can have the values from -89.59... to 89.59... degrees where the
zero plane is an observer's horizon plane.
Distance unit is in the AU (= Astromical Unit = 1.49597870E11 meters ) for
the Planets. To the Moon distance unit is the Earth's equatorial radius
(= 6378.14 kilometers ). To the Stars the distance unit is pc ( = parcek
= 206264.80624 AU = 3.26161 ly ). In the case of the Moon there are two
different kind of distances; R = Sun-Earth distance and unit is the
Earth's equatorial radius 6378.14 km and # delta is, of cource, distance
Earth-Moon and unit is the same.
The accuracy of the R.A. and Declination is few seconds within two
decade from the present -- to the past and future. Except for the Pluto.
HISTORY of Tyko 0-1.8 ...... Not published, embryo versions
1.9 ........ First publication 7.15.1991
2.0 ........ Errrorrrrs, not published
2.1 ........ 10.15.1991
3.0 ........ Rewritten program, in August 1992
Any comments are welcome about this program. Especially if there are
very bad errors in the results or the program itself ( I know there are
some odd results which can be placed under questions ).
Thank you very much for considering this program
email address; sinenmaa@cc.helsinki.fi
mail address; Kati Sinenmaa
Kamnerintie 4 B 45
00750 Helsinki
Finland
REFERENCES
Quarterly Journal of Royal Astronomical Society, 25(1),54(1984)
The Astronomical Almanac 1992
Practical Astronomy with Your Calculator, 3rd edition
The Astrophysical Journal Supplement Series, 41:391-411,1979 Nov.
Astronomical Algorithms, Jean Meeus
TYKO30S.DAT
STARS' DATA for TYKO30
From Sky Catalogue 2000, Cambridge
HD Henry Droper Catalogue
SAO Smithsonian Astrophysical Observatory
TYKO HD SAO Ancient Name RA2000 DEC2000 Spectral Type
------------------------------------------------------------------
1 10144 232481 Achenar 1.37429 -57.1412 B5 V
2 29139 94027 Aldebaran 4.35552 16.3033 K5 III
3 34085 131907 Rigel 5.14322 -8.1206 B8 Ia
4 34029 40186 Capella 5.16413 45.5953 G8 III
5 39801 113271 Betelgeuze 5.55102 7.2426 M2 Iab
6 45348 234480 Canopus 6.23571 -52.4144 F0 Ia
7 48915 151881 Sirius 6.45089 -16.4258 A1 V
8 61421 115756 Procyon 7.39181 5.1330 F5 IV
9 62509 79666 Pollux 7.45189 28.0134 K0 IIIb
10 87901 98967 Regulus 10.08222 11.5802 B7 V
11 108248 251904 Acrux 12.26359 -63.0556 B1 IV
12 111123 240259 Mimosa 12.47432 -59.4119 B0 III
13 116658 157923 Spica 13.25115 -11.0941 B1 V
14 122451 252582 Hadar 14.03494 -60.2222 B1 II
15 124897 100944 Arcturus 14.15396 19.1057 K2 IIIp
16 128620 252838 RigilKentaurus 14.39367 -60.5002 G2 V
17 148487 184415 Antares 16.29243 -23.2555 M1 Ib
18 172167 67174 Vega 18.36562 38.4701 A0 V
19 187642 125122 Altair 19.50468 8.5206 A7 IV-V
20 197345 49941 Deneb 20.41258 45.1649 A2 Ia
21 216956 191524 Fomalhaut 22.57389 -29.3720 A3 V
END
END_DOC
Technical Details
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Newsgroups: comp.sources.hp48 Path: arc1-ca.pugleaf.net!sparky!uunet!seq!spell From: Kati Sinenmaa <sinenmaa@cc.helsinki.fi> Subject: v06i017: tyko_ks - Handheld Astronomy v3.0, Part01/03 Message-ID: <cshp48-v06i017=tyko_ks.214349@seq.uncwil.edu> Followup-To: comp.sys.hp48 Sender: spell@seq.uncwil.edu (Chris Spell) Organization: University of Helsinki Date: Thu, 13 Aug 1992 01:44:58 GMT Approved: spell@seq.uncwil.edu Lines: 645