WARREN ASTRONOMICAL SOCIETY

The Warren Astronomical Society is a local, non-profit organization of amateur astronomers. The Society holds meetings on the first and third Thursdays of each month, starting at 7:30 P.M., as follows:

1st. Thursday

Cranbrook Institute of Science 500 Lone Pine Rd.

Bloomfield Hills, MI

3rd. Thursday

Macomb County Community College South Campus

Building B, Room 216 14500 Twelve Mile Rd.

Warren, MI

Membership is open to those interested in astronomy and its related fields. Dues are as follows: Student...$8 College...$12 Senior Citizen...$12 Individual...$17 Family...$22

Sky and Telescope Magazine is available for $14.50 per year, and Astronomy Magazine for $14.00 per year. Send membership applications and dues to the Treasurer, for faster service.

OFFICERS

President : Alan Rothenberg 355-5844 lst. V.P. : Ken Strom 977-9489 2nd. V.P. : Riyad Matti 548-7511 Secretary : Alice Strom 977-9489 Treasurer : Russ Patten 588-0799 Librarian : Marty Kunz 477-0546 Deep Sky Group: Doug Bock 750-9369 Lunar Group : Alan Rothenberg 355-5844

MAILING ADDRESS

Warren Astronomical Society P.O. Box 474

East Detroit, MI 48021 - Meets at Northern Cross Observatory, Fenton, MI - Meets at Stargate Observatory, Ray Center, MI

WARREN ASTRONOMICAL SOCIETY PAPER

Editor: Ken Kelly / 839-7250 Send all articles to THE WASP, 19209 Mapleview, Detroit, MI 48205.

The W.A.S.P. is the official publication of the Warren Astronomical Society and is available free to all club members. NEWSLETTER EXCHANGES: Send your Newsletters to: THE WASP, P.O. Box 474, East Detroit, MI 48021. NOTE: Newsletters or change of address notices sent to other addresses may not reach the Secretary. All Articles should be submitted at least one week prior to the Macomb meeting.

STARGATE OBSERVATORY

Observatory Chairman: Riyad Matti / 548-7511

Stargate Observatory is owned and operated by the Warren Astronomical Society in conjunction with Rotary International. Located on the grounds of Camp Rotary, Stargate features a 12.5 inch club-built Cassegrain telescope under an aluminum dome. The Observatory is open to all members of the club in accordance with 'THE STARGATE OBSERVATORY CODE OF CONDUCT'. Those wishing to use the observatory must call by 7:00 p.m. (in the evening of the observing session. Lectures are given at Stargate Observatory each weekend. The lecture will be either Friday or Saturday night, depending on the weather and the lecturer's personal schedule. The observatory is at latitude 42 deg 45 min 43.5 sec, longitude 82,deg 55 min 25.9 sec.

LECTURER’S LIST

Lecturers should check with Camp Rotary to determine whether the Scouts are staying at the camp and to inform the Ranger the day and time of the lecture. If you cannot lecture on your scheduled weekend, please make arrangements to switch weekends with another lecturer or call the Chairman as early as possible. The lecturers for the coming weekends are: Apr. 17/18 Jon Root .......... 464-7908 May 15/16 Clyde Burdette ... 749-3295 24/25 Riyad Matti ....... 548-7511 22/23 James Yax ........ 465-9897 May 1/2 Russ Patten ....... 588-0799 29/30 Steve Aggas ...... 469-8773 8/9 Mike Bennett ...... 651-7991 Jun. 5/6 Alan Rothenberg .. 355-5844

HOODED SWEATSHIRTS WITH W.A.S. LOGO ..... $20.00 JACKETS WITH W.A.S. LOGO ................ $40.00

You must have a deposit to order the above items. See Alan Rothenberg for details.

May 2 - Deep Sky observing at Doug Bock’s if clear.

8:00 P.M. Bring telecopes and cameras.

May 7 - Meeting at Cranbrook Institute of Science, 7:30 P.M.

There will be a talk on deep-sky observing.

May 9 - National Astronomy Day, at Cranbrook 1:00 P.M. Bring

Telescopes, Posters, Slides, anything else you wish

to show the public. The Lunar & Planetary group will

meet at the same time

May 21 - Gpneral Meeting at Macomb Community College, 7:30

P.M. Alan Rothenberg will talk on Lunar Observations

June 20 - Summer Solstice Party at Doug Bock’s.

MINUTES OF THE BUSINESS MEETING AT MACOMB 3/19/87

Three guest attendees introduced themselves to the group. May 9 will be the annual Astronomy Day and our club will hold an open

house at Cranbrook Institute. Observatory report: The dome should always be facing east when locking

up to avoid storm damage. Eyepieces must always be put back into their boxes. No food or trash can be left in the observatory. Please sign the sign-in sheet each time YOU use the observatory.

A focuser has been donated by Steve Franks of Science & Things. Ken Kelly reported on the Sheldon supernova and the detection of

neutrinos surrounding this event. The program tonight was “How to Develop Film” by Russ Patten. The program at Cranbrook 3/5/87 was a lecture by Dr. R. Dixon on the

“Search for Extraterrestrial Intelligence”. Alice Strom, Secretary EPHEMERIS FOR COMET 1987c Nishikawa-Takamizawa-Tago

Dear Fellow Members;

I would like to take a moment to thank all of you for the honor of electing me President of the Warren Astronomical Society. I intend to continue in the spirt of the many wonderful people who help make the W.A.S. such a respectable organization. Since I joined in 1979, my enthusiasm has never waned for this group. 1986 was such a dynamic year for the W.A.S., thanks to the hard work of so many dedicated people. Now that the fever of the comet is over we can get back to good old basic observing.

I would like to see the subgroups start to become more active. Winter is not the most motivating season to drag a telescope out in to, but since spring is now closing in on us fast it’s a good time to get a jump on your Messier catalog. Did you know that if you observe, and log at least 70 Messier objects, you can receive a certificate from the Astronomical League, and then another when you observe all 110! Just submit your notes and dates to our alcor Ken Kelly.

The Lunar and Planetary group will starting an observing program to study and photograph the five naked eye planets, plus minor planets and details on the Moon. I encourage all of you to get involved in one of the subgroups available. Clyde has started the Super Nova search subgroup, to search for extragalactic supernovie. Since this year starts the eleven year cycle for sunspots you may want to start to take notes and photos.

May ninth is National Astronomical Day, the W.A.S. will be at Cranbrook, starting at 1pm. I would really like to see all of you at this event, at least for a couple of hours. Please bring a telescope. These outings help get publicity for the club and is also a public service.

At the past few meeting we have been hosting a raffle to help out the struggling treasury to maintain a respectable balance. If you have any ideas or prize you would be willing to donate to help us out contact Marty Kunz. It’s also important to have your dues in on time, remember there is a late charge of $5.00 for dues past 30 days. If you are a member and have a problem making the meeting to get a copy of the W.A.S.P. you can request it be mailed to you for $5.00 to cover postage.

Last summer’s 25th anniversary bash was a huge success, the rocket launch is still being talked about. I would like to have another outing this summer at Stargate, complete with rockets, cookout, observing and maybe even a Messier contest. Let’s decide on a date soon so we can get the ball rolling. It may also be a good idea to go a field trip or two, you let me know what you have in mind.

Yours Truly,

Alan Rothenberg President

I have three beautiful telescopes for sale and I will give you a good price on any one of them. All three are made by the well known Tasco Company.

Here is a 600 power 60mm Refractor, with an Equatorial mount. It is an F-14 (800mm) and comes with a 3X Barlow, Lunar filter, lOX reflexing finderscope with diagonal prism, rack and pinion focusing, and a 5 foot met.al tripod. It normally sells for $550. I will take $250. 656-9372

Here is a 400 power 60mm Refractor, with an Alt-azimuth mount (all metal 4 1/2 foot high tripod), diagonal prism, rack and pinion focusing and is a F-9 (800mm). Normally sells for $2~O. 1 will take $100. or best offer. 656-9372

Here is a 30X to 90X ZOOM scope, it is mounted on a 4 1/2 foot metal tripod, rack and pinion focusing. It is excellence for land and lunar viewing. $80 or best offer, the tripod alone is worth it. 656-9372

Bill Conkis

262 Dalton

Rochester, MI 48063

TWO BOOK REVIEWS

Tom MacLaney

HOW TO USE AN ASTRONOMICAL TELESCOPE by James Muirden

Linden Press/Simon & Schuster, 1985

397 pp., $21.95. Avail. Astro. Book Club.

THE NIGHT SKY by Ian Ridpath & Wil Tirion

240 pp., $4.95. Collins, 1985, (dist. by Simon & Schuster)

The first year I spent observing, one of the books I found most useful

was James Muirden’s "Astronomy with Binoculars." Recently he has written a very

fine guide, titled "How to Use An Astronomical Telescope."

The title shows typical British understatement. This volume is more a

handbook of objects and observing techniques, with substantial background

material.

Techniques and practice are the themes that run throughout this book. For

example, Muirden devotes much space to sketching various types of objects. In

the moon’s case, he even provides crater outlines as a guide. For observing

double stars, he describes the use of aperture masks and eyepiece hairs.

The lists of multiple stars and deep-sky objects are extensive with

detailed descriptions. Items are listed by R.A., which means a star atlas would

be useful. Unfortunately, Muirden doesn't provide one.

What is given is a final chapter on "Windows in Space"-selected regions

of the sky. The lists are fine, though the author warns that they include many

unspectacular objects, for exercising one’s skills.

Unfortunately, the charts in this section don't go well with the rest of

the material. Many are located opposite wrong lists, so a lot of page-flipping

is required. No distinctions are made on the charts between different types of

objects-a further drawback.

In general, this book could have used some more illustrations. More

pictures would have broken up the text. As it stands, the layout has a rather

unrelieved feel to it. Maybe Muirden was trying to avoid giving an impression

from photos, but he went too far in this case.

All in all, this is one of the most useful books I've come across since

I started observing. It reminds me somewhat of "Burnham's Guide", in that it

makes for good browsing. There's something to learn on almost every page.

A good star atlas is needed by anyone who wants to be able to find his

way around the sky. One I have found useful is "The Night Sky" by Ian Ridpath

and Wil Tirion.

The single most obvious feature of this book is its compact size-it

measures only 3 1/2 by 4 5/8 inches. This makes it extremely portable, since

it'll fit into your pocket or many other places with ease. The book is also well

constructed with a sewn binding (relatively uncommon for a paperback). I expect

my copy will last for years easily.

The maps themselves are similar to those in “The Universe Guide to Stars

and Planets", which was an earlier collaboration between Ridpath and Tirion.

Generally, each constellation occupies its own page. The stars are shown white

on a light-blue background. Constellation boundaries are a thin white line, while

coordinates are done in black. The limiting magnitude is 5.5, which is fine for

use with binocular and small telescopes. Several smaller and more detailed charts

are also included for such areas as the Pleiades, the galactic center, etc.

Tirion's usual clear cartography is shown to advantage here. In field

use, the stars are very obvious under a red light, and pictorial information is

easy to understand. Ridpath's notes and comments briefly describe the most

prominent objects in each constellation. This little atlas has proven very useful.

It may not be as complete as, say, "Sky Atlas 2000", but for beginners and anyone

using binoculars or small scopes should find it quite handy.

CALCULATION OF AN EPHEMERIS FOR A MINOR PLANET ORBIT

By Ken Kelly

In last August's issue of the W.A.S.P., I gave an explanation of how to calculate an ephemeris for

an elliptical orbit. It was an English language explanation of the program which follows this

text. The program has since been put on my PC/XT programmed in BASIC, and is working fine, as you

can see from the next article in this issue. The subroutine to calculate G.R.C. is also included.

A minor change was also made to the calculation of the Eccentric Anomaly, in order to prevent

hang-ups which occurred infrequently. The last subroutine prints the text for the WASP article,

and may be omitted.

The orbital elements are picked up from a file called <ELEMENTS.MIN>.The field description is in

line 200. The data is put on with another program. It is assumed that if the extension is <MIN>

then the planet number is equal to the record number.

10 ' "EPHEMER4.BAS" - EPHEMERIDES OF MINOR PLANET ORBITS, WITH CALCULATION OF G. R. C. -

PRO6RAMMED FROM TATTERSFIELD'S "ORBITS FOR AMATEURS WITH A MICROCOMPUTER" - BY KEN KELLY.

20. PRINT" EPHEMER4.BAS – EPHEMERIDES OF MINOR PLANET ORBITS WITH CALC. OF G. R. C"

30 CLEAR 50=DEFDBL A-H,M,P-T,X-Z:DEFINT I-L

40 Hl$=" -------------------------------------------------------------"

50 H2$=" \ !####! \ "

60 H3$=" EPOCH R.A. (1950) DECL. SUN EARTH v "

70 H4$=" YY MM DD HR MIN DEG MIN DIST. DIST. MAG"

80 HS$=" -- -- -- -- ----- --- ----- ----- ----- ----"

90 UU$=" ### ## ## ### ##.## ### ###.## ###.### ###.### ###.#"

100 PI=3.141592653598793#:RD=l80/PI:C0=.9174369525250033#:S0=.3978811859608783*:

PK=.01770209895#

110 INPUT" WANT FILES DISPLAYED";O$

120 IF(O$="Y")OR(O$="y")THEN 130 ELSE 150

130 PRINT" FILES AVAILABLE:"

140 FILES "ELEMENTS.*"

150 INPUT" ENTER FILE EXTENTION";OP$

160 IF LEN(OP$)<>3 THEN BEEP:GOTO 130

170 IF OP$="END" THEN 1350

180 OF$="ELEMENTS."+OP$

190 OPEN OF$ AS 1 LEN=128

200 FIELD 1,2AS Nl$,2AS F1$,lAS F2$,5AS N2$,16AS N3$,2AS R1$,4AS M1$,4AS M2$,8AS

V1$,8AS V2$,8AS V3$,8AS V4$,8AS V5$,8AS V6$,8AS V7$,6AS O4$,4AS Dl$,3AS ZI$,1AS

Z2$,4AS T1$,4AS Al$,4AS P1$,8AS M3$

210 INPUT"STARTING DATE, YYMMDD";09$

220 GOSUB 2430:MS = MZ

230 INPUT"ENTER DAYS INCREMENT "; IW

240 IF IW>100 THEN BEEP:GOTO 230

250 IF IW<l THEN BEEP:GOTO 230

260 INPUT" ENDING DATE, YYMMDD";09$

270 GOSUB 2430=ME = MZ

280 INPUT" CORRECT";OS

290 IF(O$="Y")OR(O$="y")THEN 300 ELSE 210

300 INPUT" ENTER PLANET NUMBER”;K9

310 IF K9 < 1 THEN BEEP:GOTO 300

320 IF OP$="MIN" THEN K0=K9:GOTO 340

330 K0 = 1

340 IF K0 = 9999 THEN BEEP:PRINT"* PLANET NOT IN FILE *":GOTO 300

350 IF K0 > LOF(1)/128 THEN BEEP:PRINT* PLANET NOT IN FILE *" :GOTO 300

360 GET I,K0

370 K1 = CVI(Nl$):IF K1 = 0 THEN K0=K0+1 :GOTO 340

380 IF K1 <> K9 THEN K0=K0+1 :GOTO 340

390 IF O4$="870724" THEN MJ=47000.5:GOTO 420

400 IF O4$="860619" THEN MJ=46600.5:GOTO 420

410 PRINT"EPOCH ON RECORD IS WRONG":BEEP:CLOSE:END

420 IF(OL$="Y")OR(OL$="y")THEN 460

430 INPUT" DO YOU WANT LPRINTING" ;OL$

440 INPUT" WANT WASP HEADINGS";OW$

450 IF(OW$="Y")OR(OW$="y")THEN SW%=0 ELSE SW%=1

460 IF(OL$="Y")OR(OL$="y")THEN GOSUB 2670:LPRINT Hl$

470 PRINT H1$

480 E1=CVD(V1$)/RD

490 E2=CVD(V2$)/RD

500 E3=CVD(V3$)/RD

510 E4=CVD(V4$)/RD

520 E5=CVD(V5$)/RD

530 E6=CVD(V6$)/RD

540 E7=CVD(V7$)/RD

550 N4$ = N3$

560 IF(OL$="Y")OR(OL$="y")THEN LPRINT USING H2$;"EPHEMERIS FOR";"(";Kl;") ";N4$

570 PRINT USING H2$;"EPHEMERIS FOR";"(";Kl;") ";N4$

580 B = SQR((E7^2)*(1 -E5^2))

590 MI = MS

600 G1 - SIN(E2)*SIN(E3)

610 G2 = SIN(E2)*COS(E3)

620 G3 = SIN(E2)*SIN(E4)

630 G4 - COS(E2)*SIN(E3)

640 G5 = COS(E2)*COS(E3}

650 G6 = COS(E22)*SIN(E4)

660 G7 = GS*COS(E4) - G1

670 G8 = G2*COS(E4) + G4

680 IF(OL$="Y")OR(OL$="y")THEN LPRINT H3$

690 PRINT H3$

700 PX = G5 - Gl * COS(E4)

710 PY = G8 * C0 - G3 * S0

720 PZ = G3 * C0 + G8 * S0

730 QX - -G2 -G4 * COS(E4)

740 QY = G7 * C0 - G6 * S0

750 QZ = G6 * C0 + G7 * S0

760 IF(OL$="Y")OR(OL$="y")THEN LPRINT H4$

770 PRINT H4$

780 IF(OL$="Y")OR(OL$="y")THEN LPRINT H5$

790 PRINT H5$

800 AX = E7 * PX

810 AY = E7 * PY

820 AZ - E7 * PZ

830 BX = B * QX

840 BY = B * QY

850 BZ = B * Q7

860 M0 = EJ + E6 * (MI - MJ):I1 = 0

870 Ml = M0 / (1 – E5)

880 M2 = Ml- E5 * SIN(M1)

890 M3 = (M0 -M2) / (l – E5 8 COS(M1))

900 M4 = M1 + M3

910 M5 = M4 - E5 * SIN(M4)

920 M6 = ABS(M5 - M0)

930 I1 = I1 + 1:IF I1>9 THEN M1=(M4+M7)/2:M2=M5:I1=0:GOTO 890

940 IF M6>.0000001 THEN M1 = M4-M2 = M5:M7=M4:GOTO 890

950 R = E7*(1-E5*COS(M4))

960 X = AX*(COS(M4)-E5)+BX*SIN(M4)

970 Y = AY*(COS(M4)-E5)+BY*SIN(M4)

980 Z = AZ*(COS(M4)-E5)+BZ*SIN(M4)

990 MD = MI:GOSUB 1900

1000 XI = X + XX

1010 YI = Y + YY

1020 ZI = Z + ZZ

1030 DL = SQR(XI^2 + YI^2 + ZI^2)

1040 SO - ZI / DL

1050 DC = ATN(SD/SQR(1-SD^2))*RD

1060 Fl = XI

1070 F2 = YI / XI

1080 GOSUB 2170

1090 RA = F3*RD/15

1100 RH – INT(RA)

1110 RM = (RA-RH)*60

1120 L = SGN(DC)DC = ABS(DC)

1130 DD = INT(DC)

1140 DM = (DC-DD)*60

1150 DD = DO*L: IF DD = 0 THEN DM =DM*L

1160 GOSUB 2540

1170 R = E7*t1-ES*COSCM4»)

1180 RE = (XX^2 + YY^2 + ZZ^2).

1190 CP = (R^2 + DL^2 – RE^2)/(2 * R * DL)

1200 IF ABS(CP))=1 THEN PH=0:GOTO 1220

1210 PH = PI/2-ATN(CP/SQR(1-CP^2))

1220 P1 = EXP(-3.33*(TAN(PH/2))^.63)

1230 P2 = EXP(-l.87*(TAN(PH/2))^l.22)

1240 G = CVI(Fl$)/100

1250 MG = CVS(M2$)+5*LOG(R*DL)/LOG(10)-2.5*LOG((1-G)*Pl+G*P2)/LOG(10)

1260 IF':OL$="'y'1IlOR(OL$="y" )THEN

LPRINT USING UU$;IY;IM;ID;RH;RM;DD;DM;R;DL;MG

1270 PRINT USING UU$;IY;IM;ID;RH;RM;DD;DM;R;DL;MG

1280 MI = MI + IW

1290 IF El>(2*PI) THEN El = El-(2*PI)

1300 IF MI<=ME THEN 860

1310 IF(OL$="Y")OR(OL$="y")THEN LPRINT Hl$

1320 INPUT" MORE PLANETS"; 0$

1330 IF(O$="N")OR(O$="n")THEN 1340 ELSE 300

1340 IF(OL$="Y")OR(OL$="y")THEN 1350 ELSE 1380

1350 INPUT"ENTER SOURCE" ;(OO$

1360 LPRINT

1370 LPRINT TAB(30) "SOURCE: ";OO$

1380 CLOSE:END

1390 ' "GEORECO7.TXT" - SUBROUTINE TO CALCULATE GEOCENTRIC RECTANGULAR COORDINAT

ES FROM BRETAGNON & SIMON, PLANETARY PROGRAMS AND TABLES.

1400 DATA 403406#,0,4.721964#,1.621043# 1

1410 DATA 195207#,-97597#,5.937458#,62830.348067#

1420 DATA 119433#,-59715#,1.115589#,62830.821524#

1430 DATA 112392#,-56188#,5.781616#,62829.634302#

1440 DATA 3891#,-1556#,5.5474#,125660.5691#

1450 DATA 2819#,-1126#,1.5120#,125660.9845#

1460 DATA 1721,-861,4.1897#,62832.4766#

1470 DATA 0,941,1.l63#,0.813#

1480 DATA 660,-264,5.415#,125659.310#

1490 DATA 350,-163,4.315#,57533.850#

1500 DATA 334,0,4.553#,-33.931#

1510 DATA 314,309,5.198#,777137.715#

1520 DATA 268,-158,5.989#,78604.191#

1530 DATA 242,0,2.911#,5.412#

1540 DATA 234,-54,1.423#,39302.098#

1550 DATA 158,0,0.061#,-34.861#

1560 DATA 132,-93,2.317#,115067.698#

1570 DATA 129.-20,3.193#,15774.337#

1580 DATA 114,0,2.828#,5296.670#

1590 DATA 99,-47,0.52#,58849.27#

1600 DATA 93,0,4.65#,5296.11#

1610 DATA 86,0,4.35#,-3980.70#

1620 DATA 78,-33,2.75#,52237.69#

1630 DATA 72,-32,4.50#,55076.47#

1640 DATA 68,0,3.23#,26l.08#

1650 DATA 64,-10,1.22#,15773.85#

1660 DATA 46,-16,0.14#,188491.03#

1670 DATA 38,0,3.44#,-7756.55#

1680 DATA 37,0,4.37#,264.89#

1690 DATA 32,-24,1.14#,117906.27#

1700 DATA 29,-13,2.84#,55075.75#

1710 DATA 28,0,5.96#,-7961.39#

1720 DATA 27,-9,5.09#,188489.81#

1730 DATA 27,0,1.72#,2132.19#

1740 DATA 25,-17,2.56#,109771.03#

1750 DATA 24,-11,1.92#,54868.56#

1760 DATA 21,0,0.09#,25443.93#

1770 DATA 21,31,5.98#,-55731.43#

1780 DATA 20,-10,4.03#,60697.74#

1790 DATA 18,0,4.27#,2132.79#

1800 DATA 17,-12,0.79#,109771.631

1810 DATA 14,0,4.24#,-7752.82#

1820 DATA 13,-5,2.01#,188491.91#

1830 DATA 13,0,2.65#,207.81#

1840 DATA 13,0,4.98#,29424.63#

1850 DATA 12,0,0.93#,-7.99#

1860 DATA 10,0,2.21#,46941.14#

1670 DATA 10,0,3.59#,-68.29#

1880 DATA 10,0,1.50#,21463.25#

1890 DATA 10,-9,2.55#,157208.40#

1900 U# = (MD – 51545!) / 3652500#

1910 L#= 0:RR# = 0

1920 FOR Jl = 1 TO 50

1930 READ LM#,RM#,A#,V#

1940 P# = A# + V# * U#

1950 L# = L# + LM# * SIN(P#)

1960 RR# = RR# + RM# * COS(P#)

1970 NEXT Jl

1980 RESTORE

1990 L# = L# * .0000001# + 62833.196168# * 'U# + 4.9353929#

2000 RR# = RR# * .0000001# + 1.0001026#

2010 A1# = 2.18# - 3375.7# * U# + .36# * U#^2

2020 A2# = 3.51# + 125666.39# * U# + .1# * U#^2

2030 LN# = .0000001# *(-834 * SIN(Al#) - 64 * SIN(A2#))

2040 E# = .4090928# + .0000001# * (-226938# * U# -75 * U#^2 + 96926# * U#^3 -2

491 * U#^4 -12104* U#^5 + 446 * COS(Al#) + 28 * COS(A2#))

2050 T# = (MD - 33282.423#) / 365250#

2060 PA# = 50290.966# * T# + 111.1971# * T#^2 + .07732# * T#^3 - .235316# * T#^4

- .0018055# * TI^5 + .00017451# * T.^6 + .000013095# * T#^7

2070 PA# = PA# / 3600 / RD

2080 L# = L# + LN# - PA#

2090 SL# = SIN(L#)

2100 CL# = COS(L#)

2110 SE# = SIN(E#)

2120 CE# = COS(E#)

2130 XX = RR# * CL#

2140 YY - RR# * SL# * CE#

2150 ZZ = RR# * SL# * SE#

2160 RETURN

2170 ' SUBROUTINE QUADRANT – PUTS FUNCTIONS INTO THEIR PROPER QUADRANT.

2180 ' MOVE COS(VAR.) TO Fl.

2190 ' MOVE TAN(VAR.) TO F2.

2200 ' GOSUB

2210 ' RETRIEVE VARIABLE IN PROPER QUADRANT FROM F3.

2220 F3 = ATN(F2)

2230 IF F3>= 0 THEN 2250

2240 F3 - F3 + 2 * PI

2250 IF Fl > 0 THEN 2300

2260 IF F1 = 0 THEN 2410

2270 IF F2 < 0 THEN 2330

2280 IF F2 = 0 THEN 2410

2290 IF F2 > 0 THEN 2350

2300 IF F2 < 0 THEN 2370

2310 IF F2 = 0 THEN 2410

2320 IF F2 > 0 THEN 2390

2330 IF F3 < PI THEN RETURN

2340 F3 = F3 - PI:RETURN

2350 IF F3 > PI THEN RETURN

2360 F3 = F3 + PI:RETURN

2370 IF F3 > (3*PI/2)THEN RETURN

2380 F3 = F3 + PI:RETURN

2390 IF F3 < (PI/2)THEN RETURN

2400 F3 = F3 + PI:RETURN

2410 PRINT"THE COS OR TAN WAS ZERO"

2420 RETURN

2430 ' "CEPOCHJD.TXT" - SUBROUTINE TO CONVERT YYMMDD TO JULIAN DAY NUMBER.

2440 M3 = VAL(LEFT$(09$,2))

2450 I4 = VAL(MID$(09$,3,2))

2460 MD = VAL(RIGHT$(09$,2))

2470 MY = 15019.5 + INT(365.25 * M3 - .25)

2480 OM$ = "000031059090120151181212243273304334"

2490 MM = VAL(MID$(OM$,I4 * 3 - 2,3))

2500 M4 = M3 / 4 - INT(M3 / 4)

2510 IF (M4 = 0) AND (I4 > 2) THEN MD = MD + 1

2520 MZ = MY + MN + MD

2530 RETURN

2540 ' "JCTOYYMD.TXT" - SUBROUTINE TO CONVERT DATES FROM FIVE DAY JULIAN DAY NUM

BER TO FORMAT YYMMDD. INPUT IS IN MI.

2550 MY = MI - 15019.5

2560 IY = INT(MY/365.25)

2570 IR = 1 + INT(MY - IY*365.25)

2580 LY = IY/4-INT(IY/4)

2590 Z$ = "0000310590901201511812212243273304334"

2600 I = 12

2610 JM = VAL(MID$(Z$,I*3-2,3))

2620 IF (LY=0) ANC (I>2) THEN JM = JM + 1

2630 IF JM >= IR THEN I = I-1:GOTO 2610

2640 IM = I

2650 ID = IR - JM

2660 RETURN ' YYMMDO IS IY,IM,ID, RESPECTIVELY.

2670 ' SUBROUTINE TO PRINT HEADINGS FOP THE WASP.

2680 IF SW% = 1 THEN RETURN

2690 S7$=CHR$(27): ST$=CHR$(17):SO$=CHR$(19):SP$=" "SE$=CHR$(14):SC$=CHR$(20):EE

$=(CHR$(15):SW%=1

2700 OS$="(Calculated by Ken Kelly)"

2710 OT$="MINOR PLANETS FOR APRIL - MAY "

2720 IT=INT((66-LEN(OT$))/2)

2730 SH$=SP$: FOR IH = 1 TO IT-1:SH$=SH$+SP$:NEXT IH

2740 LPRINT S7$;SE$;S7$;ST$;SH$;OT$:LPRINT

2750 LPRINT TAB(31);SZ$;EE$;SZ$;SO$;OS$:LPRINT

2760 O1$="

2770 O2$="

2780 O3$="

2790 O5$="

2800 O6$="

2810 LPRINT O1$:LFRINT O2$:LPRINT O3$:LPRINT OS$:LPRINT O6$:LPRINT

2820 RETURN

Positions for the four brightest Minor Planets are listed. They are now calculated directly from

the orbital elements on a PC/XT Computer. The opposition dates are as follows: (532) Herculina,

Apr. 8; (2) Pallas, May 22; (1) Ceres June 20; (6) Hebe, July 15. Hebe has ~ diameter of 204 km,

is in Main-belt I, and has composition type S, for Stony or Silicates.