EDITOR: Judy Butcher Send all articles to- (313) 254-1786 · EDITOR: Judy Butcher Send all articles to- (313) ... MI 48195 1978 IND BIONDO, STEVE 245-2493 17130 STRASBURG DETROIT,

EDITOR: Judy Butcher Send all articles to- (313) 254-1786

45200 Keding Apt. 102

Utica, MI 48087

The W.A.S.P. is the official publication of the Warren Astronomical Society and is available free to all

club members. Requests by other clubs to receive the W.A.S.P. and all other correspondence should be

addressed to the editor. Articles should be submitted at least one week prior to the general meeting.

Warren Astronomical Society President: Frank McCullough 254-1786

P.O. Box 474 1st V.P.: Roger Tanner 981-0134

East Detroit, MI 48021 2nd V.P.: Ken Strom 977-9489

Secretary: Ken Kelly 839-7250

Treasurer: Bob Lennox 689-6139

Librarian: John Wetzel 882-6816

'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. The meeting locations are as follows:

1st

Thursday – Cranbrook Institute of Science 3rd

Thursday – Macomb County Community

500 Lone Pine Road College – South Campus

Bloomfield Hills, MI K Building (Student

Activities), 14500 Twelve

Mile Rd., Warren, MI

Membership is open to those interested in astronomy and its related fields. Dues are as follows and include

a year‟s subscription to Sky and Telescope.

Student ................... $18.00 College ........................ $22.00 Senior Citizen ................... $22.00

Individual ............... $27.00 Family......................... $32.00

Observatory Chairman: Ken Strom 977-9489

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 12½” club-built

Cassegrainian telescope under an aluminum dome. The observatory is open to all club members in

accordance with the “Stargate Observatory Code of Conduct”.

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. If you cannot lecture on your

scheduled weekend, please call the Chairman as early as possible or contact an alternative lecturer. Those

wishing to use Stargate must call by 7:00 p.m. on the evening of the observing session. The lecturers for the

coming month are:

Feb 4/5 ........... Dave Harrington ................ 879-6765 Mar 4/5 ........ Doug Bock ....................... 533-0898

Feb 11/12 ...... Frank McCullough ............ 254-1786 Mar 11/12 .... Ken Strom ...................... 977-9489

Feb 18/19 ...... Ron Vogt ........................... 545-7309 Mar 18/19 ..... John Root ...................... 464-7908

Feb 25/26 ...... Alan Rothenberg ............... 355-5844 Mar 25/26 ..... Lou Faix .......................... 781-3338

WARREN ASTRONOMICAL SOCIETY‟S COMING EVENTS

Jan 22 - Star party at Camp Rotary to meet out there at 7:30.

Dress warmly!

Jan 23 - Field trip to Jackson Space Center. Everybody meet at

Doug Bock's (533-0898) at 1:00.

Feb 10 - Workshop subgroup meeting at Doug Bock's.

Feb 12 - Executive meeting at Frank McCullough‟s commences

at 5: 00. All members welcome! Following business

meeting the deep sky subgroup meets at Frank

McCullough‟s at 7: 30.

Feb 11 - Astrofest will be held in the Modern Language Building

in Ann Arbor starting at 7:30. James Loudon gives a

talk and two movies follow. FREE!!

Feb 19 - First Annual LOWBROW FREEZE-OUT! You won't want

to miss this one!! For details see flyer in WASP.

************************************

FOR SALE

Quantum6 (all accessories), Drive corrector

Best Offer

Contact Gary Lyon at (313) 879-8219

Mead 6” f/8 reflecting telescope, like new

Only used approximately ten times

clock drive

photo guide scope

viewfinder

dust covers

eye piece tray

six eye pieces

manual adjustment

six filters

$600 firm

For more information, call Gary Agar at 274-3552

********* MEMBERSHIP LIST FOR THE WARREN ASTRONOMICAL SOCIETY *********

NAME PHONE ADDRESS CITY, STATE ZIP 1ST YR MEM MAG

BALDWIN, JEAN 264-4082 4047 HILLCREST WARREN, MI 48092 1973 IND S&T BASTITONI, ROBERT 855-5763 5581 TADWORTH PL W BLOOMFIELD, MI 48023 1981 IND S&T BIENIEK, MARK 284-7595 13431 VENNESS SOUTHGATE, MI 48195 1978 IND BIONDO, STEVE 245-2493 17130 STRASBURG DETROIT, MI 48205 1980 IND A/S BOCK, DOUG & ROBIN 533-0898 15489 PATTON DETROIT, MI 48223 1973 FAM A/S BOYD, GARY 839-0973 15050 STATE FAIR DETROIT, MI 48205 1974 IND S&T BULLOCK, RAYMOND 879-9458 2991 CHARWOOD TROY, MI 48084 1975 HON - BUTCHER, JUDY 254-1786 45200 KEDING #102 UTICA, MI 48087 1982 COL - CORKERY. JOHN R. 543-5107 1292 ANN TERRACE MADISON HTS, MI 48071 1982 IND S&T DAVIDSON, JOHN W. 538-0607 16380 DELAWARE REDFORD, MI 48240 1982 IND S&T DICHTING, JAMES E. 332-8055 3069 HIGH POINTE C BLOOMFIELD HILLS, MI 48013 1982 IND AST DONOVAN, MICHAEL & LINDA 774-2207 21567 WALTHAM WARREN, MI 48089 1982 FAM A/S DYER, KIM 835-0993 14114 GRANDMONT DETROIT, MI 48227 1982 IND - EVERINGHAM, WILLIASM P. 589-9153 513 BRECKINRIDGE FERNDALE, MI 48073 1982 IND AST FAUSEL,CHARLES A. 1-623-1663 4095 IRONSIDE WATERFORD, MI 48095 1981 IND S&T FEMMININEO, MARK 293-3017 21224 BRIARCLIFF ST. CLAIR SHORES, MI 48082 1979 IND S&T FRANKS, STEPHEN #318 255-7215 13160 W. OUTER DR. DETROIT, MI 48223 1982 IND - JOHNSTON, BRUCE 666-2186 7764 TULL COURT PONTIAC, MI 48054 1982 FAM - KALINOWSK, LARRY 776-9720 15674 FLANAGAN ROSEVILLE, MI 48066 1979 IND - KAPUSHINSKY, MARK 979-0959 13251 MONTAGO DR STERLING HGTS, MI 48077 1981 STU S&T KELLY, KEN 839-7250 19209 MAPLEVIEW DETROIT, MI 48205 1978 IND - KRUMAN, CRAIG 557-1997 16996 MORRISON SOUTHFIELD, MI 48076 1981 STU AST KUNZ, MARTY 477-0546 29036 HILLBROOK LIVONIA, MI 48152 1982 IND AST KWENTUS, PETE & GINGER 771-3203 22107 MELROSE CT EAST DETROIT, MI 48021 1973 FAM S&T LEMONS, BRIAN & MAUREEN 739-5706 11967 DIEHL STERLING HGTS, MI 48076 1982 FAM S&T LENNOX, ROBERT W. 609-6139 149 CARTER TROY, MI 48098 1982 IND S&T MCCULLOUGH, FRANK 1-254-1786 45200 REDING AP102 UTICA, MI 48087 1968 IND A-S MCMAHON, DANIEL B. 642-5041 951 RIDGEDALE BIRMINGHAM, MI 48003 1982 IND S&T MUSE, KENNETH H. 268-3486 11168 GLENIS STERLING HGTS, MI 48077 1978 IND S&T NICHOLS, KAREN & JOSEPH 268-3486 8609 HARDING CENTERLINE, MI 48015 1982 FAM AST OLAH, DAN 759-5478 25436 WAREHAM HUNTINGTON WOODS, MI 48070 1980 IND S&T PATTERSON, KENT 542-8144 4994 MEADOWBROOK L PONTIAC, MI 48055 1982 FAM - PAULAUSKY, JAMES ........ 37176 GARVIN MT CLEMENS, MI 48043 1977 IND S&T PERSHA, BEVERLY 465-3086 1033 LINCOLN LAKE LOWELL, MI 49331 1981 IND S&T FORRETTA, GEORGE 1(616)097-6224 3281 CHIKERING LN BLOOMFIELD HILLS, MI 48013 1982 IND S&T ROOT, JOHN M. 464-7908 16320 RENWICK LIVONIA, MI 48154 1976 IND A/S ROTHENBERG, ALAN 355-5844 21700 COLONY PARK SOUTHFIELD, MI 48076 1980 COL S&T SHANNON, BOB & CONNIE 893-4283 194 MORAN GROSSE PTE FRMS, MI 48236 1980 SRF - STROM, KEN & ALICE 977-9489 31653 WIXSON WARREN, MI 48092 1982 FAM S&T STRONG, PAUL B & JUDITH 791-0091 2054 15 MILE RD MT CLEMENS, MI 48043 1973 FAM - TANNER, ROGER D. 981-0134 1770 WALNUT RIDGE CANTON, MI 48187 1981 IND AST UMBARGER, JEFF 884-0227 1260 FRYS DRIVE GROSSE PTE WDS, MI 48236 1979 STU S&T VAN BELINDEN, ROSEMARY 371-0323 15073 TACOMA DETROIT, MI 48205 1982 IND - VOGT, RONALD C. 545-7309 11 ELM PARK PLEASANT RIDGE, MI 48069 1981 IND S&T WETZEL, JOHN J 802-6816 36 NEWBERRY PLACE GROSSE PTE FRMS, MI 48236 1980 SR A/S ZORATTI, EMIL J JR. 336-6698 19815 TIREMAN DETROIT, MI 48228 1982 IND -

T H E L U N A R E C L I P S E

BY ROGER WEBER

GOOD MORNING, MY FRIEND,

IT IS FIVE A.M.

AND THE LIGHT OF THE SILVERY MOON,

IS SLIPPING AWAY.

IT‟S ECLIPSE TIME TODAY,

AND IT WON'T BE COMING BACK SOON!

ON A DESOLATE SITE,

FAR AWAY FROM THE LIGHT,

TOILED NINE ASTRONOMY ADDICTS.

WERE THEY ALL LUNAR LOONIES.

OUT HERE IN THE BOONIES,

LOOKING UP AND GETTING ECSTATIC?

IT WAS EIGHTEEN DEGREES.

GOOD REASON TO SNEEZE,

BUT THE VIEW WAS WELL WORTH THE COST.

FINGER TIPS AILING,

AND CLOUDY EXHALING,

AND TELESCOPES SMOTHERED IN FROST.

AN ECLIPSE IS BORN,

WHEN THE EARTH‟S MASSIVE FORM,

GOES BETWEEN THE MO0N AND THE SUN.

WITH US IN THE WAY,

A SHADOW IS DISPLAYED.

AND THE LUNAR VIEW IS UNDONE.

THE CELESTIAL STARE,

INTO THE NIGHT AIR,

WAS INSPIRED, INTENSE AND INCESSANT.

THE SHADOW'S BITE GREW.

AND AT SIX 0‟CLOCK ON CUE,

DEVOURED THE LAST BIT OF CRESCENT.

I AM UNABLE TO SAY.

WHY THE RED WENT ASTRAY,

AND I HOPE YOU'LL EXCUSE ME THIS TIME.

BUT I HAVE TO BE LEERY,

OF THAT LUNAR THEORY,

CAUSE FOLKS, IT JUST DOESN'T RHYME.

BUT I WILL LET YOU KNOW,

THAT THE MOON'S NORMAL GLOW,

PEEKED THROUGH PRECISELY AT SEVEN.

AN HOUR WENT BY,

AND DAWN FILLED THE SKY,

FOR A DAZZLING VIEW OF THE HEAVENS.

SO, GOODBYE MOON RIVER,

HERE'S A SMILE AND A SHIVER.

YOU SHOWED US A REALLY GOOD TIME.

WE'LL STUDY IT ALL.

TIL YOUR NEXT CURTAIN CALL.

IN AUGUST, NINETEEN EIGHTY NINE.

S0, AGAIN IN SIX YEARS,

WHEN THE MOON DISAPPEARS.

THESE ASTRONOMY BUFFS WILL COME COURTING,

BENEATH THE ECLIPSE.

WITH FROZEN LIPS.

I'M ROGER WEBER, NEWS FOUR, REPORTING!

THE ABOVE POEM WAS COMPOSED BY ROGER WEBER OF CHANNEL 4

NEWS, ABOUT MEMBERS OF THE WARREN ASTRONOMICAL SOCIETY

WHO OBSERVED THE TOTAL ECLIPSE OF THE MOON ON DEC. 30.

1982.

E A R T H C R O S S E R S

PART I

AS OF DEC. 1, 1982, 2818 MINOR PLANETS (ASTEROIDS) HAVE BEEN GIVEN NUMBERS,

INDICATING THAT THEIR ORBITS HAVE BEEN COMPUTED TO ENOUGH ACCURACY SO THAT THEY CAN

LATER BE RECOVERED. THIS INCLUDES SIX OBJECTS THAT WERE TOO HASTILY NUMBERED AND

WERE LATER LOST. OF THESE MINOR PLANETS, PROBABLY THE MOST INTERESTING ARE THOSE

WHICH CROSS THE EARTH’S ORBIT, AND HAVE THE REMOTE POSSIBILITY OF COLLIDING WITH

THE EARTH. IN ORDER TO ALLAY EVERYBODY’S FEARS, IT MUST BE SAID THAT ON THE

AVERAGE, ONLY ONE OF THESE OBJECTS HITS THE EARTH EVERY 300,000 YEARS OR SO. THIS

WILL BE COVERED IN MORE DETAIL IN A LATER ARTICLE.

ALL EARTH CROSSERS WITH RELATIVELY GOOD ORBITS ARE LISTED IN TABLE I. THEY ARE

ARRANGED IN ORDER OF PERIHELION DISTANCE, OR CLOSEST DISTANCE FROM THE SUN. AN

EXPLANATION OF THE TABLE FOLLOWS:

1. PLANET NUMBER. THE NUMBER GIVEN TO A PLANET WHEN ITS ORBIT HAS BEEN

CALCULATED ACCURATELY ENOUGH TO BE RECOVERED.

2. TEMPORARY DESIGNATION. A TEMPORARY DESIGNATION IS GIVEN TO A PLANET AS SOON

AS IT IS DISCOVERED, BASED ON THE YEAR AND HALF-MONTH OF ITS DISCOVERY. IT

IS LISTED HERE BECAUSE OTHER PUBLICATIONS REFER TO THESE OBJECTS BEFORE IT

IS GIVEN A NUMBER.

3. GIVEN NAME. MOST OF THE NUMBERED OBJECTS RECEIVE NAMES.

4. REFERENCE. ‘E-83’ MEANS THAR RJE ELEMENTS OF THE ORBIT CAN BE FOUND IN THE

LENINGRAD ‘EPHEMERIDES OF MINOR PLANETS’ FOR 1983 – OTHERWISE IT IS THE

NUMBER OF THE MINOR PLANET CIRCULAR WHERE THE BEST ORBIT IS PUBLISHED.

5. B(a,0) MAG. THIS IS THE BLUE MAGNITUDE OF THE OBJECT WHEN IT IS AT ITS MEAN

DISTANCE FROM THE SUN AND IN OPPOSITION TO THE SUN.

6. MEAN DISTANCE. THIS IS THE SEMI-MAJOR AXIS OF THE PLANET’S ORBIT IN

ASTRONOMICAL UNITS (A.U. - MEAN DISTANCE OF THE EARTH FROM THE SUN.

7. ECCENTRICITY. THIS TELLS HOW ELONGATED THE ORBIT IS. E = C / A, WHERE ‘E’ IS

THE ECCENTRICITY, ‘C’ IS THE DISTANCE BETWEEN THE CENTER OF THE ORBIT AND

THE FOCUS AND ‘A’ IS THE SEMI-MAJOR AXIS.

8. PERIHELION DISTANCE. THIS TELLS HOW CLOSE THE PLANET GETS TO THE SUN. Q = A

8 ( 1 - E ) WHERE Q IS THE PERIHELION DISTANCE. IT IS MEASURED IN A.U.

9. APHELION DISTANCE. THIS TELLS HOW FAR AWAY THE OBJECT GETS FROM THE SUN. Q =

A 8 ( 1 + E ) WHERE ‘Q’ IS THE APHELION DISTANCE. IT IS ALSO MEASURED IN

A.U.

AT THIS POINT, YOU ARE PROBABLY WONDERING WHY THE LAST NINETEEN ASTEROIDS ARE

LISTED IN THE TABLE. SINCE THE PERIHELION DISTANCES ARE GREATER THAN ONE. THE

ANSWER IS THAT THESE BODIES ARE PART-TIME EARTH CROSSERS. THE ECCENTRICITY OF THE

ORBIT VARIES SO THAT THESE PLANETS HAVE CROSSED THE EARTH’S ORBIT IN THE PAST, AND

WILL DO SO AGAIN IN THE FUTURE. FOR EXAMPLE, 1915 QUETZALCOATL ACTUALLY CROSSED THE

ORBIT OF THE EARTH BEFORE 1943. THESE BODIES ARE CALLED ‘AMOR’ TYPE PLANETS BECAUSE

1221 AMOR WAS THE FIRST SUCH OBJECT TO BE RECOGNIZED.

AMOR OBJECTS ARE DEFINED ON THE BASIS OF THE PERIHELION DISTANCE BEING GREATER

THAN 1.017 (THE PRESENT APHELION DISTANCE OF THE EARTH) AND LESS THAN 1.3 A.U. THE

LATTER DISTANCE WAS PICKED BECAUSE THERE SEEMS TO BE A GAP IN THE PERIHELION

DISTANCES AT THAT POINT. THIRTEEN AMOR TYPE OBJECTS WERE NOT LISTED IN THE TABLE

BECAUSE THEY ARE NOT KNOWN EARTH CROSSERS.

FOUR OF THE MINOR PLANETS IN THE TABLE ARE CALLED ‘ATEN’ TYPE OBJECTS BECAUSE

2062 ATEN WAS THE FIRST TO BE RECOGNIZED. THESE PLANETS HAVE A MEAN DISTANCE OF < 1

A.U. FROM THE SUN. THE OTHER THREE ATEN’S IN THE TABLE ARE 2340 HATHOR, 2100 RA-

SHALOM, AND 1954XA, THESE PLANETS ARE ESPECIALLY INTERESTING BECAUSE THEIR MEAN

DAILY MOTION IS GREATER THAN THE EARTH’S. SO THEY BEHAVE LIKE AN INFERIOR PLANET

SUCH AS MERCURY AND VENUE. SINCE THEY ALSO CROSS THE EARTH'S ORBIT, IT IS POSSIBLE

FOR THEM TO BE IN SUPERIOR CONJUNCTION AS WELL AS INFERIOR CONJUNCTION, AT

DIFFERENT TIMES, OF COURSE.

THE OTHER TWENTY NINE MINOR PLANETS LISTED ARE CLASSED AS ‘APOLLO’ TYPE

OBJECTS, AFTER THE FIRST ONE TO BE SO RECOGNIZED, 1862 APOLLO. THESE PLANETS CAN

ALSO BE IN INFERIOR AS WELL AS SUPERIOR CONJUNCTION AT DIFFERENT TIMES. ONE OF THEM

IN FACT, 1620 GEOGRAPHOS, HAS TWO OPPOSITIONS THIS YEAR, WITH AN INFERIOR

CONJUNCTION IN BETWEEN! ONE OPPOSITION IS ON MARCH 1, AND THE SECOND ONE IS ON

OCTOBER 25. THE CLOSEST IT WILL COME TO EARTH IS ABOUT 8.27 MILLION MILES ON MARCH

16-17. AT THAT TIME IT WILL HAVE A MAGNITUDE OF 12.7 AND MOVING RAPIDLY SOUTH WEST.

THE DIVISION BETWEEN AMOR AND APOLLO TYPE MINOR PLANETS IS EXPECTED TO BE

TEMPORARY, BECAUSE OF PERTURBATIONS IN THEIR ORBITS (DISTURBANCES DUE TO MAJOR

PLANETS), JUST AS 1915 QUETZALCOATL WAS AT ONE TIME AN APOLLO TYPE, OTHER AMOR

OBJECTS ARE EXPECTED TO BECOME APOLLO TYPE, AND VICE VERSA. 1566 ICARUS, FOR

EXAMPLE, CROSSES THE ORBITS OF MERCURY, VENUS, EARTH AND MARS, AND CONSEQUENTLY,

THIS BODY IS SUBJECT TO LARGE PERTURBATIONS IN ITS ORBIT. THE SAME IS TRUE FOR 2212

HEPHAISTOS. ALL BUT FIVE OF THESE ASTEROIDS CROSS THE ORBIT OF MARS, AND THE FIRST

18 OBJECTS IN TABLE 1 CROSS THE ORBIT OF VENUS, SO THAT MANY CLOSE APPROACHES TO

MAJOR PLANETS ARE POSSIBLE, GIVEN ENOUGH TIME. THE ULTIMATE FATE OF THESE BODIES IS

EITHER TO COLLIDE WITH ONE OF THE MAJOR PLANETS, OR TO BE EJECTED OUT OF THE SOLAR

SYSTEM.

IT IS UNLIKELY THAT THESE ASTEROIDS COULD HAVE SURVIVED AS EARTH CROSSING

OBJECTS SINCE THE BEGINNING OF THE SOLAR SYSTEM. SO, IT IS NATURAL TO ASK WHERE

THEY CAME FROM. THIS WILL BE THE SUBJECT OF PART II OF THIS SERIES.

REFERENCES

1. MINOR PLANET CIRCULARS - SMITHSONIAN ASTROPHYSICAL OBSERVATORY - 60 GARDEN

STREET - CAMBRIDGE, MASS. 02138.

2. EPHEMERIDES OF MINOR PLANETS - INSTITUTE OF THEORETICAL ASTRONOMY LENINGRAD,

U.S.S.R. THIS IS AN ANNUAL VOLUME WHICH CAN BE OBTAINED FROM THE S.A.O.

(REF. 1) FOR 1982 AND 1983.

3. ASTEROIDS - EDITED BY TOM GEHRELS (1979) - UNIVERSITY OF ARIZONA PRESS.

SOMEWHAT TECHNICAL, BUT IT CONTAINS THE LATEST RESULTS IN THE FIELD. MAY BE

PURCHASED FROM SKY PUBLISHING CORP.

4. TABLES OF MINOR PLANETS -BY FREDERICK PILCHER AND JEAN MEEUS (1973).

CONTAINS MUCH VALUABLE INFORMATION ON THE FIRST 1813 MINOR PLANETS.-

5. MOONS AND. PLANETS - BY WILLIAM K. HARTMANN (1972) - CHAPTER 8 CONTAINS MUCH

INFORMATION NOT FOUND ELSEWHERE.

E A R T H C R O S S E R S – T A B L E I

PLANET TEMP GIVEN REF B(a,0) MEAN ECCEN- PERI. APHA.

NUMBER DESIG. NAME MAG. DIST. TRICITY DIST. DIST.

1566 1949MA ICARUS E-83 12.3 1.0779 .8267 0.1868 1.9691

2212 1978SB HEPHAISTOS E-83 17.2 2.1641 .8352 0.3567 3.9716

1974MA 4659 15.7 1.7752 .7620 0.4226 3.1279

2101 1936CA ADONIS E-83 20.6 1.8740 .7641 0.4422 3.3058

2340 1976UA HATHOR E-83 17.1 0.8440 .4498 0.4643 1.2237

2100 1978RA RA-SHALOM E-83 12.7 0.8320 .4364 0.4689 1.1952

1954XA 4823 16.2 0.7772 .3454 0.5088 1.0456

1982TA 7461 18.2 2.3019 .7693 0.5311 4.0728

1864 1971FA DAEDALUS E-83 15.5 1.4609 .6148 0.5628 2.3590

1865 1971UA CERPERlI5 E-83 12.3 1.0801 .4669 0.5758 1.5844

1937UB HERMES 3014 19.1 1.6393 .6236 0.6170 2.6616

1981 1973EA MIDAS E-83 18.8 1.7760 .6499 0.6217 2.9303

2201 1947XC E-83 18.7 2.1740 .7117 0.6267 3.7213

1981VA 6702 20.8 2.4600 .7439 0.6299 4.2901

1863 1932HA APOLLO E-83 16.3 1.4709 .5599 0.6473 2.2944

1979XB 5131 22.3 2.2624 .7133 0.6487 3.8762

2063 1977HB BACCHUS E-83 13.4 1.0778 .3496 0.7011 1.4546

1959LM 2025 18.0 2.1552 .6745 0.7016 3.6089

1685 1948OA TORO E-83 13.2 1.3672 .4560 0.7711 1.9632

2062 1976AA ATEN E-83 11.0 0.9665 .1826 0.7900 1.1429

2135 1977HA ARISTAEUS E-83 19.1 1.5999 .5034 0.7946 2.4053

1982HR 6952 17.0 1.2097 .3224 0.8196 1.5998

2329 1976WA ORTHOS E-83 18.9 2.4036 .6586 0.8206 3.9867

1620 1951RA GEOGRAPHOS E-83 14.1 1.2446 .3354 0.8271 1.6620

1950DA 3015 17.2 1.6834 .5020 0.8384 2.5283

1866 1972XA SISYPHUS E-83 15.7 1.8933 .5392 0.8724 2.9142

1973NA 4659 18.1 2.4272 .6381 0.8784 3.9760

1918CA 4660 14.7 1.1248 .2148 0.8832 1.3664

1863 1948EA ANTINOUS E-83 18.9 2.2602 .6066 0.8892 3.6311

2102 1975YA TANTALUS E-83 15.4 1.2901 .2983 0.9053 1.6749

1982BB 6951 14.8 1.4070 .3549 0.9078 1.9062

1982DB 6952 18.8 1.4893 .3602 1.9529 2.0257

1979VA 5319 20.5 2.6354 .6274 0.9821 4.2888

1981ET3 7234 16.2 1.7682 .4224 1.0212 2.5151

2608 1978DA SENECA 6827 21.6 2.4772 .5872 1.0227 3.9317

1980PA 5899 20.8 1.9263 .4586 1.0429 2.8097

2061 1960UA ANZA E-83 20.4 2.2647 .5375 1.0475 3.4818

1980AA 5279 21.6 1.8915 .4435 1.0526 2.7304

1943 1973EC ANTEROS E-83 15.5 1.4306 .2562 1.0642 1.7971

1917 1968AA CUYO E-83 18.6 2.1493 .5047 1.0645 3.2340

1915 1953EA QUETZALCOATL E-83 22.3 2.5278 .5774 1.0693 3.9874

1981QB 6895 19.2 2.2391 .5181 1.0790 3.3992

1980WF 5841 21.7 2.2308 .5141 1.0839 3.3777

1980 1950LA TEZCATLIPOCA E-83 15.9 1.7096 .3651 1.0854 2.3339

1221 1932EA1 AMOR E-83 20.5 1.92133 .4346 1.0858 2.7547

1972RB 4659 22.0 2.1487 .4875 1.1012 3.1962

1982DV 6952 18.1 2.0329 .4571 1.1036 2.9622

887 1918DB ALINOA E-83 19.0 2.4998 .5554 1.1113 3.8882

2202 1972RA PELE E-83 20.9 2.2904 .5123 1.1170 3.4637

1580 1950KA BETULIA E-83 17.9 2.1963 .4898 1.1206 3.2720

1627 1929SH IVAR E-83 15.2 1.8639 .3967 1.1245 2.6033

1982RA 7461 16.1 1.5750 .2838 1.1279 2.0220

The Calculating Astronomer

by Kenneth Wilson

This begins a new, and I hope a regular, mini-column for the W.A.S.P. In it I

hope to acquaint you with some useful, astronomically related formulas. Some of

these formulas will be elementary, basic ones for the novice and others will be more

involved. You should, however, be able to use them all with the assistance of one of

the many inexpensive scientific calculators that are so readily available these days.

Those of you with access to microcomputers are welcome to try your hand at adapting

these to them if you like, although that is not the purpose of this present effort. And,

of course, those traditionalists among you that prefer to use slide rules, tables, fingers

or other such paraphernalia are welcome to do so.

This month‟s formula will allow you to calculate the field of view of any of your

eyepieces in a particular telescope by simply timing the passage of a star across the

field and plugging that value into the formula. Choose a star near the meridian and

whose declination is known. Then switch off your clock drive, if you have one and let

the star drift from one edge of the field to the other across the widest part (diameter)

of the field. Now, take the time, „T‟, that it took for the star to cross the field and

insert it into the following formula:

F = 15 X T X cos δ

where F is the true field of view of the eyepiece in minutes of arc (60 minutes = 1

degree), T is the time in minutes for the star to cross the field and δ is the declination

of the star in degrees.

For a star on the celestial equator (e.g. Mintaka, the top star in Orion‟s Belt) the

cosine δ becomes 1, so you can forget about the cosine δ. This formula will work for

any telescope: equatorial, Dobsonian, transit, etc. You might want to work out the

field for each of your eyepieces and type the information on a 3” X 5” index card to be

kept with your eyepieces or taped on the telescope tube near the eyepiece holder.

If you have any questions, comments, corrections and/or suggested formulae for

this column please send them to: Ken Wilson 1750 Clarkson Apt. C, Richmond, VA

23224. Happy calculating!

The Slingshot Effect . . . . . . . . . Why?

By - Bruce Johnston

As a small object -- Voyager, for instance -- passes a large body -- Jupiter, for example

-- it is possible for the smaller object to gain energy in the form of velocity from the large

object. It is also possible that the reverse can happen. If the small object passes the large

object under different circumstances, the small object can be caused to LOSE energy to the

large object and, in fact, slow down.

How? It might seem that the angle of approach of the small object to the larger one is

very critical. It isn‟t. It might seem that the fact that the large object is travelling more-or-

less in a circle is very important. It isn‟t.

Now, don't let the above statements mislead you. The angle of approach does have an

effect on the total amount of slingshot effect we get, but the PRINCIPLE of the slingshot

effect doesn‟t require any very critical angle. There are many things which will have an

effect on the total amount of energy gain or loss, such as the velocities of the two objects,

their mass, the distance between them as they pass, etc., but this discussion is only

concerned with the PRINCIPLE of the slingshot effect and not how such energy is gained

or lost in a particular encounter.

To compound the possible confusion, an article In the February, 1982 issue of

Astronomy Magazine explains in detail the fact that the satellite from the planned “Galileo”

mission to Jupiter will be able to derive most of its orbit-shaping energy by, repeated close

passes to Jupiter‟s moons.

To quote from the article: “How can close encounters shape an orbit? From a strictly

trajectory point of view there are only four types of spacecraft encounters with the moons -

an inside equatorial pass, an outside equatorial pass . . .” and two polar passes which need

not concern us in the discussion of the slingshot effect.

All is well so far, but then the article explains that there are four combinations of

close encounter equatorial passes the spacecraft might make. In one case, the spacecraft

passes between the moon and Jupiter and GAINS energy, while in another it also passes

between the moon and Jupiter, but LOSES energy!

Likewise, there is a case where the moon is between the spacecraft and Jupiter and

the spacecraft GAINS energy, while In another case where the moon is between the

spacecraft and Jupiter, the spacecraft LOSES energy!

Rather than condemn the article as confusing (It Is a very GOOD article, as a matter

of fact), it is better to use it as a guide to tell us what is NOT necessary to gain or lose

energy by close encounters between the spacecraft and one of Jupiter‟s moons.

The position of Jupiter can‟t make a difference, for in the Jupiter-moon-spacecraft

system, we consider Jupiter as being stationary.

Passing “inside” or “outside” the moon can't be significant because, as I‟ve just

described, in one case of each, the spacecraft gains energy, and in another it loses energy.

Let‟s just forget about circles and ellipses, and deal just with straight lines. A little bit

of vector analysis comes into play, but it isn‟t too bad.

Let‟s begin by assuming our moon (or planet, in the case of Voyager) is moving in a

straight line.

Let‟s also assume that our spacecraft is moving in a straight line, so as to cross the

path of the planet.

The path can‟t be more than 90 degrees, for that would mean that the spacecraft is

moving in retrograde (backward) motion compared to the planet. Let‟s not confuse things

any more than necessary. We‟ll assume that both planet and spacecraft are moving in the

same GENERAL direction.

One very significant factor which must be present in order to get the slingshot effect is

that the planet must be MOVING! If it isn‟t, the path of the spacecraft will be altered

toward the planet somewhat, due to the gravitational attraction of the planet, but the

spacecraft will not gain or lose energy.

First, let‟s see the path of the spacecraft as it crosses the path of the planet when the

planet isn‟t there. It doesn‟t even exist as far as we‟re concerned, in this particular

drawing.

Since the spacecraft is moving lower-left to upper-right, it has kinetic energy. This

energy cannot be destroyed. It can be changed to another form, but not destroyed. In our

discussion of the slingshot effect, the energy will stay there, always trying to move the

spacecraft lower-left to upper-right, the same distance in a given time.

Now let‟s get the planet back into the picture.

If the planet isn‟t moving, as I said before, the path of the spacecraft will be altered,

but the total distance it travels in a given time will be unchanged. It would start at point

“x” and would end up at point “A” if the planet wasn‟t there, but, due to the force of

gravity it will end up travelling to point “B” In the same period of time. The velocity is

represented by the lengths of lines „X-A‟ and „X-B‟. If they‟re the same length, their velocity

must be the same.

The total amount of movement caused by the nearby field of gravity is represented by

line “G”.

Of course, the line „X-B‟ will be a curved line, but it is easier to picture the result if we

assume that the path is a nice straight line. This will hold true for the remainder of this

discussion.

Why doesn‟t the planet‟s gravity add to --- or subtract from --- the total velocity of the

spacecraft? After all, it has the ability to accelerate or decelerate an object. As a matter of

fact, the gravitational field DOES affect the velocity of the spacecraft, but it does it in such a

way that the net effects are cancelled by the time the spacecraft gets an equal distance past

the planet, (I just have to be careful in my drawings, in order for things to look like they

really are).

During the time the spacecraft is moving from point “X” toward the planet, the planet

causes the spacecraft to continually accelerate. The planet is pulling the spacecraft toward

the upper-right.

Once the spacecraft passes the planet, it is now continually being pulled backward by

the planet, causing it to decelerate. By the time it travels an equal distance past the planet,

It will have lost all the extra velocity it had gained, and it will be back to travelling at the

same velocity at which it started.

But, for the sake of the slingshot effect, we need the planet to be moving. This changes

the picture. As the spacecraft approaches the planet, it gains velocity, as before. However,

since the planet is moving UP in our diagram, the spacecraft will be dragged upward also,

by the gravitational field of' the planet.

The closer the spacecraft gets to the planet, the better the gravitational field can „grab‟

it. The faster the planet is moving, the faster it can drag the spacecraft. The slower the

spacecraft is moving, the 1onger it will stay near the planet and be dragged upward before

it finally moves far enough to the right that the drag' gets too weak to have a significant

effect.

This is actually an over-simplification of the role that planet velocity, spacecraft

velocity, and distance plays a part in the slingshot effect, but it gives a very general idea of

their role in the big picture of the slingshot effect.

In the next picture, line „G‟ is, again, the distance the spacecraft is deflected from its

original path by the gravitational field of the planet, just as before. Line „C‟ is the extra

distance added to the motion of the spacecraft, caused by the upward movement of the

planet. As you can see the line connecting „X‟ to „D‟ is longer than line „X-A‟. Since both

distances are covered in the same time, the spacecraft following line „X-D‟ has a higher

velocity.

The spacecraft has gained velocity --- and therefore, energy --- from the planet, by

passing BEHIND the planet when the planet is in motion.

This energy isn‟t free, however. It has to come from somewhere, and where it comes

from is the kinetic energy of the planet itself. We must, in speeding the spacecraft up, slow

the planet down. (Have no fear; due to the tremendous difference in mass between the

planet and the spacecraft, the amount that the planet slows down is vanishingly small.)

How does the spacecraft slow the planet down, however slight? Notice in the drawing

that the spacecraft is nearly always below the position of the planet. This means that the

spacecraft is BEHIND the planet as it moves. The spacecraft, then, is trying to pull the

planet backward. Instead, it just slows it slightly, lowering its kinetic energy exactly the

amount that the spacecraft gained.

In summary, because the spacecraft passed behind the planet as it moved, the

spacecraft gained speed. Slingshot!!

However, that's only half of the story. We need to see now how the spacecraft can be

made to LOSE energy. As you may have guessed, we do this by having the spacecraft pass

IN FRONT, of the planet. But that‟s no explanation. Why, by passing in front of a moving

planet, does the spacecraft lose energy (and the planet, in return, gain an equal amount of

energy)?

We already know that if the planet doesn't move, the spacecraft will alter its course

toward the planet, but will not gain or lose velocity. We needn‟t go through all that again.

Since the planet is moving TOWARD the intersection of the paths in this example, that

means that the planet is a goodly deal down the drawing when the spacecraft leaves point

„X‟.

Since it is so far away, it doesn't have too much tendency to pull the spacecraft to the

right or down. As time passes, however, the spacecraft moves closer to the intersection

point and so does the planet. The spacecraft gets pulled to the right even more, as well as

being pulled down (which is actually backward) even more.

Eventually, the spacecraft will pass the point where the two paths intersect. The

planet, in the meantime, is moving closer and closer to the point of intersection.

By the time the spacecraft would have reached point „A‟, it has been deflected

downward by the gravitational field of the planet (Just as if it hadn't been moving during

this time), but it gets further deflected downward because of the fact that the planet has

moved even closer to the spacecraft and its gravitational field is even stronger in its pull on

the spacecraft now. The spacecraft gets pulled downward an even greater amount, to point

„D‟.

The line „G‟ again represents the movement due to the stationary planets gravitational

field and the line „C‟ is the result of the increased gravitational field due to the fact that the

planet has moved even closer.

The spacecraft, rather than moving along line „X-A‟, or even „X-B‟ will move along the

line „X-D‟. Since it moves a shorter distance („X-D‟ is shorter than „X-A‟) in the same

period of time, it must be moving slower, or have a slower velocity. It then has LOST

velocity or energy.

The Planet has gained the energy that the spacecraft lost because, during all the time

the spacecraft and planet were moving, the spacecraft was in front of the planet, pulling it

forward with a feeble gravitational field. Feeble though it may be, it is still strong enough

to increase the velocity of the planet and raise its energy level, exactly the amount the

spacecraft lost.

To summarize: If the planet is moving and the spacecraft passes IN FRONT of the

planet, the spacecraft will LOSE energy. The planet, in turn, will gain whatever energy the

spacecraft loses.

Now, how about the four possible conditions of the Galileo spacecraft, and how is

their energy gain/loss accounted for with the previous explanation?

1. If the satellite passes the moon when the moon is in position “A” (Outbound-

Inside, as it's called), the spacecraft passes IN FRONT of the moon, and so loses energy. Its

orbit rotates clockwise and the orbit moves in closer to Jupiter, since it now has less

energy.

2. If the moon is at position “B” when the satellite passes it (Outbound-Outside),

the satellite passes BEHIND the moon, so the satellite GAINS energy and its orbit rotates

counter-clockwise, while the orbit gets larger, due to the increased energy.

3. If the moon is at point “C”, the satellite passes IN FRONT (Inbound-Outside)

of the moon, so the satellite LOSES energy. The orbit lowers closer to Jupiter and rotates

counter-clockwise.

4. If the moon is at location “D” as the satellite passes (Inbound-Inside), it

passes BEHIND the moon, so it GAINS energy and the orbit gets larger while rotating

clockwise.

The direction of rotation is incidental to the energy gain/loss, but I pass it along

because it should become apparent as to WHY the orbit rotates, from our discussion of how

the gravitational field effects the direction of our spacecraft.

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