"Annenberg Media" "¶" "CAPTIONING IS MADE POSSIBLE BY THE ANNENBERG/CPB PROJECT" "KEPLER'SSECONDLAW" "ANIMAGINARYLINE FROMTHESUNTOA PLANET" "SWEEPSOUTEQUALAREAS INEQUALTIMES." "THISLAWOF EQUALAREAS ALSO APPLIES TO THE VORTICES" "OF HURRICANES, FIRESTORMS, EVENBATHTUBS." "ANDATTHECENTER OFTHISSWIRLINGMOTION" "ISTHELAWOFTHECONSERVATION OFANGULARMOMENTUM." "IN THE 16th AND 17th CENTURIES," "THAT BRILLIANT REAWAKENING KNOWN AS THE RENAISSANCE" "CAME TO AN END." "EUROPE TURNED ITS ATTENTION TO A LIVELY DEBATE" "ON FINER POINTS OF CHRISTIAN THEOLOGY." "THAT PERIOD, THE REFORMATION AND COUNTER REFORMATION," "CULMINATED IN THE BLOODY THIRTY YEARS' WAR." "DURING THAT TIME, THREE GIANTS WALKED THE EARTH." "IN THE LONG RUN OF HISTORY," "THEY WOULD TURN OUT TO BE MORE IMPORTANT" "THAN THE BISHOPS AND KINGS." "THEIR NAMES WERE GALILEO GALILEI," "JOHANNES KEPLER," "AND TYCHO BRAHE." "GALILEO, OF COURSE, WE'VE ALREADY MET." "I'LL TELL YOU MORE ABOUT BRAHE LATER." "THE TIME HAS COME TO SPEAK OF JOHANNES KEPLER." "KEPLER CERTAINLY DIDN'T SEEM LIKE A GIANT." "IN FACT, HE WAS SMALL, FRAIL, NEARSIGHTED." "HE SUFFERED FROM FEVERS AND STOMACH DISORDERS." "HE WAS SUBJECT TO CYCLES" "OF DEEP DEPRESSION AND SOARING ELATION." "THE ELATION WAS USUALLY ASSOCIATED" "WITH SOME SCIENTIFIC DISCOVERY THAT HE HAD MADE" "OR THOUGHT HE HAD MADE." "HE WAS ALSO RIGOROUSLY HONEST." "FOR EXAMPLE, HE DESCRIBED HIS OWN MOTHER" "AS GARRULOUS AND BAD-TEMPERED" "AND HIS FIRST WIFE AS FAT, CONFUSED, AND SIMPLE-MINDED." "HE WROTE ABOUT HIS SCIENCE IN THE SAME WAY." "HE WROTE ABOUT HIS FAILURES," "ABOUT HIS FEELINGS WHILE HE WAS DOING IT." "THAT'S NOT THE WAY" "SCIENTIFIC PAPERS ARE WRITTEN TODAY," "EACH SEEMINGLY A TRIUMPH OF LOGIC," "WHICH, OF COURSE, IS NEVER TRUE." "HE WAS ALSO A MYSTIC." "IN FACT, HE WAS A PROFESSIONAL ASTROLOGER." "IN THOSE DAYS, MATHEMATICIANS CAST HOROSCOPES FOR A LIVING." "KEPLER THOUGHT ALL ASTROLOGERS WERE CHARLATANS AND FRAUDS" "THAT IS, ALL ASTROLOGERS OTHER THAN HIMSELF." "HE CAST HIS OWN HOROSCOPE," "DECIDING THAT HE HAD BEEN CONCEIVED" "AT 4:07 A.M. ON MAY 16, 1571." "WELL, MAYBE, OR MAYBE NOT." "IT WAS HIS PARENTS' WEDDING NIGHT," "AND HE WAS BORN SEVEN MONTHS LATER." "HE WAS AN AUTHENTIC GENIUS." "FOR EXAMPLE, IN THE COURSE OF RESOLVING A DISPUTE" "ABOUT THE SHAPE OF WINE BARRELS," "HE VERY NEARLY INVENTED THE INTEGRAL CALCULUS." "HE ALSO DISCOVERED MANY LAWS." "THREE OF THEM TURNED OUT TO BE CORRECT." "IT'S FOR THOSE THAT WE REMEMBER HIM." "ONE OF JOHANNES KEPLER'S THREE LAWS, THE SECOND," "REVEALS A MOST BEGUILING AND PERVASIVE PRINCIPLE OF NATURE," "A PRINCIPLE THAT EXPLAINS THE SHAPE OF GALAXIES" "AND FURY OF HURRICANES." "AND EVEN THOSE COMPARATIVELY CALM WHIRLPOOLS" "IN THE FAMILY BATH." "IN THE END, KEPLER'S SECOND LAW WAS SEEN" "AS A SIMPLE CONSEQUENCE" "OF THE LAW OF CONSERVATION OF ANGULAR MOMENTUM." "BUT IN THE BEGINNING," "HIS IDEA WAS VIEWED AS A WAY AROUND" "A BODY OF GREEK KNOWLEDGE CAST IN STONE" "AN OUTRAGE AGAINST THECCEPTED ANATOMY OF THE UNIVERSE." "KEPLER STOOD UP TO THE CLASSICAL ASTRONOMERS," "TURNING HIS BACK ON 2,000 YEARS OF COLLECTIVE WISDOM." "ASTRONOMY, EVEN BEFORE MEDICINE," "WAS PRACTICED AS THE FIRST PHYSICAL SCIENCE." "IN ANCIENT CHINA AND GREECE..." "IN BABYLON..." "IN ALEXANDRIA AROUND THE BIRTH OF CHRIST..." "IN COPAN" "SACRED SCIENTIFIC CENTER OF THE MAYANS" "WITHIN THE WISDOM OF THE CALIPHATE OF BAGHDAD," "IN THE MOORISH ALHAMBRA," "WHERE MATHEMATICS AND ART COMBINED TO MAKE GRAND DESIGNS." "WHEREVER PEOPLE RELIED ON THE CYCLES OF NATURE" "AND THAT'S WHEREVER CROPS WERE PLANTED" "PEOPLE RELIED ON ASTRONOMERS" "TO POINT THE WAY FORETOLD BY THE STARS." "THE MORE ASTRONOMERS KNEW ABOUT THE HEAVENS," "THE MORE EFFECTIVE THEY WERE ON EARTH." "SO THEY ATTEMPTED TO REPRODUCE HEAVEN ON EARTH," "A MODEL OF THE UNIVERSE" "THAT DUPLICATED THE STAR-FILLED CONFIGURATION" "THEY'D OBSERVED FOR AGES." "THIS WAS NO EASY TASK," "NOT EVEN FOR THE BEST MINDS OF THE GOLDEN AGE." "THE GREEKS CREATED ALL SORTS OF ORIGINAL SCHEMES" "UNTIL ABOUT 350 B.C." "THAT'S WHEN A PHILOSOPHER NAMED ARISTOTLE CAME ALONG" "TO SHARE A FEW THOUGHTS" "ABOUT EVERYTHING UNDER AND INCLUDING THE SUN." "ONE OF ARISTOTLE'S IDEAS HELD FIRMLY" "THAT THE EARTH IS THE CENTER OF THE UNIVERSE." "HE ALSO CONVINCINGLY ARGUED" "THAT ALL HEAVENLY BODIES MOVE IN PERFECT, UNIFORM CIRCLES." "THEY REALLY DON'T." "THEREFORE, TO DRAW THE PLANETARY MOTIONS" "ALONG ARISTOTELIAN LINES," "ASTRONOMERS HAD TO RECREATE" "A COSMOS OF COMPLICATED CIRCLES" "MOVING AROUND ON TOP OF OTHER COMPLICATED CIRCLES." "THIS ROUNDABOUT SYSTEM OF EPICYCLES WAS BIZARRE," "COMPLEX TO THE POINT OF BEING ALMOST INCOMPREHENSIBLE." "BUT IT SAVED THE APPEARANCES," "WHICH WAS SCIENTIFIC DOUBLETALK," "TO JUSTIFY FITTING ROUNDS PEGS INTO SQUARE HOLES." "IN MANY PRACTICAL WAYS, IT ACTUALLY WORKED." "FOR EXAMPLE, IT MORE OR LESS PREDICTED" "THE POSITIONS OF STARS AND PLANETS." "IT AIDED NAVIGATION." "PERHAPS MOST IMPORTANT," "IT HELPED ASTRONOMERS CAST ROYAL HOROSCOPES," "WHICH WAS A VITAL COMPONENT IN THEIR JOB SECURITY." "INDEED, THE ARISTOTELIAN VIEW," "WITH THE EARTH AT THE CENTER OF A UNIVERSE" "IN WHICH ALL MOTION WAS UNIFORMLY CIRCULAR," "SATISFIED ALMOST EVERYONE" "ALMOST EVERYONE EXCEPT NICOLAUS COPERNICUS" "WHO, AROUND 1500," "WROTE AN INTELLECTUAL TORNADO OF A BOOK," "THEREVOLUTION OFHEAVENLYORBS." "WITHIN THESE PAGES WERE IDEAS POWERFUL ENOUGH" "TO UPROOT AND SEND THE EARTH HURTLING THROUGH SPACE," "TOSSING ASIDE THE VERY FOUNDATION" "OF PHYSICAL SCIENCE IN THE PROCESS." "IN ONE OTHERWISE INNOCENT CHAPTER," "COPERNICUS RECREATED THE UNIVERSE." "HE PUT THE SUN, NOT THE EARTH, AT ITS CENTER." "AND HE PUT THE EARTH IN ORBIT AROUND THE SUN." "THE COPERNICAN UNIVERSE WAS AN IDEA AS REVOLUTIONARY" "AS ANY BEFORE OR SINCE." "FROM COPERNICUS ONWARD," "THE WORD REVOLUTION HAS MEANT RADICAL CHANGE." "YET EVEN WHILE ATTEMPTING" "TO OVERTHROW THE ARISTOTELIAN STRONGHOLD," "COPERNICUS RETAINED THAT INGRAINED PRACTICE" "OF THE ASTRONOMER'S TRADE-- SAVING APPEARANCES." ""PLANETS ORBIT THE SUN," HE VENTURED," ""AND NOT IN PERFECT CIRCLES AT UNIFORM RATES."" "HOWEVER, IN ORDER TO SAVE APPEARANCES," "HE VENTURED NO FURTHER." "COPERNICUS CONCLUDED HIS BOOK" "BY SPINNING THE AGE-OLD YARN OF EPICYCLES." "IN THE END, THE COPERNICAN SYSTEM" "WAS NOT ONLY BIZARRE," "ITS REVOLUTION WAS ALMOST HIDDEN" "BEHIND A SMOKESCREEN OF ASTRONOMICAL COMPLEXITY." "NONETHELESS, SUCH IDEAS GAVE OFF SPARKS" "THAT FIRED THE IMAGINATION OF JOHANNES KEPLER." "HE KNEW COPERNICUS HAD UNDERMINED" "THE FIRST GREAT DICTUM OF ANTIQUITY." "SINCE EARTH WASN'T THE STATIONERY CENTER OF THE UNIVERSE," "KEPLER WAS FREE TO GO AROUND UNIFORM CIRCULAR MOTION." "BUT WHAT COULD TAKE ITS PLACE?" "ANSWERING THAT QUESTION" "TOOK THE BETTER AND THE WORST PART OF KEPLER'S LIFE" "A JOURNEY WITH CALCULATIONS THAT STRETCHED ACROSS EUROPE." "FINDING THE ANSWER" "TOOK EVERYTHING HE HAD AND ANYTHING HE COULD BORROW." "EVENTUALLY, THE MAN CALLED THE WANDERING MATHEMATICIAN" "COULD DESCRIBE THE MOTIONS OF THE PLANETS." "GOING FURTHER THAN COPERNICUS," "KEPLER FOUND THE THREE LAWS OF PLANETARY MOTION." "KEPLER'S FIRST LAW GAVE THE ORBITS OF THE PLANETS" "A NEW, NONCIRCULAR SHAPE" "AND PUT THE SUN A LITTLE OFF THE CENTER OF THINGS." "IN THE COURSE OF ITS TRAVELS," "A PLANET IS SOMETIMES CLOSER TO THE SUN" "AND SOMETIMES FARTHER AWAY." "ACCORDING TO KEPLER'S SECOND LAW," "THE CLOSER IT GOT TO THE SUN," "THE FASTER IT MOVED." "THE FARTHER AWAY THE PLANET GOT," "THE SLOWER IT MOVED." "HIS THIRD LAW SAID THAT THE LARGER A PLANET'S ORBIT," "THE LONGER IT TOOK TO GO AROUND." "KEPLER'S THREE LAWS DESCRIBE THE HEAVENS" "WITH MATHEMATICAL PRECISION." "AT THE SAME TIME," "HIS PRINCIPLES ARE AT WORK CLOSER TO HOME." "KEPLER'S SECOND LAW" "EXPLAINS WHY EVEN THE MOST PLAYFUL WATER" "SPIRALS DOWN THE DRAIN IN A VERY STRICT MANNER." "GOING ROUND AND ROUND, CIRCLING FASTER AND FASTER," "THE WATER FINALLY RUPTURES AND FORMS A HOLE IN THE CENTER," "A WHIRLPOOL SCIENTISTS CALL THE VORTEX." "NOT EVERY VORTEX REMAINS SO CALM" "OR WITHIN HUMAN REACH." "AN UPWELLING OF AIR," "MOVING AT FIRST IN GENTLE CIRCLES," "CAN TWIST ITSELF INTO AN AWESOME VORTEX," "THE HURRICANE." "AS AN ASTRONOMER OF THE 1600s," "KEPLER WAS CONCERNED WITH THE WEATHER." "BUT HIS SEARCH FOR THE ANSWER" "TO WHY THE PLANETS MOVE AS THEY DO" "LED HIM ABOVE THE EARTH'S ATMOSPHERE." "IT WOULD TAKE NEWTON TO DETERMINE WHY" "PLANETS MOVE FASTER WHEN CLOSER TO THE SUN," "BUT KEPLER DID DISCOVER" "HOW MUCH FASTER THEY APPROACHED IT." "AS A PLANET MOVES AROUND THE SUN," "THE VECTOR FROM SUN TO PLANET" "SWEEPS OUT EQUAL AREAS IN EQUAL TIMES." "WHEN THE PLANET'S FAR FROM THE SUN, MOVING SLOWLY," "IT SWEEPS OUT AN AREA IN A CERTAIN TIME." "WHEN IT'S CLOSER TO THE SUN, MOVING FASTER," "IT SWEEPS OUT THE SAME AREA IN THE SAME AMOUNT OF TIME." "IN TWO SWEEPING GESTURES, THATR'ND LAW." "THE VECTOR SWEEPS OUT AN AREA IN THE FORM OF A TRIANGLE." "THE AREA OF THE PARALLELOGRAM FORMEDBYTWOVECTORS" "ISTHECROSSPRODUCT." "THEAREAOF THETRIANGLE ISJUSTHALFTHAT." "TURN THIS INTO A DERIVATIVE," "THERESULTIS THERATE" "OF CHANGE OF THE AREA VECTOR." "dA/dtISEQUALTO 1/2rx v ,A CONSTANT," "THESAMEIN ALLPARTS OFTHEPLANET'SORBIT." "KEPLER'S LAW OF EQUAL AREAS" "DOESN'T APPLY ONLY TO ORBITING PLANETS." "HERE, EACH DROP WILL OBEY THE SAME LAW." "THE WATER SEEMS CALM, STILL, MOTIONLESS." "BUT DUE TO THE EARTH'S ROTATION," "AMONG OTHER REASONS," "WATER IN ANY CONTAINER CIRCULATES," "AND SOMETIMES CIRCULATING WATER" "HAS AN INCREASINGLY AMAZING EFFECT." "AT FIRST, IT DRAINS NICE AND SMOOTH." "BUT FLOWING INWARD," "THE WATER BEGINS TO CIRCLE AROUND THE DRAIN." "JUST LIKE KEPLER'S PLANETS," "IT SWEEPS OUT EQUAL AREAS IN EQUAL TIMES." "UNLIKE THE PLANETS," "THE WATER MOVES IN SMALLER AND SMALLER CIRCLES," "FASTER AND FASTER UNTIL ITS VORTEX DEVELOPS." "THE WHIRLPOOL REMAINS UNTIL THE WATER'S GONE." "ONCE THE VORTEX GETS GOING, IT'S HARD TO STOP." "CIRCULATING OR ROTATING OBJECTS" "A PLANET, WATER, EVEN AN ICE SKATER" "ALL OBEY THE SAME BASIC LAW." "IT'S NOT THE LAW OF EQUAL AREAS," "WHICH IS A RELATED BUT INCIDENTAL CONSEQUENCE" "OF A DEEPER LAW OF NATURE." "IT'S THE LAW" "OF THE CONSERVATION OF ANGULAR MOMENTUM." "WHAT IS ANGULAR MOMENTUM?" "THE CONSERVATION OF ORDINARY MOMENTUM" "COMES FROM NEWTON'S LAW." "FORCE EQUALS RATE OF CHANGE OF MOMENTUM." "IF THERE'S NO FORCE, MOMENTUM DOESN'T CHANGE." "IT'S CONSTANT." "IN OTHER WORDS, THE MOMENTUM IS CONSERVED." "BUT THERE'S A STRANGE TWIST WHEN THE MOMENTUM IS ANGULAR." "EVEN IF THERE IS A FORCE APPLIED TO A BODY," "SOMETHING MAY STILL BE ZERO." "AND SOMETHING IS EQUAL TO ZERO" "NOT THE FORCE, BUT THE TWIST." "TO PUT IT MATHEMATICALLY, r x F = 0." "OBVIOUSLY, NOT ALL FORCES BEHAVE THAT WAY." "FOR EXAMPLE, TO OPEN A VALVE" "OR TO GET A WHEEL ROLLING," "TWIST IS JUST WHAT'S NEEDED." "HOWEVER, FOR A PLANET IN ORBIT," "OR FOR WATER FLOWING AROUND AND DOWN A DRAIN," "EVEN FOR A HURRICANE," "THERE'S NO SUCH TWISTING FORCE." "GRAVITY AND FLUID PRESSURE" "THE MAIN FORCES AT WORK ON VORTICES" "CAN'T TWIST ABOUT THE CENTER OF THE MOTION." "WHY?" "BECAUSE IN THESE CASES, r x F = 0." "WHEN FORCE IS 0, MOMENTUM IS CONSERVED." "WHEN r x F IS 0, SOMETHING ELSE IS CONSERVED." "SO WHAT IS r x F THE DERIVATIVE OF?" "THEANSWERIS FOUND BYDIFFERENTIATINGrx v." "USETHEPRODUCTRULE." "dr/dt IS v," "AND v x v IS 0." "SO THE DERIVATIVE OF r x v" "IS r x a." "NOWMULTIPLYBY THEMASS." "LISmTIMESrxv." "IFr x F ISO," "THE QUANTITY L IS CONSERVED." "L IS THE ANGULAR MOMENTUM." "r x F, THE TWISTING FORCE, ISCALLEDTORQUE." "FOREXAMPLE," "APLANETIN ORBIT HASNOTORQUE." "ITCONSERVES ANGULARMOMENTUM." "THAT'SWHYKEPLER'S SECONDLAWIS TRUE." "ACCORDING TO THE LAW OF INERTIA," "A BODY MOVING IN A STRAIGHT LINE" "WILL CONTINUE AT CONSTANT SPEED" "UNLESS A FORCE IS APPLIED TO IT." "A SPINNING BODY CONTINUES ROTATING" "UNLESS A TWIST, OR TORQUE, IS APPLIED." "THIS IS THE ESSENCE" "OF THE LAW OF CONSERVATION OF ANGULAR MOMENTUM." "THEANGULARMOMENTUM,L," "ISA VECTORFOLLOWING THERIGHT-HANDRULE." "FORCIRCULARMOTION,WHENv ANDr AREPERPENDICULAR," "THESIZEOF LISmrv." "TOKEEPLCONSTANT," "IF THE CIRCLE GETS SMALLER," "THE SPEED MUST GET BIGGER." "THE SAME BASIC RULE EXPLAINS KEPLER'SSECONDLAW." "INANELLIPTICALORBIT," "APLANETMUSTMOVEFASTER WHENIT'SCLOSERTOTHESUN" "ANDSLOWER WHENIT'SFARTHERAWAY." "THE SAME IDEA APPLIES TO A SPINNING ICE SKATER." "WHEN SHE PULLS IN HER ARMS," "HER WHOLE BODY SPINS FASTER TO CONSERVE ANGULAR MOMENTUM." "OF COURSE, WARM WATER DIFFERS FROM ICE," "BUT THE PHYSICS IS MUCH THE SAME." "WATER THAT'S NOT IN A SOLID STATE" "LACKS ENOUGH VISCOSITY TO APPLY MUCH TORQUE." "ITS MAIN FORCE IS DIRECTED TOWARD THE HOLE" "TO REPLACE THE DRAINING WATER." "FAR FROM THE CENTER," "WATER CIRCULATES IN GREAT, LAZY CIRCLES." "BUT AS IT'S FORCED TOWARD THE CENTER," "ITS SPEED INCREASES UNTIL, LIKE A TORNADO," "IT RUPTURES INTO A VORTEX." "A TORNADO, OFTEN CALLED A TWISTER," "IS THE SAME PHENOMENON AS THE WHIRLPOOL," "ONLY UPSIDE-DOWN." "THIS VORTEX STARTS" "WHEN CALM AIR AT THE CENTER MOVES UPWARD," "FORCING CIRCULATING AIR INWARD TO REPLACE IT." "SOMETIMES THE UPWELLING OCCURS BECAUSE OF FIRE." "WHEN A VORTEX DEVELOPS, IT'S CALLED A FIRESTORM," "LITERALLY, A HURRICANE OF FIRE." "IT WASN'T MRS. O'LEARY'S COW" "THAT CAUSED CHICAGO'S DEVASTATION IN 1871." "IT WASAS THE VORTEX OF HER FIRESTORM." "AND AS VICTIMS LEARNED" "DURING THE SECOND WORLD WAR," "ONCE FIRESTORMS GET STARTED," "THEY'RE HELL TO STOP." "SEEMINGLY, THEY LAST FOREVER." "THE RED SPOT OF JUPITER IS AN ENORMOUS HURRICANE," "AND ONE THAT'S RAGED AT LEAST SINCE 1610." "GALILEO WAS THE FIRST TO VIEW IT," "AS WELL AS JUPITER'S MOONS, ORBITING IN A PLANE." "LIKEWISE, SATURN'S RINGS ARE SATELLITES ON A PLANE" "SURROUNDING A CENTRAL BODY." "THE ENTIRE SOLAR SYSTEM IS BUILT ALONG THE SAME LINES." "BEYOND THAT, MANY GALAXIES SHARE THE BASIC SHAPE" "OF A FLAT DISK AROUND A GLOBULAR CENTER." "IN THE STRUCTURE OF THE UNIVERSE," "WHY IS THIS DISK SHAPE SO PERVASIVE?" "PROBABLY BECAUSE OF THE CONSERVATION" "OF ANGULAR MOMENTUM." "PICTURE A GALAXY STARTING OUT" "AS AN ENORMOUS SPHERICAL GLOB," "A MASSIVE SLOW ROTATION OF MATTER," "OF PROTOSTARS AND DEBRIS AND COSMIC DUST." "PICTURE EACH BIT OF MATTER" "ATTRACTED BY THE GRAVITY OF ALL THE MATTER INSIDE," "AND PIECE BY PIECE, CONDENSING TOWARD A POINT IN THE CENTER." "AS THE PARTICLES MOVE INWARD, THEY PICK UP SPEED," "WHIPPING AROUND FASTER AND FASTER," "RATHER THAN FALLING TO THE CENTER." "THEY'RE IN ORBIT." "THEY CONTINUE IN ORBIT FOREVER." "THAT'S THE WAY ANGULAR MOMENTUM" "HELPS TO DESIGN THE UNIVERSE." "IN 1562, THERE WAS A MAJOR CONJUNCTION" "OF THE SUPERIOR PLANETS." "THIS EVENT WAS WATCHED WITH BATED BREATH" "BY A WORLD STEEPED IN ASTROLOGY." "IT TURNED OUT THAT THE OLD ASTRONOMICAL TABLES" "WERE A FEW DAYS OFF." "THE NEW COPERNICAN TABLES WERE EVEN WORSE." "ALL OF THIS HAD A STUNNING EFFECT" "ON A YOUNG DANISH ARISTOCRAT." "HIS NAME WAS TYCHO BRAHE." "HE REALIZED THAT THE PREDICTIONS WERE POOR IN BOTH SYSTEMS" "BECAUSE THE NECESSARY, PRECISE, AND CONTINUOUS OBSERVATIONS" "HAD NEVER BEEN MADE." "HE DECIDED TO BECOME AN ASTRONOMER HIMSELF." "HE PERSUADED KING FREDERICK" "TO GIVE HIM AN ISLAND CALLED HVEEN" "OFF THE COAST OF DENMARK" "WHERE HE BUILT A PALATIAL OBSERVATORY" "AND THE FINEST ASTRONOMICAL INSTRUMENTS" "THAT HAD EVER BEEN CONSTRUCTED." "HE NOT ONLY MADE THE NECESSARY OBSERVATIONS," "HE ALSO CREATED HIS OWN UNIVERSE" "CALLED THE TYCHONIC UNIVERSE." "IN THE ARISTOTELIAN UNIVERSE," "THE EARTH WAS AT THE CENTER." "THE OTHER BODIES ROTATED AROUND THE EARTH" "ON CRYSTAL SPHERES." "THE COPERNICAN UNIVERSE CHANGED ALL THAT" "BY PUTTING THE SUN AT THE CENTER" "AND MAKING THE EARTH ONE OF THE PLANETS." "BUT IT WAS STILL A UNIVERSE" "THAT ROTATED ON CRYSTAL SPHERES." "IN THE TYCHONIC UNIVERSE, EARTH WAS AT THE CENTER," "AND THE SUN ROTATED AROUND THE EARTH." "ALL THE OTHER PLANETS ROTATED AROUND THE SUN." "TO US, THE TYCHONIC SYSTEM SEEMS LIKE A COMPROMISE" "BETWEEN THE ARISTOTELIAN AND THE COPERNICAN WORLDS," "BUT IT WAS A RADICAL INNOVATION." "HAVING THE PLANETS ROTATE AROUND THE SUN" "AND THE SUN AROUND THE EARTH" "SMASHED THE CRYSTAL SPHERES OF BOTH OLDER SYSTEMS." "OF COURSE, TYCHO BELIEVED PASSIONATELY IN HIS OWN SYSTEM." "IN FACT, HE CONSIDERED IT" "HIS MOST IMPORTANT ACCOMPLISHMENT." "BUT WE KNOW, LOOKING BACK IN HISTORY," "THAT HIS REAL MOST IMPORTANT ACCOMPLISHMENT" "WERE THOSE CAREFUL, SYSTEMATIC OBSERVATIONS OF THE SKIES." "BEFORE TYCHO, THE POSITIONS OF THE HEAVENLY BODIES" "WERE KNOWN WITH AN UNCERTAINITY OF 10 MINUTES OF ARC," "ABOUT 1/6 OF A DEGREE." "1 DEGREE IS ABOUT THE WIDTH OF 1 FINGER AT ARM'S LENGTH." "IMAGINE PRIMITIVE OBSERVATIONS" "WITH AN UNCERTAINITY OF ABOUT 1/6 THAT." "WHEN TYCHO WAS FINISHED," "THE UNCERTAINTIES IN THE POSITIONS" "OF THE HEAVENLY BODIES" "HAD BEEN REDUCED TO 2 MINUTES OF ARC." "IT WAS FROM THAT CRUCIAL IMPROVEMENT" "THAT THE REST OF OUR STORY FLOWS." "WE'LL CONTINUE THAT STORY NEXT TIME." "THEANGULARMOMENTUM OFANOBJECT" "ISDEFINEDAS  THECROSSPRODUCT" "OFTHERADIUS FROMA SPECIFIEDPOINT" "ANDITSMOMENTUM." "A FORCE THAT APPLIES A TWIST ISCALLEDATORQUE" "ANDISEQUAL TOTHECROSSPRODUCT" "OFTHERADIUSAND FORCE, rx F." "TORQUEISEQUAL TOTHERATEOFCHANGE" "OFANGULARMOMENTUM." "WHENNOTORQUESACT  ONANOBJECT," "THEOBJECT'S ANGULARMOMENTUMIS CONSERVED." "CAPTIONING PERFORMED BY THE NATIONAL CAPTIONING INSTITUTE, INC." "CAPTIONS COPYRIGHT 1985 CALIFORNIA INSTITUTE OF TECHNOLOGY" "THE CORPORATION FOR COMMUNITY COLLEGE TELEVISION THE ANNENBERG/CPB PROJECT" "PUBLIC PERFORMANCE OF CAPTIONS PROHIBITED WITHOUT PERMISSION OF NATIONAL CAPTIONING INSTITUTE" "Annenberg Media" "¶" "For information about this and other Annenberg Media programs call 1-800-LEARNER and visit us at"