"Annenberg Media" "¶" "CAPTIONING IS MADE POSSIBLE BY THE ANNENBERG/CPB PROJECT" "STUDYINGTHEORBITOFMARS  AROUNDTHESUN," "JOHANNESKEPLERDISCOVERED ITSPATHCOULDBEEXPLAINED" "ONLYIFTHEPLANET TRAVELEDALONGAN ELLIPSE." "ITWASTHEFIRST OFKEPLER'STHREELAWS." "I'M SURE YOU'LL REMEMBER" "THAT TYCHO BRAHE HAD HIS OWN SYSTEM OF THE UNIVERSE." "IN THE TYCHONIC SYSTEM," "THE EARTH WAS STATIONARY" "AT THE CENTER." "THE SUN WENT AROUND THE EARTH," "AND ALL THE OTHER PLANETS WENT AROUND THE SUN." "OF COURSE," "TYCHO BELIEVED PASSIONATELY IN HIS OWN SYSTEM," "AND ON HIS DEATHBED," "HE BEGGED KEPLER TO USE THE NEW OBSERVATIONS" "TO PROVE THE CORRECTNESS OF THE TYCHONIC SYSTEM." "I HAVE NO IDEA WHAT KEPLER THOUGHT" "AT THAT MOMENT," "BUT DOING WHAT TYCHO HAD ASKED HIM TO DO" "NEVER CROSSED HIS MIND." "KEPLER WAS A COPERNICAN TO HIS CORE." "WHEN HE GOT HIS HANDS ON TYCHO'S DATA," "THE FIRST THING HE SET OUT TO DO" "WAS ANALYZE MARS' ORBIT." "IT WAS ENORMOUSLY DIFFICULT." "NO MATTER WHAT HE DID," "HE COULDN'T MAKE MARS' ORBIT FIT A CIRCLE." "THE DISAGREEMENT BETWEEN MARS' ANGULAR POSITION" "AND THE BEST CIRCULAR ORBIT WAS EIGHT MINUTES OF ARC." "IF HE HAD TRIED THE SAME THING" "BEFORE TYCHO'S OBSERVATIONS," "IT WOULD HAVE BEEN POSSIBLE." "WITH THE DATA, IT COULD NOT WORK." "AND SO KEPLER WAS FACED WITH A DIRECT CONFLICT" "BETWEEN THE ANCIENT PLATONIC DICTUM" "THAT ALL MOTIONS IN THE HEAVENS" "HAD TO BE CIRCULAR MOTIONS" "AND THE NEW TYCHONIC OBSERVATIONS." "FACED WITH THAT CONFLICT, HE MADE HIS CHOICE." "HE CHOSE THE OBSERVATIONS." "HE STARTED TO SEARCH FOR A DIFFERENT SMOOTH CURVE" "THAT WOULD DESCRIBE THE ORBIT OF MARS." "AFTER YEARS OF AGONIZING WORK," "HE HIT UPON THE ANSWER." "IT WAS A CURVE" "THAT HAD BEEN KNOWN FOR THOUSANDS OF YEARS," "AND IT'S CALLED AN ELLIPSE." "IN THE MOST GRAPHIC TERMS," "A PIECE OF STRING AND TWO PINS" "ILLUSTRATE THE SIMPLE ELEGANCE OF AN ELLIPSE." "SINCE THE STRING DOESN'T STRETCH INTO A DIFFERENT LENGTH," "THE TOTAL DISTANCE" "FROM ONE PIN TO THE PENCIL TO THE OTHER PIN" "IS CONSTANT." "A SINGLE POINT IS CALLED THE FOCUS," "TWO POINTS, THE FOCI." "THE LENGTH OF THE SEMIMAJOR AXIS IS a." "THE SEMIMINOR AXIS HAS THE LENGTH b." "THE REGION BOUNDED BY THE ELLIPSE" "HAS AREA PIab." "THE DISTANCE FROM THE CENTER TO EITHER FOCUS" "IS SOME FRACTION OF a, ea." "THE SYMBOL e REPRESENTS THE AMOUNT OF ECCENTRICITY." "AS IN THE SOCIAL CONTEXT OF THE WORD," "ECCENTRICITY MEANS SOMEWHAT OFF CENTER." "SO WHEN e SHRINKS TO ZERO," "WHEN THERE'S NO ECCENTRICITY," "THE RESULT IS A PERFECTLY ROUNDED FIGURE," "AN ELLIPSE CALLED A CIRCLE." "BUT WHEN e INCREASES," "THE ELLIPSE BECOMES INCREASINGLY ECCENTRIC" "AND INCREASINGLY FLAT." "FOCUS IS LATIN FOR FIREPLACE." "IT WAS FIRST USED FOR THE ELLIPSE" "BY A MAN WHO BECAME KNOWN AS THE WANDERING MATHEMATICIAN." "HE WAS JOHANNES KEPLER." "IN THE SUN," "HE SAW THE GREATEST FIREPLACE IN THE UNIVERSE." "IN HIS EMOTIONAL LIFE, HOWEVER," "PARTICULARLY AS A CHILD," "HE SAW VERY LITTLE WARMTH." "KEPLER'S FATHER, A LOW-RANK SOLDIER OF FORTUNE," "DESERTED THE FAMILY EARLY." "HIS MOTHER WAS LATER TRIED FOR WITCHCRAFT." "IT'S UNKNOWN WHETHER KEPLER SENIOR FLED" "BECAUSE SHE MIGHT HAVE BEEN A WITCH." "IN HIS FATHER'S ABSENCE," "JOHANNES WAS CONSTANTLY VISITED BY POVERTY," "AND DESPITE HIS MOTHER'S ALLEGED CHARMS," "BY ILLNESS AS WELL." "HIS BACKGROUND CHALLENGES MANY CONTEMPORARY NOTIONS" "ABOUT HEREDITY AND ENVIRONMENT." "THOUGH HE DISPLAYED THE SKILL AND CURIOUSITY" "OF MATHEMATICAL GENIUS," "JOHANNES KEPLER SEEMED AN UNLIKELY CANDIDATE" "TO SOLVE SOME FUNDAMENTAL PROBLEMS OF THE UNIVERSE." "EARLY IN HIS CAREER," "KEPLER TAUGHT SCHOOLBOYS IN GRAZ," "ON THE MUR RIVER IN SOUTHEASTERN AUSTRIA." "LIKE MANY BEFORE AND SINCE," "HE FOUND TEACHING MORE FRUSTRATING THAN REWARDING." "HE STRUGGLED WITH GEOMETRICAL MODELS" "OF PLANETARY MOTION," "BUT SOON REALIZED HIS ASTRONOMICAL DATA" "WERE NOT RELIABLE ENOUGH." "AT THE DAWN OF THE NEW CENTURY," "JANUARY 1, 1600," "KEPLER SET OFF IN SEARCH OF" "THE MOST ACCURATE ASTRONOMICAL DATA ON EARTH" "AND THE MAN WHO POSSESED THEM, TYCHO BRAHE." "BORN INTO THE LET-THEM-EAT-CAKE CLASS OF SOCIETY," "TYCHO SURPRISED DANISH NOBILITY" "BY DECIDING TO DO SOMETHING WORTHWHILE." "ASTRONOMY BECAME HIS REASON FOR LIVING." "FOR THE LAST 38 YEARS OF HIS LIFE," "HE CHARTED THE HEAVENS WITH EXTRAORDINARY PRECISION." "NOBODY ON EARTH APPRECIATED THE POTENTIAL VALUE" "OF TYCHO'S OBSERVATIONS BETTER THAN JOHANNES KEPLER." "TO HIM, THE DATA WERE THE KEY" "TO UNLOCK THE DOOR TO THE UNIVERSE" "AND TO REVEAL WHAT HE CALLED "THE SECRETS OF THE SKIES."" "BUT MUCH TO KEPLER'S DISMAY," "TYCHO KNEW HOW TO KEEP A SECRET." "SO KEPLER STRUGGLED WITHOUT TYCHO'S PRECIOUS DATA" "FOR ALMOST TWO YEARS." "THEN, ON OCTOBER 24, 1601, FATE STEPPED IN." "TYCHO'S DYING WORDS WERE," ""LET ME NOT SEEM TO HAVE LIVED IN VAIN."" "THE DANE'S FAMILY WITHHELD THE DATA," "BUT KEPLER MANAGED TO MAKE TYCHO'S LAST WISH COME TRUE." "ADVANCING SCIENCE MORE THAN ETHICS," "HE STOLE THE MATERIAL." "THE OTHERWISE MILD-MANNERED LITLE MATHEMATICIAN" "WAS FINALLY READY, IN HIS OWN WORDS," "TO "WAGE MY WAR ON MARS."" "MARS, THE RED PLANET." "MARS, AN EARLY ROMAN GOD OF AGRICULTURE AND OF WAR." "MARS, THROUGH THE AGES, POWERFUL AND MYSTERIOUS." "WITHIN THE ANCIENT WORLD'S CONCEPT" "OF THE EARTH-CENTERED UNIVERSE," "THE PLANETS MOVED IN EPICYCLES." "SOMETIMES, AS WITH MARS," "THE EPICYCLES WERE VERY ERRATIC." "TO ACCOUNT FOR SUCH ERRATIC BEHAVIOR," "TYCHO CONCEIVED HIS OWN UNIVERSE," "THE TYCHONIC SOLAR SYSTEM." "LIKE PTOLEMY, HE PLACED THE EARTH AT THE CENTER," "WITH THE SUN REVOLVING AROUND IT." "BUT LIKE COPERNICUS," "TYCHO HAD THE OTHER PLANETS ORBITING THE SUN." "WHILE TYCHO'S SYSTEM FIT THE APPEARANCES" "MORE SIMPLY THAN PTOLEMY'S," "KEPLER EMBRACED THE VIEWS OF NICOLAUS COPERNICUS." "BESIDES BEING AN UNPOPULAR VIEW" "GALILEO WOULD BE TRIED IN ROME FOR SHARING IT" "IT WAS AN EXTREMELY DIFFICULT ONE" "TO JUSTIFY SCIENTIFICALLY." "CONSIDER THE COPERNICAN SOLAR SYSTEM" "AND THE PROBLEMS IT PRESENTED KEPLER." "FROM COPERNICUS' REVOLUTIONARY VIEWPOINT," "KEPLER HAD TO MAKE MATHEMATICAL OBSERVATIONS" "FROM A PLANET THAT," "RATHER THAN BEING CENTRAL AND STATIONARY," "WAS IN MOTION WITH THE OTHER PLANETS." "IMAGINE THE DIFFICULTY" "OF TRYING TO COMPUTE THE ORBIT OF MARS" "FROM A MOVING PLATFORM." "THIS PLATFORM SPINS ON ITS AXIS IN A NONCIRCULAR ORBIT" "WITH CONSTANTLY VARYING VELOCITY" "AND WITH AN UNKNOWN CENTER." "THIS WAS KEPLER'S DILEMMA," "AND HE APPROACHED IT WITH A POETIC FAITH" "IN A LOGICAL UNIVERSE." ""DO WE ASK WHAT PROFIT" "THE LITTLE BIRD HOPES FOR IN SINGING?" KEPLER ASKED," "EXPRESSING HIS VIEW OF HIS PURPOSE" "TO DISCOVER "THE SECRET OF THE SKIES."" "AS SOME CREATURES SEEM TO HAVE BEEN CREATED TO SING," "KEPLER SEEMS TO HAVE BEEN CREATED TO CALCULATE," "AND HIS CALCULATIONS, WHICH TOTALED OVER 900 PAGES," "WERE ENORMOUSLY DIFFICULT." "HIS WAR ON MARS WAS A SIEGE" "IN WHICH MANY WEAPONS WERE IMPERFECT AND FAULTY," "BUT HE EMPLOYED THEM WITH A STRIKING BRILLIANCE." "FOR EXAMPLE," "TO FIND THE LOCATION OF HIS MOVING PLATFORM," "KEPLER USED OBSERVATIONS OF MARS AS IT RETURNED," "MARS YEAR AFTER MARS YEAR," "TO THE SAME POINT IN ITS ORBIT." "THEN HE REVERSED THEM" "TO FIND THE ORBIT OF THE EARTH." "BY FINDING A CIRCLE," "EVEN THOUGH IT WASN'T QUITE CENTERED ON THE SUN," "KEPLER HAD TAKEN A STEP IN THE RIGHT DIRECTION." "ONCE AGAIN, HE ATTACKED THE PROBLEM OF MARS." "UNABLE TO FIND ITS EXACT PATH," "HE MANAGED TO FIND SOMETHING SUGGESTIVE" "IN ITS IRREGULAR SPEED." "MARS MOVED FASTER WHEN IT WAS CLOSER TO THE SUN" "AND SLOWER WHEN IT WAS FARTHER AWAY." "THIS BECAME KEPLER'S SECOND LAW." "HE STILL HADN'T FOUND HIS FIRST LAW." "APPROXIMATELY EVERY TWO YEARS," "THE SUN, THE EARTH, AND MARS ARE IN OPPOSITION." "SEEN FROM EITHER THE EARTH OR THE SUN," "MARS' POSITION IS THE SAME." "WITH ANOTHER OBSERVATION ONE MARS YEAR LATER," "KEPLER COULD TRIANGULATE A PRECISE POINT" "ON THE ORBIT OF MARS." "COULD A CIRCULAR ORBIT," "EVEN ONE OFFSET FROM THE SUN," "FIT ALL OF THE POINTS?" "ALMOST, BUT NOT QUITE." "THAT IS, NOT WITHIN THE UNPARALLELED PRECISION" "OF TYCHO BRAHE'S OBSERVATIONS." "WHAT CURVE THEN WOULD DESCRIBE THE ORBIT?" "THE ANSWER TO THAT QUESTION" "REVEALED THE SECRET OF THE HEAVENS." "WITH THE SUN AT ONE FOCUS, AN OVAL ORBIT," "A SLIGHTLY DISTORTED CIRCLE WAS CALLED FOR." "AND THAT TYPE OF ORBIT WAS AN ELLIPSE." "THE ELLIPSE, KNOWN TO THE ANCIENT GREEKS" "AND FINALLY REDISCOVERED IN THE HEAVENS" "BY JOHANNES KEPLER," "CAN BE VIEWED TIME AND TIME AGAIN" "RIGHT HERE ON EARTH." "IT'S SIMPLY A MATTER OF LOOKING AT THINGS" "IN THE RIGHT PERSPECTIVE." "ANY CIRCLE, VIEWED OBLIQUELY," "APPEARS AS AN ELLIPSE." "THE GREEKS KNEW THE PARABOLA AND THE HYPERBOLA" "AS WELL AS THE ELLIPSE." "BY SLICING A CONE WITH A PLANE," "THEY GENERATED CURVES CALLED CONIC SECTIONS." "IF THE CUTTING PLANE IS PERPENDICULAR TO THE AXIS," "IT CUTS OUT A CIRCLE." "WHEN THE PLANE IS TILTED," "THE CIRCLE BECOMES AN ELLIPSE." "TILTING IT ENOUGH FOR THE PLANE TO BE PARALLEL" "TO A SIDE OF THE CONE" "PRODUCES A PARABOLA." "TILTED FARTHER," "THE CONIC SECTION BECOMES A HYPERBOLA." "THE ANCIENT GREEKS WERE REMARKABLY SKILLED" "IN GEOMETRIC GAMES." "BY 200 B.C., APOLLONIUS EARNED THE TITLE" "OF "THE GREAT GEOMETER"" "FOR DESCRIBING SUCH REMARKABLE CURVES" "IN EIGHT LONG VOLUMES." "YET EVEN HIS PEN HAD BARELY SCRATCHED THE SURFACE" "OF THE CONIC SECTIONS." "IN 300 A.D., PAPPUS OF ALEXANDRIA" "FOUND ANOTHER WAY TO DESCRIBE THESE CURVES." "AMOVINGPOINTTRACESOUT ACONICSECTION" "IFITSDISTANCE FROMSOMEFIXEDPOINT," "THEFOCUS," "HASA CONSTANTRATIO WITHITSDISTANCE" "FROMSOMEFIXEDLINE, THEDIRECTRIX." "THERATIONOF THEDISTANCES ISTHEECCENTRICITY,e." "FORTHEELLIPSE, THIS RATIO IS SMALLER THAN 1" "ANDSHOWSHOWFAR  THISFOCUSIS OFFCENTER." "IFTHETWODISTANCES AREEQUAL," "THERESULTIS APARABOLA," "ACONICSECTION WITH ECCENTRICITY EQUAL TO 1." "IFTHEPOINTISCLOSER TOTHEDIRECTRIX," "THERESULTIS AHYPERBOLA," "WITHECCENTRICITY GREATERTHAN1." "ALL THREE CONIC SECTIONS SHARE A COMMON PROPERTY" "AND ALL THREE CAN BE DESCRIBED" "BY A COMMON ALGEBRAIC EQUATION," "AN EQUATION THAT IS USEFUL FOR STUDYING PLANETARY MOTION." "THIS IS THE BASIC FORMULA" "FOR DESCRIBING ALL THE CONIC SECTIONS" "THE ELLIPSE, THE PARABOLA, AND THE HYPERBOLA." "THE ANCIENT GREEKS WERE FIRST TO STUDY CONIC SECTIONS." "THEY NEVER DREAMED THESE CURVES" "WOULD INFLUENCE THE SHAPE OF THINGS TO COME." "THE PARABOLA IS AN EXAMPLE." "FROM THE DAZZLING GLARE OF AUTOMOBILE HEADLIGHTS" "TO THE VERY LIMITED EDITION 10-METER CALTECH TELESCOPE," "OVER A BILLION PARABOLAS" "HAVE ENTERED THE MARKETPLACE OF MODERN SOCIETY." "TODAY, AMONG MANY OTHER THINGS," "PARABOLAS ARE THE PATHS OF PROJECTILES" "AND THE HEAT WAVE OF THE FUTURE," "SOLAR FURNACES." "OF COURSE, JOHANNES KEPLER NEVER IMAGINED" "THAT THE HYPERBOLA AND THE PARABOLA" "COULD BE FOUND IN THE HEAVENS." "HIS USE OF THE ELLIPSE FOR MARS' ORBIT" "WAS POSSIBLE ONLY BECAUSE" "IT WAS THE ONLY PLANETARY ORBIT ECCENTRIC ENOUGH" "ABOUT 9%" "TO BE NOTICEABLY NONCIRCULAR." "HAD KEPLER WAGED WAR ON ANY OTHER PLANET," "HE PROBABLY WOULD HAVE DIED BELIEVING" "CIRCLES REIGN SUPREME THROUGHOUT THE UNIVERSE." "OF THE BATTLES HE COULD CHOSE, HE CHOSE WELL." "WITH TYCHO'S DATA, HE WAS VICTORIOUS IN THE KNOWLEDGE" "THAT THE ELLIPSE," "AS PERFECT A FIT AS COULD BE MEASURED," "WAS THE MATHEMATICAL SECRET OF GOD'S CREATION." "THESE SECRETS WERE REVEALED," "PERHAPS EVEN PARADED AS THE SPOILS OF WAR WITH MARS," "AS KEPLER'S THREE LAWS." "KEPLER'S FIRST LAW STATES" "THAT EACH PLANET MOVES IN AN ELLIPSE" "WITH THE SUN AT ONE FOCUS." "WHILE WAGING WAR ON MARS, KEPLER FOUND HIS SECOND LAW" "A LINE FROM THE SUN TO A PLANET" "SWEEPS OUT EQUAL AREAS IN EQUAL TIMES." "KEPLER'S SECOND LAW" "PERMITTED ASTOUNDINGLY ACCURATE COMPUTATIONS" "OF DISTANCE AND VELOCITY." "HIS THIRD LAW CAME 10 YEARS LATER." "IT STATES THAT THE SQUARE OF THE PERIOD OF A PLANET" "IS PROPORTIONAL TO THE CUBE" "OF THE LENGTH OF THE SEMIMAJOR AXIS." "IT REVEALS A CONNECTION" "BETWEEN THE MOTIONS OF DIFFERENT PLANETS." "BUT IN 1619," "THE YEAR KEPLER PUBLISHED HIS THIRD LAW," "THE THIRTY YEARS' WAR WAS BEING WAGED," "A CONFLICT MUCH CLOSER TO HOME THAN MARS." "KEPLER'S PATRONS TURNED FROM ASTRONOMY" "TO KILLING RELIGIOUS ENEMIES." "HE FLED FROM CITY TO CITY," "TRYING TO COLLECT OLD DEBTS." "YET EVEN IN THESE WORST OF TIMES," "PERHAPS BECAUSE THEY WERE SO BAD," "SEVERAL PATRONS PAID KEPLER" "TO CAST THEIR ASTROLOGICAL CHARTS." "KEPLER WASN'T VERY RELIGIOUS OR POLITICAL," "BUT WITH A LARGE FAMILY TO SUPPORT," "HE WAS ASTUTE ENOUGH" "TO USE ASTROLOGY TO HIS ADVANTAGE." "HIS PREDICTIONS WERE A COMBINATION" "OF COMMON SENSE, GOOD FORTUNE," "AND, WHEN THINGS LOOKED BLEAK FOR THE PAYING NOBILITY," "A BIT OF POETIC VAGUENESS." "IN HIS BOOK HARMONYOFTHEWORLD," "KEPLER WROTE," "WITHSUCHFULLNESS OFAGREEMENT" "BETWEEN MY 17 YEARS' LABOR ON THE OBSERVATIONS OF BRAHE" "ANDTHISPRESENTSTUDY OFMINE," "IATFIRSTBELIEVED THATI WASDREAMING." "HIS PERCEPTION THAT THE ELLIPSE" "IS ETCHED DEEPLY INTO THE UNIVERSE'S GRAND DESIGN" "WAS GREATER THAN ANY FUTURE HE FORETOLD" "IN THE SERVICE OF ROYALTY." "A WANDERER PLAGUED BY FATE AND CIRCUMSTANCE," "JOHANNES KEPLER FINALLY UNLOCKED THE MYSTERY" "OF PLANETARY MOTION." "THERE ARE FIVE PERFECT REGULAR SOLIDS" "THAT COME TO US FROM ANTIQUITY," "SOLIDS WHOSE PLANE FACES ARE ALL IDENTICAL." "THEY ARE THE CUBE, THE TETAHEDRON," "THE DODECAHEDRON, THE ICOSAHEDRON," "AND THE OCTAHEDRON." "KEPLER REALIZED THAT IF HE PUT A CUBE INSIDE A SPHERE," "A SPHERE INSIDE OF THAT," "A TETRAHEDRON INSIDE OF THAT, AND SO ON," "THE SIX SPHERES HAD THE SAME RATIO OF RADII" "AS THE RATIOS OF THE ORBITS OF THE SIX PLANETS." "KEPLER WAS CONVINCED HE DISCOVERED THE SECRET" "OF THE STRUCTURE OF THE UNIVERSE." "I HAVE HERE THE BOOK" "IN WHICH HE PUBLISHED THAT GREAT DISCOVERY." "THIS BOOK WAS PUBLISHED IN TUBINGEN IN 1596." "IT'S CALLED" "ON THE ADMIRABLE PROPORTIONS OFTHEHEAVENLYORBS," "AND SO ON." "THE BOOK HAS A DIAGRAM SHOWING HIS GEOMETRICAL MODEL." "AND HERE IT IS." "INCIDENTALLY, THERE'S SOMETHING INTERESTING" "ABOUT THIS DIAGRAM ITSELF." "THIS DIAGRAM HAS A DATE WHICH IS 1597," "A YEAR LATER THAN THE BOOK WAS PUBLISHED." "APPARENTLY THE DIAGRAM WASN'T READY" "WHEN THE BOOK WAS PUBLISHED." "IT WAS SENT OUT A YEAR LATER" "AND GLUED INTO COPIES OF THE BOOK." "LOOKING BACK ON THAT INCIDENT," "WE TEND TO THINK THAT KEPLER'S PICTURE" "OF A SKY FULL OF CUBES AND TETRAHEDRONS" "IS QUAINT AND RATHER FOOLISH." "I WOULD LIKE, FOR A MOMENT, TO TAKE IT SERIOUSLY" "AND SEE WHAT IT WAS REALLY ABOUT." "FIRST OF ALL, IN A PERIOD WHEN ALMOST NO ONE ELSE" "BELIEVED IN COPERNICUS," "THIS MODEL IS SOLIDLY COPERNICAN." "IT MAKES NO SENSE WITHOUT THE SUN AT THE CENTER." "SECONDLY, IT'S ONLY MUCH LATER," "IN THE TIME OF NEWTON," "THAT WE START TO IMAGINE A UNIVERSE HELD TOGETHER" "BY INVISIBLE FORCES." "BEFORE KEPLER, THE UNIVERSE WAS A PLENUM." "THAT MEANS IT WAS FILLED WITH CRYSTAL SPHERES." "KEPLER WAS REPLACING THE CRYSTAL SPHERES" "WITH THESE PERFECT GEOMETRIC SOLIDS." "KEPLER'S IDEA WAS BOTH DARING" "AND YET SOLIDLY IN THE SCIENTIFIC TRADITION" "OF HIS TIME." "THE THIRD POINT IS THAT IT WAS VERY SUCCESSFUL." "HIS PICTURE EXPLAINED THE RATIOS OF THE ORBITS" "OF ALL THE KNOWN PLANETS." "IT GAVE HIM A REASON WHY THERE MUST BE SIX" "AND EXACTLY SIX PLANETS" "BECAUSE THERE WERE FIVE" "AND EXACTLY FIVE REGULAR SOLIDS." "FINALLY, THE MODEL SERVED TO MOTIVATE KEPLER" "IN THE ENORMOUS WORK HE DID THROUGHOUT HIS LIFE" "THAT LED TO HIS THREE GREAT LAWS." "ALL OF THAT WORK WAS DONE TO JUSTIFY THIS PICTURE" "WHICH HE ALWAYS HAD AT THE BACK OF HIS MIND." "HIS IDEA IS WRONG," "BUT IT'S WRONG" "FOR A PERFECTLY LEGITIMATE SCIENTIFIC REASON." "IT SAYS THERE MUST BE SIX AND ONLY SIX PLANETS." "WE NOW KNOW THERE ARE NINE PLANETS" "AND MAYBE EVEN MORE," "AND SO IT'S WRONG." "IT MAKES A PREDICTION WHICH IS INCORRECT." "IT'S NOT A VIABLE THEORY OF THE UNIVERSE," "BUT IT SHOULDN'T BE LAUGHED AT." "THE VALUE OF A SCIENTIFIC IDEA" "LIES NOT IN WHETHER IT'S RIGHT OR WRONG." "IT LIES IN WHETHER IT LEADS US TO NEW IDEAS," "WHETHER IT LEADS TO PROGRESS." "AND BY THAT STANDARD, KEPLER'S SILLY MODEL," "WHICH TURNED OUT TO BE WRONG," "NEVERTHELESS, BY ANY REASONABLE STANDARD," "MUST BE REGARDED AS ONE OF THE MOST IMPORTANT," "LEGITIMATE SCIENTIFIC IDEAS IN ALL OF HISTORY." "I'LL SEE YOU NEXT TIME." "ALTHOUGHKEPLER'SGEOMETRIC MODELWASINCORRECT," "ITLEDHIMTODISCOVER THREELAWS" "THATPRECISELYDESCRIBE THEHEAVENS." "EACHPLANETORBITSTHE SUN  ALONGANELLIPTICALPATH" "WITHTHESUNATONEFOCUS ." "ALINEFROMTHE SUN  TOA PLANET" "SWEEPSOUTEQUALAREAS INEQUALTIMES." "THEPERIOD OFA PLANET'SORBITSQUARED" "ISPROPORTIONALTO THECUBE OFITSSEMIMAJORAXIS." "THESEARE KEPLER'STHREELAWS." "CAPTIONING PERFORMED BY THE NATIONAL CAPTIONING INSTITUTE, INC." "CAPTIONS COPYRIGHT 1985 CALIFORNIA INSTITUTE OF TECHNOLOGY" "THE CORPORATION FOR COMMUNITY COLLEGE TELEVISION AND 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"