"Annenberg Media" "¶" "CAPTIONING IS MADE POSSIBLE BY THE ANNENBERG/CPB PROJECT" "ACCORDING TO NEWTON'S LAWS," "ALLOBJECTS INA GRAVITATIONALFIELD" "TRACEOUTCONICSECTIONS." "THEPRECISESHAPE OFANORBIT" "DEPENDSONTHEINTERPLAY" "BETWEENENERGY ANDECCENTRICITY." "WE'RE ALL SET TO SEE WHY TRAJECTORIES IN SPACE" "FOLLOW THE CONIC SECTIONS." "BUT BEFORE WE DO," "THERE'S SOMETHING CURIOUS I'D LIKE TO DISCUSS." "THE CONIC SECTIONS HAVE NOT ONLY MATHEMATICAL PROPERTIES," "BUT ALSO GRAMMATICAL PROPERTIES." "FOR EACH CONIC SECTION," "THERE'S A CONSTRUCTION IN THE ENGLISH LANGUAGE." "FOR ELLIPSE..." "THERE IS ELLIPSIS." "FOR PARABOLA..." "PARABLE." "AND FOR HYPERBOLA..." "HYPERBOLE." "ELLIPSIS MEANS OMITTING SOMETHING FROM A SENTENCE" "THAT CAN BE UNDERSTOOD." ""PHYSICS IS MORE FUN THAN CHEMISTRY."" "THAT'S ELLIPSIS BECAUSE YOU SHOULD SAY," ""PHYSICS IS MORE FUN THAN CHEMISTRY IS."" "A PARABLE IS A STORY INTENDED TO TEACH SOMETHING." "HYPERBOLE IS AN EXTRAVAGANT EXAGGERATION," "SUCH AS "THIS IS THE WORLD'S GREATEST PHYSICS COURSE."" "THESE WORDS ARE RELATED TO THE CONIC SECTIONS." "NOBODY SEEMS TO KNOW WHY." "THAT'S A MYSTERY." "I'D LIKE TO GO INTO A MUCH DEEPER MYSTERY." "WHEN I WAS OLD ENOUGH TO KNOW ABOUT CONIC SECTIONS," "BUT NOT ABOUT ISAAC NEWTON," "I WENT TO A SHOW AT THE PLANETARIUM." "AN EXHIBIT THERE SAID THAT BODIES FLYING AROUND IN SPACE" "PLANETS, METEORS, AND ASTERIODS" "FOLLOW TRAJECTORIES WHICH ARE EITHER ELLIPSES," "PARABOLAS, OR HYPERBOLAS." "I REMEMBER BEING ABSOLUTELY STUNNED BY THAT." "WHY SHOULD THOSE BODIES FLY AROUND IN COURSES" "WHICH ARE CURVES HAVING THESE MATHEMATICAL PROPERTIES?" "IT'S A BREATHTAKING FACT" "BECAUSE IT BRINGS US FACE TO FACE" "WITH THAT SAME MYSTERY THAT HAS AWED EVERYONE" "FROM GALILEO TO ALBERT EINSTEIN." "NATURE OBEYS MATHEMATICS." "TODAY OUR JOB IS TO DO THE MATHEMATICS" "THAT NATURE OBEYED IN DESIGNING THE SOLAR SYSTEM." "FROM A SCIENTIFIC VIEWPOINT," "THE STRATEGY FOR FINDING THE SECRETS OF THE UNIVERSE" "IS GENERALLY STILL UNKNOWN." "BUT SCIENTISTS KNOW THAT STRATEGY" "HAS SOMETHING TO DO WITH LOGIC," "WITH TRIAL AND ERROR," "WITH TAKING RISKS AND GOING TO THE LIMIT." "IF VIEWED IN A CERTAIN LIGHT," "NOT ONLY THE STRATEGY, BUT THE UNIVERSE ITSELF," "MAY BE A COSMIC GAME," "PLAYED FOR THE HIGHEST STAKES" "AND FOR THE LONGEST TIME." "SOMETIMES PLAYING CONDITIONS HAVE BEEN LESS THAN IDEAL." "THERE'S BEEN WAR, POVERTY," "AND POOR HEALTH." "AND THERE'S BEEN THE THREAT OF TORTURE." "NO MATTER THE ODDS OR THE OBSTACLES," "THERE HAVE BEEN GREAT PLAYERS," "SCIENTISTS SUCH AS KEPLER AND GALILEO, WHO," "TO SATISFY THEMSELVES ABOUT THE RULES," "HAD TO PLAY THE GAME." "IT'S A GAME OF SERIOUS CONSEQUENCES," "BUT LIKE STAR WARS," "LIKE A HAND OF FIVE-CARD STUD," "OR A STICK OF EIGHT BALL," "A GAME NONETHELESS." "AFTER ALL, HUMAN KNOWLEDGE, LIKE ANY NUMBER OF GAMES," "EVOLVES WITH INCREASING SKILL." "AND THE REWARDS OF SCIENCE" "PAY OFF IN THE CURRENCY OF MATHEMATICS." "OF COURSE, NOT ALL GAMES REQUIRE GENIUS." "AND CERTAINLY NOT ALL GAMES" "REQUIRE THE GENIUS OF GALILEO GALILEI," "EVEN THOUGH HE, TOO," "WAS CREATIVE, INSPIRED, AND VERY COMPETITIVE." "FOR EXAMPLE, IN A FIELD ALONG THESE LINES," "GALILEO HAD NO COMPETITION." "PERHAPS THAT WAS BECAUSE AT LEAST ON THIS LEVEL," "IT WAS THE ONLY GAME IN TOWN." "GALILEO ROLLED THE BALL HOURS ON END." "BUT IT WASN'T ALL PLAY AND NO WORK." "IN FACT, WITH JUST SUCH A GAME," "HE WAS ACTUALLY ABLE TO SLOW DOWN FALLING MOTION." "LOCKED IN COMPETITION WITH NATURE ITSELF," "GALILEO MADE SOME REMARKABLE DISCOVERIES." "FOR EXAMPLE, THE DISTANCE FALLEN" "IS PROPORTIONAL TO THE SQUARE OF THE TIME," "THOUGH ALL BODIES, EVEN HIS OWN," "FALL WITH THE SAME CONSTANT ACCELERATION." "GALILEO MADE MANY OTHER REMARKABLE DISCOVERIES." "IN EUROPE, TOWARD THE END OF THE 16th CENTURY," "ANOTHER ASTRONOMER PLAYED WITH ANOTHER COLLECTION OF TOYS." "HIS NAME WAS TYCHO BRAHE," "AND HIS PLAYTHINGS WERE SEXTANTS AND QUADRANTS" "OF HIS OWN DESIGN AND CONSTRUCTION." "LIKE GALILEO WITH THE INCLINED PLANE," "THE GAME TYCHO PLAYED" "WOULD REINTERPRET THE RULES GOVERNING THE UNIVERSE." "THE STRATEGY ITSELF WOULD BE REWRITTEN" "BECAUSE IN 1600," "JOHANNES KEPLER SAT DOWN TO PLAY." "AT THIS GAME," "AND ESPECIALLY IN TYCHO BRAHE," "KEPLER MET HIS MATCH." "BUT AFTER ALMOST TWO YEARS," "A LITTLE LUCK FINALLY CAME KEPLER'S WAY." "THAT LUCK, IN THE FORM OF TYCHO'S HEAVENLY OBSERVATIONS," "KEPT KEPLER AT THE TABLE ALMOST THREE DECADES." "THE GAME WASN'T EASY TO BEGIN WITH," "AND IN SOME WAYS," "THE LONGER HE PLAYED, THE MORE COMPLICATED IT GOT." "BUT BY THE END, JOHANNES KEPLER HAD WON" "HIS FINAL ROUND OF COSMIC MATHEMATICS." "THE VICTORY BECAME KNOWN" "AS KEPLER'S THREE LAWS OF PLANETARY MOTION" "THE LAW OF ELLIPSES..." "THE LAW OF EQUAL AREAS..." "AND THE LAW OF HARMONY." "ISAAC NEWTON WOULD POLISH THESE LAWS TO PERFECTION." "IN HIS MIND, KEPLER WAS A GIANT," "AND HE REALIZED THOSE THREE LAWS WERE CORRECT." "NEWTON IMAGINED GALILEO AS A GIANT AS WELL" "AND SAW THAT HIS LAW OF FALLING BODIES" "WAS LIKEWISE CORRECT." "BUT IN SCIENCE AS WELL AS HISTORY," "TIMING IS EVERYTHING." "IT TOOK NEWTON'S ERA AND GENIUS" "TO EXPLAIN WHY THEY'RE CORRECT." "HE EXPLAINED THE LAWS OF GALILEO AND KEPLER" "BY DEDUCING THEM FROM HIS OWN LAWS," "THE LAWS OF GRAVITY AND MOTION." "BECAUSE OF THOSE LAWS," "THE EQUATION OF THE EARTH'S ORBIT" "IS THAT OF A CONIC SECTION," "AND IN PARTICULAR, AN ELLIPSE." "THIS IS ONE OF THE UNDERLYING MATHEMATICAL PATTERNS" "OF THE UNIVERSE." "PLANETS MOVE IN ELLIPSES" "DETERMINED BY THE ANGULAR MOMENTUM," "THE MASS OF THE PLANET," "THE MASS OF THE SUN," "AND THE ECCENTRICITY OF THE ORBIT." "BUT NEWTON'S SOLUTION DOESN'T SAY" "THAT THE ORBIT OF EVERY HEAVENLY BODY" "MUST BE ELLIPTIC." "IT CAN BE A PARABOLA, A HYPERBOLA," "OR EVEN A PERFECTLY PLATONIC CIRCLE." "IS THIS THE SHAPE OF THINGS IN THE HEAVENS?" "AND IF SO," "WHAT DETERMINES THE PRECISE SHAPE" "OF A BODY'S ORBIT?" "ALL CONIC SECTIONS APPEAR IN THE HEAVENS." "THE KEY TO THE PRECISE SHAPE" "IS FOUND IN THE BODY'S ENERGY." "PICTURE WHAT HAPPENS TO THAT ENERGY" "AS A PLANET ZIPS AROUND ITS ORBIT." "WHEN THE PLANET FALLS CLOSE TO THE SUN," "ITS POTENTIAL ENERGY IS LOW." "BUT THE PLANET SPEEDS UP" "SO THE KINETIC ENERGY BECOMES HIGH." "AT THE OUTER REACH OF THE ELLIPSE," "WITH ITS LOW KINETIC ENERGY," "THE PLANET SORT OF LOAFS ALONG." "AT THE SAME TIME," "BECAUSE OF THE GREATER DISTANCE FROM THE SUN," "ITS POTENTIAL ENERGY IS HIGH." "THE PLANET'S POTENTIAL ENERGY AND KINETIC ENERGY" "KEEP TRADING BACK AND FORTH." "LIKE THE POTENTIAL AND KINETIC ENERGY" "OF A SWINGING PENDULUM," "ONE GOES UP, THE OTHER GOES DOWN." "HOWEVER, BECAUSE THE PLANET MOVES IN A VACUUM," "WITH NO DRAG," "THE TOTAL ENERGY DOES NOT CHANGE." "THIS TOTAL ENERGY IS THE KEY" "TO THE SHAPE OF THE ORBIT." "THE QUEST TO FIND THE SHAPES OF ORBITS" "WAS UNDERTAKEN LONG BEFORE KEPLER'S ATTEMPT." "PTOLEMY SIGHTED THE STARS WITH A SMALL QUADRANT." "SUCH INSTRUMENTS HAVE ENHANCED ASTRONOMICAL OBSERVATIONS" "FOR CENTURIES." "WITH THE HELP OF URANIA, THE MUSE OF ASTRONOMY," "PTOLEMY SAW TO THE LIMITS OF HIS VISION." "LATER, TYCHO BRAHE" "NAMED HIS ISLAND OBSERVATORY URANIBURG," "AFTER THE SAME MUSE." "THERE TYCHO BUILT STARGAZING GADGETS" "THAT WERE BEYOND COMPARE" "BEFORE THE INVENTION OF THE TELESCOPE." "TYCHO'S BRILLIANCE IN SEEING AFAR" "WAS ONLY OUTDISTANCED BY HIS VANITY." "FANCYING HIMSELF A SCIENTIST KING," "IN ONE SWEEPING GESTURE," "TYCHO POINTED OUT HIS KINGDOM" "WHICH TOOK IN NOTHING LESS THAN ALL OF HEAVEN." "WITH INSTRUMENTS ALMOST AS STRONG" "AS HIS SENSE OF SELF-WORTH," "TYCHO WAS HEADS ABOVE ALL OTHER ASTRONOMERS." "HIS TWO MINUTES OF ARC," "EQUIVALENT TO ABOUT 1/15 OF THE MOON'S DIAMETER," "WAS FIVE TIMES MORE ACCURATE" "THAN ANY MEASUREMENT IN HISTORY." "ONLY AFTER 1609," "WHEN GALILEO LOOKED THROUGH HIS TELESCOPE," "DID ASTRONOMICAL VISION IMPROVE TO ANY DEGREE." "IT'S IMPROVED CONSIDERABLY." "BY MEANS OF RADIO TELESCOPES," "ACCURACY HAS INCREASED TO 1/1,000 OF 1 SECOND OF ARC." "IN HUMAN PERSPECTIVE," "THAT'S ABOUT THE WIDTH OF A HAIR" "SEEN AT A DISTANCE OF 10 KILOMETERS." "FEATURING BOTH POWER AND PRECISION," "MODERN TELESCOPES CAN SEE COUNTLESS OBJECTS" "THAT PREVIOUSLY COULD BE SEEN ONLY IN ASTRONOMERS' DREAMS." "FOR INSTANCE, PLUTO," "THOUGH INVISIBLE TO THE NAKED EYE," "STANDS OUT CLEARLY IN THESE PHOTOGRAPHS." "TRYING TO EXPLAIN IRREGULARITIES" "IN THE ORBITS OF URANUS AND NEPTUNE," "AN ASTRONOMER NAMED PERCIVAL LOWELL" "PREDICTED PLUTO'S DREAMLIKE EXISTENCE" "BEFORE ITS VISUAL REALITY CAME TRUE." "LATER, CLYDE TOMBAUGH SEARCHED HUNDREDS OF PHOTOGRAPHS" "FOR ONE TINY LITTLE BLIP MOVING AMIDST THE FIXED STARS." "WHEN HE FOUND IT, HE FOUND PLUTO," "AND WHEN HE FOUND PLUTO," "HE FOUND AN ECCENTRIC ELLIPSE." "IT ACTUALLY CROSSES INSIDE THE ORBIT OF NEPTUNE." "HALLEY'S COMET, DISCOVERED BY EDMUND HALLEY," "HAS AN ELLIPTICAL ORBIT THAT'S EVEN MORE ECCENTRIC." "THESE ORBITS ARE IN MARKED CONTRAST" "TO THOSE OF VENUS AND THE EARTH," "WHICH GO AROUND THE SUN IN VERY NEARLY CIRCULAR FASHION." "BUT ALL OF THEM, ELLIPTIC OR ALMOST ROUND," "ARE PATHS OF CONSTANT ENERGY." "THIS FACT IS NOTHING LESS THAN A MATHEMATICAL MIRACLE." "BEHOLD A PLANET MOVING IN AN ELLIPSE," "SWEEPING OUT EQUAL AREAS IN EQUAL TIMES." "IT HAS KINETIC ENERGY AND POTENTIAL ENERGY." "ATANYPOINT INTHEORBIT," "THETOTALENERGY ISTHESUM" "OFKINETICENERGY" "AND POTENTIAL ENERGY." "FIRSTCALCULATE THEPOTENTIALENERGY." "THEPOTENTIALENERGY FOLLOWSA COSINECURVE." "NOW,CALCULATE THEKINETICENERGY." "THE KINETIC ENERGY FOLLOWS ANOTHERCOSINECURVE." "THETOTALENERGY, KINETICPLUSPOTENTIAL," "ISCONSTANT." "THAT'S BECAUSE THE COSINE TERMS" "CANCEL IN THE ADDITION." "AND THAT'S IT," "THE CONNECTION BETWEEN ENERGY AND ECCENTRICITY." "IT'S TRUE FOR A HYPERBOLA," "A PARABOLA, OR AN ELLIPSE." "JOHANNES KEPLER'S DISCOVERY" "THAT THE PLANETARY ORBITS ARE ELLIPTICAL" "WASN'T MADE ON THE BASIS OF TELESCOPIC OBSERVATIONS." "EVEN BEFORE THE EXISTENCE OF THE MOST ELEMENTARY TELESCOPE," "KEPLER MADE HIS DISCOVERIES" "BASED ON TOTALLY HUMAN OBSERVATIONS." "AND THOSE EYES AND OBSERVATIONS ALIKE" "HAD BELONGED TO TYCHO BRAHE." "BY THE TIME HE MET KEPLER," "TYCHO HAD RECORDED 777 STARS." "CONSIDERING ALL THE STARS IN HEAVEN," "THAT MAY NOT SEEM LIKE MANY." "BUT AS JOHANNES KEPLER KNEW," "IT WAS THE SUM TOTAL OF ALL THE NAKED EYE COULD SEE." "WHEN KEPLER ASKED TO LOOK AT THE DATA," "TYCHO TOLD HIM TO TAKE A WALK." "TYCHO CONSIDERED THE SERIOUS-MINDED KEPLER" "AS SOMEWHAT OF A PLAYTHING." "THE GAME, DESIGNED AS CLEVERLY AS HIS INSTRUMENTS," "WAS TYCHO'S VERSION OF FOLLOW-THE-LEADER" "WHICH KEPLER COULDN'T PLAY WITHOUT THE OBSERVATIONS." "BUT EVENTUALLY, AS FATE WOULD HAVE IT," "THE TABLES TURNED." "ON HIS DEATHBED," "TYCHO BRAHE WOULD HAVE A CHANGE OF HEART." "HE BEGGED KEPLER TO TAKE HIS DATA," "TO USE IT WELL," "AND TO CONCLUDE THE MOST SERIOUS GAME" "OF THEIR LIVES." "ALMOST 30 YEARS LATER," "KEPLER FINALLY GOT TYCHO'S DATA PUBLISHED," "BUT NOT BEFORE HE USED THEM" "TO DISCOVER THE SHAPE OF MARS' ORBIT." "THE SHAPES OF ORBITS" "DEPEND ON THEIR ENERGIES." "FOR A GIVEN ANGULAR MOMENTUM," "THE ENERGY DETERMINES THE ECCENTRICITY," "ANDTHEECCENTRICTY" "DETERMINESTHEORBIT." "THEELLIPSE." "WHENTHETOTALENERGY ISNEGATIVE" "AND THE ECCENTRICITY" "IS LESS THAN ONE," "THEORBITIS AN ELLIPSE." "POSITIVEKINETICENERGY ISTOOSMALL" "TOOVERCOME THENEGATIVEPOTENTIALENERGY." "THEREFORE, TRAPPED IN A CLOSED ORBIT," "THE BODY CAN NEVER ESCAPE THE SOLAR SYSTEM." "THEPARABOLA." "WHENTHETOTALENERGY ISZERO" "ANDTHEECCENTRICTY" "ISEXACTLYONE," "THEORBITIS APARABOLA." "IFA BODYSTARTED WITHZEROKINETICENERGY" "ANDFELLFROMINFINITY," "ITWOULDWHIP ONCEAROUNDTHESUN" "ANDRETURNTO INFINITY." "IT'S UNLIKELY THAT POSITIVE KINETIC ENERGY" "AND NEGATIVE POTENTIAL ENERGY WOULD BALANCE THIS WAY," "BUT IT'S POSSIBLE." "THEHYPERBOLA." "WHEN THE TOTAL ENERGY IS POSITIVE" "AND THE ECCENTRICITY" "IS GREATER THAN ONE," "THE ORBIT IS A HYPERBOLA." "IF AN OBJECT WERE SHOT TOWARDTHESUN" "FROM VERY FAR AWAY," "ITS POSITIVE KINETIC ENERGY" "WOULD OVERCOME ITS NEGATIVE POTENTIAL ENERGY." "SOME COMETS HAVE HYPERBOLIC ORBITS." "THECIRCLE." "IF THE ENERGY HAS A SPECIAL VALUE," "THEECCENTRICITY ISZERO." "THE ORBIT IS A PERFECT CIRCLE." "THIS IS THE LOWEST ENERGY A PLANET CAN HAVE" "FOR A GIVEN ANGULAR MOMENTUM." "THE RINGS OF SATURN," "FOR ALL THEIR BEAUTY," "ARE NOTHING MORE THAN A PILE OF EVOLVING JUNK," "COSMIC SCRAPS THAT HAVE RUBBED TOGETHER" "FOR A BILLION YEARS." "AS A RESULT OF ALL THIS BRUSHING AND BRUISING," "THEIR ORBITS WERE CHIPPED ENCOUNTER BY ENCOUNTER" "INTO NICE SMOOTH CIRCLES." "THAT'S KNOWN TO BE TRUE BECAUSE OF THE RELATION" "BETWEEN ENERGY AND ECCENTRICITY," "EVEN THOUGH COMPUTING A MILLION INTERACTING ORBITS" "IS BEYOND THE MATHEMATICAL CAPABILITY" "OF THE MOST POWERFUL COMPUTERS ON EARTH." "TO THE DEGREE" "THAT MODERN ASTRONOMY IS EFFECTIVE," "IT OWES ITS EFFECTIVENESS" "TO THE INVENTION OF THE REFLECTOR TELESCOPE." "THE MIRROR OF THIS ONE HAS BEEN GROUND AND POLISHED" "TO TOLERANCES MEASURED IN THOUSANDS OF A CENTIMETER." "SUCH ACCURACY WASN'T ALWAYS POSSIBLE," "BUT THE PRINCIPLE WAS NEARLY ALWAYS THE SAME." "TO FOCUS THE LIGHT PROPERLY," "THE RELECTING MIRROR MUST BE GROUND" "IN THE SHAPE OF A PARABOLA." "THE GRINDING REQUIRES SKILL, PATIENCE," "AND A COMPOUND OF MUDLIKE LENS-GRINDING POLISH." "THE FIRST MAN TO DO THIS" "IT WAS A MESSY JOB, BUT SOMEBODY HAD TO DO IT" "WAS INVITED TO JOIN THE ROYAL SOCIETY." "HIS NAME WAS ISAAC NEWTON." "IT WAS THE REFLECTING TELESCOPE," "NOT HIS OTHER DISCOVERIES," "THAT FIRST MADE HIM FAMOUS," "A FAME, THAT LIKE THE PARABOLIC MIRROR," "ENDURES AND EVOLVES." "TODAY'S GIANT TELESCOPE" "AND THIS IS NO SMALL WONDER" "IS AN EXTENSION OF NEWTON'S PRINCIPLE." "HUMAN EXPLORATION INTO SPACE," "THE GRANDEST GAME IN THE SOLAR SYSTEM," "DIDN'T BEGIN WITH SIR ISAAC NEWTON." "THERE WERE, AFTER ALL," "THOSE SHOULDERS UPON WHICH HE STOOD TO PLAY" "GALILEO AND HIS TOYS," "OF WHICH THE LAW OF FALLING BODIES WAS MADE," "TYCHO AND HIS OBSERVATIONS," "PIECES OF A PUZZLE THAT CHANGED THE COURSE OF COSMIC HISTORY," "KEPLER, WHO PLAYED WITH TYCHO'S OBSERVATIONS" "IN T MOST CALCULATING MANNER," "AND WHO REWROTE THE RULES." "WHILE THE GAME DIDN'T BEGIN WITH NEWTON'S GENIUS," "NEITHER DID IT END THERE." "MODERN SCIENTISTS, LIKE NEWTON BEFORE THEM," "TAKE THEIR TURNS AT TRYING TO UNLOCK THE COSMOS." "IT'S STILL A FANTASTIC AND ONGOING GAME" "IN WHICH NOW THE BEST PLAYERS" "SEE 15 BILLION YEARS INTO THE PAST." "AND THE ANSWER," "THE WINNER'S PRIZE," "IS A PEEK AT THE ORIGIN OF THE UNIVERSE." "SO THE QUESTION IS, WHO'S UP NEXT?" "AS I TOLD YOU BEFORE," "THE FIRST TO KNOW WHAT NEWTON HAD DONE" "WAS HIS YOUNG FRIEND, EDMUND HALLEY." "HALLEY REALIZED THAT ACCORDING TO NEWTON," "ALTHOUGH THE PLANETS' ORBITS" "HAPPEN TO BE VERY NEARLY CIRCULAR," "IT WAS POSSIBLE FOR A BODY TO HAVE" "A VERY ECCENTRIC ELLIPTICAL ORBIT LIKE THIS." "IF THERE WERE SUCH A BODY, IT WOULD BE SIGHTED." "THEN IT WOULD GO FAR AWAY FOR MANY YEARS" "BEFORE IT RETURNED TO BE SIGHTED AGAIN." "HE CONSULTED THE HISTORICAL RECORD" "AND FOUND SIGHTINGS IN 1531," "IN 1607, AND AGAIN IN 1682" "THAT WERE SO NEARLY IDENTICAL" "THAT THEY HAD TO BE THE SAME OBJECT." "THAT WAS HALLEY'S COMET." "THE CRITICAL TEST WAS PREDICTING" "WHEN IT WOULD BE SEEN AGAIN." "AND HE DID." "UNFORTUNATELY, TO KNOW WHETHER HE WAS RIGHT," "HE WOULD HAVE HAD TO LIVE TO BE 102." "HE ONLY LIVED TO BE 86." "NEVERTHELESS, JUST AS PREDICTED," "ON CHRISTMAS DAY OF 1758," "HALLEY'S COMET WAS SPOTTED ONCE AGAIN." "ITS MOST RECENT ROUND TRIP BRINGS IT BY US" "IN 1910 AND AGAIN IN 1986." "SO THAT'S IT." "WE'VE EXPLAINED THE STRUCTURE OF THE HEAVENS," "THAT MYSTERY FROM TIME OUT OF MIND" "HAS FINALLY BEEN SOLVED." "MANY YEARS AGO, THERE WAS SOMETHING CALLED THE PYTHAGOREAN BROTHERHOOD." "THEY WERE FOLLOWERS OF THE MASTER PYTHAGORAS OF SAMOS." "IT WAS A SEMIMYSTICAL MATHEMATICAL PRIESTHOOD." "NEOPHYTES WENT THROUGH A LONG AND DIFFICULT APPRENTICESHIP" "TO PURIFY THE MIND AND CLEANSE THE SOUL" "BEFORE THEY COULD BE ENTRUSTED" "WITH THE AWESOME POWER OF MATHEMATICAL KNOWLEDGE." "TODAY, AFTER A LONG AND DIFFICULT APPRENTICESHIP," "YOU HAVE BEEN PERMITTED TO PEEK" "INTO THE INNER TEMPLE OF HUMAN KNOWLEDGE." "I HOPE YOU USE THAT POWER WISELY." "BUT RIGHT NOW," "YOU CAN GET OUT OF HERE." "THEECCENTRICITY OFANORBIT" "DEPENDSONTHEENERGY OFTHEMOVINGBODY." "NEGATIVEENERGYMEANS ANELLIPTICALORBIT." "WHENTHETOTALENERGY ISZERO," "THEORBITIS APARABOLA." "WHENTHETOTALENERGY ISPOSITIVE," "THEORBITIS HYPERBOLIC." "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" "Annenberg Media" "¶" "For information about this and other Annenberg Media programs call 1-800-LEARNER and visit us at"