More about Celestial Motion“The reality whichscientific thought isseeking must beexpressionable inmathematical terms,mathematics beingthe most precise anddefinite kind ofthinking that we arecapable of” -- PlatoThis photo from space demonstratespretty well that the Earth is round.PolarisRadio Signals to PolarisPolaris FactsPolaris is 431 light years away from Earth.Light travels at 3.0×108 m/s (meters per second)431 years = 431 × 3.1×107 seconds/year = 1.3×1010 sDistance = velocity x timeDistance = 3.0×108 m/s x 1.3×1010 s = 4.0×1018 mPolaris is 0.7 degrees away from the Earth’s rotation poleand so moves only slightly as the Earth’s rotate.Metric System and SI units• Metric system refers to use of meters orkilometers, grams, or kilograms,centigrade, etc. irrespective of prefix.• SI (System Internationale) refers to a veryspecific set of units including only meters(not kilometers), kilograms (not grams),Kelvins.Plato (428-348 BC)• Argued for a model of theheavens that was simple andaesthetic.• Believed that the Sun andMoon were perfect spheres thatmoved around the sphericalEarth, along with the stars, incrystalline spheres. Thisconcept was to last for roughly1000 years.• Made many other contributionsto philosophy.•The theory of celestial spheres was incorrect, but it was a nobleattempt in the sense that it was falsifiable. In fact, it is the firstexample of what we consider today to be a scientific theory.Anaxagoras of Clazomenae (499-428 B.C.)was a follower of Pythagoras butplaced more emphasis on thematerial world. He broughtphilosophy from the edges of theGreek world to Athens. He was thefirst to realize that the moon shinesby reflected sunlight. He thoughtthat celestial objects were made ofsensible materials and that the sunshone brightly because it was hot.This got him in a lot of trouble andhe was banned from Athens.Why do we believe that the Earthis round?Your suggestions please…usingonly low technologyobservations…Aristotle (384-322 BC)A student of Plato, but quite different in hisapproach.Used physical arguments to explain nature.For example, the Earth must be a spherebecause;• ships disappear over the horizon,• the shadow of Earth on the moon is round,•travelers see new stars above the horizon.Eratosthenes of Alexandria (276-195 B.C.)The second librarian at the Library ofAlexandria.Made many contributions to Mathematics(The Sieve of Eratosthenes), Astronomy,and Geography.He determined the size of the Earth and thetilt of the Earth’s axisHe constructed an accurate calendarincluding leap yearsHe made a good map of the Nile river anddeduced the correct explanations for itsperiodic flooding.A Well with no Shadow in Ancient EgyptEratosthenes, while working at the library inAlexandria, was told about a well in the city ofSyene (now Aswan) where on a certain day insummer the walls casts no shadow, i.e. the sunshone directly down the well. He knew, as didother educated Greeks, that the Earth was asphere and realized that he could use this well tomeasure the size of the Earth. Being busy with hisduties at the library, he had a student measure thedistance from Alexandria to Syene by counting thesteps required to walk there. The name of thestudent so privilege has been lost to history.Fortunately, the other details of Eratosthenesmethod were carefully recorded.l = Distance from Alexandria toSyeneD = Circumference of the Earthl = (7.2/360)*D l = 5000 stadesD=(360/7.2)*l D=250,000 stades1 stade = 157 meters (a Greekstadium at, for example, Olympia)D=157*250000 metersD=39,250,000 metersD = 39,250 kilometersModern Value = 40,070 kilometersSIZE OF THE EARTHMoon MoviePhasesof theMoonFigure from AstronomyToday by Chaisson andMcMillanLunar Rotation and Orbital Motion• The moon orbits Earth onceevery 27.32 days.• The moon rotates on its axiswith exactly the same period.This is called synchronousrotation. The moon presentsthe same face to the Earth atall times.• Because the Earth is alsorotating, it takes 29.53 days forthe moon to return to the samelocation in the sky. This is thesynodic period.• The moon’s orbital period isgetting longer and its orbitlarger by about 3 cm/year.From Astronomy: from the Earth to the Universe byPasachoffMotion of the Planets• The most difficult challenge facing ancientastronomers was explaining the motion ofthe planets. The word “planet” derivesfrom the Greek “planetes,” which meanswanderer. Planets move in the skyrelative to stars. They also vary inbrightness and, on occasion, even changedirection. This is known as retrogrademotion.Planets known to the Ancients• Mercury (Hermes), dim and close to the horizon,Mercury is difficult to see. He moves quicklyacross the sky. Messenger of the gods.• Venus (Aphrodite), the morning and eveningstar, very bright but variable, goddess of love.• Mars (Ares), the red planet, god of war.• Jupiter (Zeus), very bright, king of the gods.• Saturn (Kronos), bright and pale yellow, first ofthe Titan’s, father of Zeus.Layout of the Solar SystemFrom Astronomy: from the Earth to the Universe by PasachoffRetrograde MotionThe MoviePtolemy (85-150 AD) lived in Alexandria, Egypt, where hewrote The Almagest , which recorded a sophisticatedsystem for describing the motion of celestial bodies.Learning in the Greek/Roman worlddeclined in the centuries after Ptolemy,but was kept alive in the Muslim world.Almagest means “greatest” in Arabic.Ptolemy’s Geocentric System, codifiedin the AlmagestThis is getting complicated.Figures from Astronomy Today by Chaisson and McMillanArguments for a Geocentric Universe• If the Earth were moving, we would have asense of motion. There is no sensation ofmotion; therefore, the Earth is not moving.• We don’t fall off as the Earth speeds ahead.• The apparent positions of the stars do notchange, i.e. we see no parallax.• The Earth is an important place and it is naturalthat it is at the center of the Universe.Ptolemy’s Own Defense• Ptolemy’s model can be criticized on thegrounds that it is cumbersome and lackingin beauty and symmetry.• “Let no one, seeing the difficulty of ourdevices, find troublesome suchhypotheses. For it is not proper to applyhuman things to divine things from suchdissimilar examples.”• Translation: What seems complicated tohumans may seem simple to the gods.Summary and a Look Ahead• The concept of Celestial Spheres allows us topredict the motion of the
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