Astronomy 101The Solar SystemTuesday, Wednesday, ThursdayTom [email protected] 101The Solar SystemTuesday, Wednesday, ThursdayTom [email protected] #2• Next Tuesday•Will cover today’s lecture and your presentationsQuiz #2Will cover today’s lecture and your presentationsThis week•No class Wednesday or ThursdayThis weekNo class Wednesday or ThursdayNext week’s presentations•Pick an object in the solar systemNext week’s presentationsPick an object in the solar systemTycho Brahe (1546•Tycho Brahe was the greatest naked eye observer of all time•He lived before the invention of the telescope•He lived before the invention of the telescope•His observations of the alignment of Jupiter and Saturn occurred two days later than when predicted by Copernicus•Tycho came up with a model where the planets orbit the Sun but the Sun orbits EarthTycho Brahe (1546-1601)Tycho Brahe was the greatest naked eye observer He lived before the invention of the telescopeHe lived before the invention of the telescopeHis observations of the alignment of Jupiter and Saturn occurred two days later than when predicted by CopernicusTycho came up with a model where the planets orbit the Sun but the Sun orbits EarthJohannes Kepler (1571•Tried to match circular orbits to Tycho’s data• Couldn’t do it•Because Tycho’s observations were so good, •Because Tycho’s observations were so good, Kepler had to come up with a new modelJohannes Kepler (1571-1630)Tried to match circular orbits to Tycho’s dataBecause Tycho’s observations were so good, Because Tycho’s observations were so good, Kepler had to come up with a new modelKepler was trying to match an orbit to Tycho’s observations of Mars•“If I believed that we could ignore these eight minutes of arc, I would have patched up my hypothesis accordingly. But, since it was not hypothesis accordingly. But, since it was not permissible to ignore, those 8 minutes pointed to the road to a complete reformation in astronomy.”•Kepler came up with his 3 laws of planetary motionKepler was trying to match an orbit to Tycho’s observations of Mars“If I believed that we could ignore these eight minutes of arc, I would have patched up my hypothesis accordingly. But, since it was not hypothesis accordingly. But, since it was not permissible to ignore, those 8 minutes pointed to the road to a complete reformation in astronomy.”Kepler came up with his 3 laws of planetaryKepler’s 1•The orbit of each planet about the Sun is an ellipse with the Sun at one focus (there is nothing at the other focus)at the other focus)Kepler’s 1stLawThe orbit of each planet about the Sun is an ellipse with the Sun at one focus (there is nothingDifferences between ellipses and circlesDifferences between ellipses and circlesEccentricity (e)•e = distance between the two foci/length of major axis• e of circle is 0•The larger e becomes, the more eccentric the orbit•The larger e becomes, the more eccentric the orbitEccentricity (e)e = distance between the two foci/length of major axisThe larger e becomes, the more eccentric the orbitThe larger e becomes, the more eccentric the orbitDefinitions• Perihelion –planet closest to the Sun• Aphelion –planet farthest from the sun•Semi-major axis (a) –the average of a planet’s •Semi-major axis (a) –the average of a planet’s perihelion and aphelion distances Definitionsplanet closest to the Sunplanet farthest from the sunthe average of a planet’s the average of a planet’s perihelion and aphelion distancesKepler’s 2•As a planet moves around its orbit, it sweeps out equal areas in equal times.•This means that the planet travels faster when it is •This means that the planet travels faster when it is nearer the Sun and slower when it is farther from the SunKepler’s 2ndlawAs a planet moves around its orbit, it sweeps out equal areas in equal times.This means that the planet travels faster when it is This means that the planet travels faster when it is nearer the Sun and slower when it is farther fromKepler’s 3•More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship relationship p2where pis a planet’s orbital period in years and ais the average distance from the Sun in astronomical units.Kepler’s 3rdLawMore distant planets orbit the Sun at slower average speeds, obeying the precise mathematical = a3is a planet’s orbital period in years and is the average distance from the Sun in astronomical units.Calculations•The period for the Earth to go around the Sun is 1 year•The average distance of th•The average distance of th1 Astronomical UnitCalculationsThe period for the Earth to go around the Sun is e of the Earth to the Sun is e of the Earth to the Sun isHow long does it take Jupiter to go around the Sun•If Jupiter is 5.2 Astronomical Units from the Sun, how long does it take Jupiter to go orbit the Sun onceonce• p2= a3= 5.23 = 140.6• p = √140.6 = 11.9 yearsHow long does it take Jupiter to go around the SunIf Jupiter is 5.2 Astronomical Units from the Sun, how long does it take Jupiter to go orbit the Sun 11.9 yearsAnother example•Mercury is 0.4 Astronomical Units from the Sun. •How long does it take Mercury to orbit the sun once?once?– A) 1 year– B) 3 months– C) 9 months– D) 5 yearsAnother exampleMercury is 0.4 Astronomical Units from the Sun. How long does it take Mercury to orbit the sunThe calculation• p2= a3= 0.43 = 0.064 • p = √0.064 = 0.25 yearsThe calculation0.25 years•An asteroid takes 8 years to go around the Sun•How far is the asteroid away from the Sun?–A) 1 AU–A) 1 AU– B) 3 AU– C) 4 AU– D) 8 AUAn asteroid takes 8 years to go around the SunHow far is the asteroid away from the Sun?The calculation• a3= p2= 82= 64• a = (64)1/3 = 4 AUThe calculationYou can calculate a planet’s orbital speed•Since you know a planet’s orbital distance•And you know its orbital time•You can calculate a planet’s average orbital speed•You can calculate a planet’s average orbital speedYou can calculate a planet’s orbital speedSince you know a planet’s orbital distanceAnd you know its orbital timeYou can calculate a planet’s average orbital speedYou can calculate a planet’s average orbital speedOrbits•all the planets orbit the counterclockwise direction (but they do not orbit it at