Transcript February 18
Survey of the Universe Tom Burbine [email protected] • HW #2 and Assignment #1 are due Wednesday Stellar Parallax • Stellar Parallax – The apparent shift in the position of a nearby star (relative to distant objects) that occurs as we view the star from different positions in the Earth’s orbit of the Sun each year The distance the star moves is greatly exaggerated in this figure. Stellar parallax can only be seen by a telescope. Ancient astronomers could not detect stellar parallax • If Earth orbited the Sun, ancient astronomers believed that they would see differences in angular separation of stars as the Earth rotated around the Sun • Since they saw no changes in angular separation of the stars, they assumed the Earth was the center of the universe • They could not fathom that stars are so far away that stellar parallax is undetectable by the human eye Nicholas Copernicus (1473-1543) • Copernicus came up with a model that the Earth revolves around the Sun (heliocentric model) • Similar to what Aristarchus (310 – 230 BC) thought 2,000 years before • However, Copernicus’ models did not match observations since he wanted everything to go around in perfect circles Tycho Brahe (1546-1601) • Tycho Brahe was the greatest naked eye observer of all time • 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 Earth Johannes Kepler (1571-1630) • Tried to match circular orbits to Tycho’s data • Couldn’t do it • Because Tycho’s observations were so good, Kepler had to come up with a new model Kepler 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 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 motion Kepler’s st 1 Law • The orbit of each planet about the Sun is an ellipse with the Sun at one focus (there is nothing at the other focus) Differences between ellipses and circles Eccentricity (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 Definitions • Perihelion – planet closest to the Sun • Aphelion – planet farthest from the sun • Semi-major axis (a) – the average of a planet’s perihelion and aphelion distances Kepler’s nd 2 law • 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 nearer the Sun and slower when it is farther from the Sun Kepler’s rd 3 Law • More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p2 = a3 where p is a planet’s orbital period in years and a 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 the Earth to the Sun is 1 Astronomical Unit How 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 once • p2 = a3 = 5.23 = 140.6 • p = √140.6 = 11.9 years Another example • Mercury is 0.4 Astronomical Units from the Sun. • How long does it take Mercury to orbit the sun once? – – – – A) 1 year B) 3 months C) 9 months D) 5 years The calculation • p2 = a3 = 0.43 = 0.064 • p = √0.064 = 0.25 years • An asteroid takes 8 years to go around the Sun • How far is the asteroid away from the Sun? – – – – A) 1 AU B) 3 AU C) 4 AU D) 8 AU The calculation • a3 = p2 = 82 = 64 • a = (64)1/3 = 4 AU You 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 Orbits • all the planets orbit the Sun in a counterclockwise direction (but they do not orbit it at the same rate). • The Earth rotates counterclockwise • The Sun, the Moon, the planets, and the stars all rise in the east and set in the west Arguments against the Sun being the center of the solar system • 1) If the Earth was moving, objects such as birds and clouds would be left behind as the Earth moved • 2) The heavens must be perfect and unchanging. Noncircular orbits do not fit this model • 3) Stellar parallax would be observable Kepler’s Laws • http://www.youtube.com/watch?v=dRT3m2Wzyh4 Any Questions?