Survey of the Universe Tom Burbine

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 ( ) 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 ( ) 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 ( ) 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 1 st 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 2 nd 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 3 rd Law More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p 2 = a 3 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 p 2 = a 3 = = 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 p 2 = a 3 = = 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 a 3 = p 2 = 8 2 = 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

Any Questions?