Claudius Ptolemaeus Second Century AD Jan 5 7:37 AM Copernicus: The Foundation Nicholas Copernicus (Polish, 1473 1543): Proposed the first modern heliocentric model, motivated by inaccuracies of the Ptolemaic model and based on aesthetic principles only indirectly on evidence. Features of the model: It was still based on circles and epicycles, and was not more accurate than the Ptolemaic model; However, it allowed the calculation of distances to planets in AU, and provided the correct explanation for retrograde motion. What happened: Copernicus' model was not widely read or accepted right away, because it is difficult to change established ideas (although it did spark debates, and eventually condemnation by the Catholic church), because of its limitations, and because it did not address some of the better arguments in favor of geocentric models. Jan 5 7:03 AM 1
Tycho Brahe: The Data Tycho Brahe (Danish, 1546 1601): The greatest pretelescope astronomer; Became famous after observing a (super)nova in 1572 and a comet in 1577, and proving that they were farther than the Moon: Heavens can change! Was given an island on which to build his observatory. His Solar System model: Believed in a mixed model, with the Sun and Moon orbiting the Earth (no stellar parallax!); Few people ever believed in it. The observations: He made the best and most systematic naked eye observations up to that time, accurate to 1', kept extensive detailed records of them,... and hired Johannes Kepler as his assistant. Jan 5 7:03 AM Kepler: From Observation to Model of the Solar System Johannes Kepler (German, 1571 1630): Started trying to explain Tycho's data on Mars; Ended up developing the empirical model we still accept today for the solar system (basically). Laws of planetary motion: Three simple laws, 1. Ellipses: All planets move along ellipses, with the Sun at one focus; 2. Areas: Planets sweep out equal areas around the Sun in equal times (they move faster when closer to the Sun); 3. Periods: The period 2 is proportional to the distance 3. [Verification: Helped by 1631 observations of a Mercury transit, and 1655 observations by Giandomenico Cassini of the Sun.] Are there other laws? Is there a pattern in the spacings or periods among the planets? Not the way Kepler hoped for, but there are resonances. How good are these laws? We now know that they need small corrections, but they hold for any planetary system, any moon around a planet. Jan 5 7:06 AM 2
Galileo: Observations and Response to Aristotle Galileo Galilei (Italian, 1564 1642): Introduced the concept of inertia, with which he could address Aristotle's objection to a moving Earth. Observations: The first to use telescopes in astronomy (1609) and publish his results; Saw stars in Milky Way (so stars can be so distant that they don't show parallax), features on Moon and Sun (so not all heavenly bodies are perfect), four "little stars" around Jupiter (so another body and a moving one at that can have orbiting moons), phases of Venus (a complete set); Why is this important? Ideas: He supported the Copernican Model, but was forced to recant. Thought that planets are "worlds," not just dots of light. Other observations: He also saw that Saturn sometimes has things sticking out from its sides (like ears), and looked for stellar parallax in Mizar Jan 5 7:09 AM Tycho Brahe 1546 1601 Jan 5 6:46 AM 3
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Jan 5 6:49 AM Kepler's 3rd Law...the ratio of the orbital radius cubed to the period squared of all inferior objects to a common superior object is constant. r o 3 T 2 = K What do the planets circle? the Sun, the Sun is Superior and the planets Inferior Because the 3rd Law is a ratio you do not have to use standard units! Jan 5 9:42 AM 6
What is the period of Pluto? r oe = 1.5 x 10 11 m r op = 5.91 x 10 12 m Pluto is 39.4 x further from the Sun than the Earth is... Jan 11 11:03 AM r om = orbital radius of Mercury Jan 23 1:22 PM 7
1) Mercury, Venus, and the Earth all circle the Sun 2), they all that the same ratio of r 3 /T 2 3) Compare Mercury and Venus to the Earth Venus: r ov = 1.08 x 10 11 m 3 3 r oe = r ov 2 2 T e T v Mercury: r om = 5.79 x 10 10 m 3 r oe 3 = r om 2 T e 2 T m (1.50 x 10 11 m) 3 = (1.08 x 10 11 m) 3 (1 yr) 2 (T v ) 2 (1.50 x 10 11 m) 3 = ( x 10 m) 3 (1 yr) 2 (T m ) 2 T v = 0.611 yr or, 223 days T m =? Jan 23 1:22 PM Where do you put a satellite if you want it to circle the earth once a day? inferior Superior Jan 11 11:02 AM 8
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Law of Universal Gravitation Every object in the universe attracts every other object in the universe with a force that directly proportionate to the product of the masses and inversely proportionate to with the square of the distance between Jan 5 6:41 AM Jan 23 7:11 AM 11
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