Ast 1001 lecture Sept 11 (kd) 3. The Copernican Revolution and Newton’s Revolution or, The Revolution Revolution: what revolves about what, and why? Astronomy 1001, Sept 2007 – Prof. K. Davidson

Ast 1001 lecture Sept 11 (kd) Principal players Nicolaus Copernicus (1473 – 1543) Galileo Galilei (1564 – 1642) Johannes Kepler (1571 – 1630) Isaac Newton (1642 – 1727) Notable supporting roles Thomas Digges (1546 – 1595) Tycho Brahe (1546 – 1601) René Descartes (1596 – 1650)

Ast 1001 lecture Sept 11 (kd) Before Copernicus: GEOCENTRIC universe

Ast 1001 lecture Sept 11 (kd) CLAUDIUS PTOLEMY’s mathematical theory from c. 140 during the Roman Empire: perfect circles, epicycles, etc.

Ast 1001 lecture Sept 11 (kd) COPERNICUS’ theory, around 1530: Heliocentric, but otherwise much like Ptolemy’s universe: celestial sphere, planets moved in perfect circles and epicycles, etc., -- pretty complicated.

Ast 1001 lecture Sept 11 (kd)

1530 – 1610: WHICH WAS RIGHT? Ptolemy’s geocentric universe vs. Copernicus’ heliocentric universe There was no obvious way to decide, until GALILEO and KEPLER settled the question in two very different ways during the years 1600 – 1620.

Ast 1001 lecture Sept 11 (kd) Meanwhile (around 1570?), Thomas Digges realized something tremendously important: If Earth moves around the Sun, then the stars might be like the Sun but very, very far away! -- Infinite space instead of a celestial sphere, and maybe each star has its own planets.

Ast 1001 lecture Sept 11 (kd) GALILEO used small telescopes to make several critical discoveries:

Ast 1001 lecture Sept 11 (kd) 1. The Moon has mountains and surface features, like Earth.

Ast 1001 lecture Sept 11 (kd) 2. Jupiter has four satellites = moons.

Ast 1001 lecture Sept 11 (kd) 3. Venus shows a complete set of phases from “crescent” to “full”. When “full”, it’s obviously much farther away.

Ast 1001 lecture Sept 11 (kd) Galileo’s discoveries: 1. Surface features on the Moon 2. Jupiter’s moons 3. “Full” phases of Venus None of these made sense in Ptolemy’s theory, but they were all perfectly OK in Copernicus’ universe. The phases of Venus are especially decisive.

Ast 1001 lecture Sept 11 (kd) (Parenthetically, mention Galileo’s troubles with the Church – basically a matter of internal politics in the Vatican.)

Ast 1001 lecture Sept 11 (kd) Johannes KEPLER

Ast 1001 lecture Sept 11 (kd)

TYCHO BRAHE

Ast 1001 lecture Sept 11 (kd) From 1572 to about 1599, Tycho observed the motions of the planets with far better precision than anyone had ever done before. He had good reasons to doubt BOTH Ptolemy’s and Copernicus’ scenarios. He tried to invent an alternative, the “Tychonic theory”.

Ast 1001 lecture Sept 11 (kd)

Kepler started by assuming that Earth moves around the Sun. But he didn’t assume anything about epicycles, or perfect circles. Instead he decided to use trigonometry to find the real path of Mars in space. (Why Mars? -- Because Tycho had observed Mars many, many times over almost 30 years.)

Ast 1001 lecture Sept 11 (kd) Kepler’s triangulation of Mars (1600—1610), using Tycho’s earlier observations

Ast 1001 lecture Sept 11 (kd)

In almost 10 years of calculations, Kepler discovered a fact that would have big consequences later: The orbit of Mars is an ellipse with the Sun at one focus. Next we’ll see what this means.

Ast 1001 lecture Sept 11 (kd) AN ELLIPSE IS A FLATTENED CIRCLE.

Ast 1001 lecture Sept 11 (kd) ELLIPSE, continued

Ast 1001 lecture Sept 11 (kd)

Two more words: PERIHELION and APHELION

Ast 1001 lecture Sept 11 (kd) Kepler noticed that Mars moves faster near perihelion, slower near aphelion. On closer inspection he found a rule that describes the variations in speed at all times.

Ast 1001 lecture Sept 11 (kd) KEPLER’S SECOND LAW

Ast 1001 lecture Sept 11 (kd) “EQUAL AREAS IN EQUAL TIMES”

Ast 1001 lecture Sept 11 (kd) ( In reality the planets’ orbits are almost circular. Here’s a scale drawing of Mars’ orbit.)

Ast 1001 lecture Sept 11 (kd) Finally, Kepler found a rule that relates the speeds of different planets. If P = orbital period (“year”) and a = average distance from Sun, then P 2 / a 3 = the same number for all the planets (but not the Moon)

Ast 1001 lecture Sept 11 (kd) Example --- Earth: P = 1 year, a = 1 AU (“astronomical unit”), P 2 / a 3 = 1 / 1 = Jupiter: P = years, a = 5.20 AU, P 2 / a 3 = / = It also works for Mercury, Venus, Mars, and Saturn.

Ast 1001 lecture Sept 11 (kd) KEPLER’S LAWS FOR THE PLANETS 1. Each orbit is an ellipse, with the Sun at one focus* 2. Equal areas in equal times 3. Period squared = radius cubed * (Note: the orbits aren’t aligned)

Ast 1001 lecture Sept 11 (kd) Kepler’s “Rudolphine Tables” -- very accurate predictions

Ast 1001 lecture Sept 11 (kd) KEPLER’S LAWS Why do they work? -- The question that led to modern physics

Ast 1001 lecture Sept 11 (kd) 1620 — 1665: Kepler’s laws were obviously right, but only a few people tried to understand why. In those days, “why?” was almost a new type of question in science.

Ast 1001 lecture Sept 11 (kd) DESCARTES (1596 – 1650): “Vortex” theory

Ast 1001 lecture Sept 11 (kd) Isaac Newton (1642 – 1727)

Ast 1001 lecture Sept 11 (kd) Newton’s crucial “thought experiment” (1665)

Ast 1001 lecture Sept 11 (kd)

Brief digression... A VECTOR IS A QUANTITY THAT HAS A DIRECTION IN SPACE. examples: ** POSITION ** ** VELOCITY ** ** ACCELERATION **

Ast 1001 lecture Sept 11 (kd)

The Moon’s orbit around Earth R = km = about 60 x (radius of Earth), V = 1160 km/hr = 320 m/s. So the required acceleration toward earth is A = V 2 / R = cm / s / s.

Ast 1001 lecture Sept 11 (kd) Moon’s acceleration toward Earth is about cm / s / s. So what? -- Our acceleration toward Earth is g = 980 cm / s / s. Newton noticed that these have the ratio x farther makes gravity weaker by a factor of 3600 x. This is obviously 60 x 60 = 60 2 !

Ast 1001 lecture Sept 11 (kd) “Newton’s second law”: force = M x A. His law of gravity: ( attractive force between M and m ) = G x M x m / (distance) 2. For instance, 3 x farther makes it 9 x weaker.

Ast 1001 lecture Sept 11 (kd) THE “INVERSE SQUARE LAW” OF GRAVITY WAS ENOUGH TO EXPLAIN KEPLER’S LAWS! 1. Orbits are ellipses, Sun at one focus 2. Equal areas in equal times 3. Period squared = radius cubed

Ast 1001 lecture Sept 11 (kd) NEWTON’S REVOLUTION WAS AS IMPORTANT AS COPERNICUS’. There are “laws of physics” that apply everywhere, from this room to the edge of the universe. In 1680 this was a breathtaking new idea! It led to modern physical science.

Ast 1001 lecture Sept 11 (kd) Mention Newton’s influence on the following century -- “the age of reason”, at least for philosophers. His historical importance was recognized in his own time -- arguably “the most important man in the world”, outranking even Louis XIV.

Ast 1001 lecture Sept 11 (kd) Next time: the amazing diversity of orbital behavior

Ast 1001 lecture Sept 11 (kd)