PHYS2081 The old astronomers

PHYS2081 ANCIENT ASTRONOMY DATABASE

-500	Pythagoras: Concentric spheres (Music of the spheres). Heavenly bodies were spherical (moon/eclipse/terminator).
-400	Philolaus: Earth in motion, central fire. Just an idea…
-384 -322	Aristotle: Knew all about moon phases and eclipses. Sun is farther than the moon (total eclipses). Earth is sphere, altitude of Polaris is proportional to latitude. Realized the heliocentric and geocentric models give the same observational result but chose geocentric.
-310 -330	Aristarchus: On The Sizes & Distances of the earth and the moon" From observation of size of earth shadow on moon (he assumed shadow had twice moon’s diameter, it is actually about 8/3) and the angle between quadrature and quarter moon (he used three degrees it is actually twenty times less than this and quite unobservable) he found the Sun to be 19 times larger and farther than the moon, the Moon to be 3/8 size of earth and 59 earth radii distant. Since the Sun would be 7 times larger than earth and less prone to move, he first proposed the heliocentric hypothesis.
-200	Eratosthenes: Size of earth (Syene-alexandria latitude difference).
-160 -127	Hipparchus: Star catalogue with 850 entries. Magnitude classes. Noted effects of precession. Moon distance is 59 earth radii (Aristarchus’ method with error estimate). Determined year to six minutes. Geocentric model with eccentric accurately predicted sun moon positions and, hence, eclipses. Very good observations.
140	Ptolemy: The Almagest (13 vol) summarises past works (including Hipparchus) as well as his own. Found moon was 59 earth radii distant using the earth ("rotational synthesis") as a baseline. Developed an exotic system of cycles, epicycles, eccentrics and equants to quite accurately predict lunar and planetary positions. Tetrabiblios (treatise on astrology).

PH223 MEDIEVAL/BAROQUE ASTRONOMY DATABASE

1473- 1543	Nicolaus Copernicus De Revolutionibus (On the revolutions of the heavenly bodies). Heliocentric hypothesis first widely accepted (the printing press, 1515, helped a lot). Model of solar system explains why planet speed is greatest and planet brightest and retrograde motion near opposition. Introduces idea of superior and inferior planets, sidereal and synodic periods, and gives relative scale of the solar system. But still need epicycles eccentrics and equants to explain motions. The Copernican revolution.
1546- 1601	Tycho Brahe Brilliant observational astronomer. With a ton of gold from king Frederick II of Denmark built Uraniborg, "castle of the heavens" on Hveen (across the water from Hamlet’s castle at Elsinore). With his large quadrants he made positional observations good to a minute of arc (1’) and made a continuous record of planetary positions between 1576-1597 when he was booted out of Denmark by Christian IV. In 1572 observed Tycho’s star (supernova): absence of p" showed it lay three times farther than the moon. In 1577 observed comet. Again, no p".
1571-1630	Johannes Kepler: Conceived 4:37am 16 May 1571 was an astrologer for money and curious mathematician for fun. Met Tycho in 1600 who hired him to "do something" with his observations. Big personality clash. Tycho loses it at a party, Kepler takes over T’s job and eventually gets T’s observations and "does something". Publishes The New Astronomy (1609). First (lucky) he works on Mars’ orbit (Commentaries on the motions of Mars). After much work discovers his three laws of planetary motion: Harmony of the Worlds. He verifies the harmonic law for the Galilean satellites. In 1618-1621 published The Epitome (of the Copernican Astronomy) which included observations by Galileo as well as his own. In 1627 he published the Rudolphine Tables.
1564-1642	Galileo Galilei Performed experiments in physics, g=constant, developed laws of mechanics, law of inertia, galilean transformation of coordinate systems (relativity). First scientific use of telescope (pirated from design by Hans Lippershay) in 1609: The Sidereal Messenger. Resolved nebulae (Pleiades) and the milky way into stars. Discovered the Galilean satellites, phases of Venus, and something odd about Saturn. Found craters, mountain ranges, valleys and maria on the moon. Observed sunspots and differential rotation of the sun. The Dialogue (of the two chief world systems) got him into a bit of trouble.

First law: Planetary orbit is ellipse with sun at one focus.
Second law: Planet sweeps out equal areas in equal times.
Third law: "Harmony of the worlds" (harmonic law), p²=a³.

Some ellipse things:
a=semimajor axis=1/2 "long" axis.
b=semiminor axis. e²=(a²-b²)/a².
e=eccentricity. (circle has a=b so e=0, parabola has e=1.)
foci are on major axis and separated by g=2ae.

the distance from one focus to the ellipse to the other focus is 2a.
if e is small just draw a circle offset by ae. (deferrant!)
perihelion: a(1-e), aphelion: a(1+e)

1656

Cristian Huygens: Theoretician, from reports of observations of Saturn he concluded that the planet was surrounded by a thin ring of matter. When earth passes through a node the rings disappear then a quarter of a Saturn year later were seen at maximum projection.

1643-1727

Isaac Newton: Best physicist of all time. At the behest of Halley and others put his work down in The Principia. Put forward his Laws of Motion:

Newton’s Laws

I. Galileo’s law of inertia.
Basically this sets up the framework of the newtonian physics and should be thought of as saying "there exist inertial observers" or inertial reference frames (IRF's). That is, there exists a reference frame in which the rest of Newton’s laws work.
The state of motion (momentum) of an object does not change with respect to any IRF unless that object is compelled to change that state by forces impressed upon it.
Momentum is usually demoted p and is the product of mass and velocity p=mv. v=speed, v=velocity. Some features of IRF’s: there are an infinity of them, none is any better than another. The IRF’s are related through the Galilean transformation. Some examples: space between galaxies, interstellar space, interplanetary space for a few minutes, earth orbit or free fall for a few seconds, a frictionless table (restricted to two dimensions). Some names in the great inertia debate: Galileo, Pierre Gassendi, Newton, Mach, Einstein.

II. The change in momentum is proportional to the force impressed, and is made in that direction of the straight line in which that force is impressed. The law is usually written F=ma or better F=dp/dt. This is Newton’s equation of motion.

III To every action there is an equal and opposite reaction. This is written F=-F’ or better dp/dt=-dp’/dt which says momentum is conserved.

Angular momentum is important too and is also conserved, L=mv´ rà mvr sinq

Newton also proposed his universal law of gravitation which states that a force acts between two point masses whose magnitude is proportional to the product of the masses and is inversely proportional to separation squared, F=GMm/r² 

1656	Cristian Huygens: Theoretician, from reports of observations of Saturn he concluded that the planet was surrounded by a thin ring of matter. When earth passes through a node the rings disappear then a quarter of a Saturn year later were seen at maximum projection.
1643-1727	Isaac Newton: Best physicist of all time. At the behest of Halley and others put his work down in The Principia. Put forward his Laws of Motion: