Foundations of Astronomy

The scientific method-winning or loosing?

II) Astrological and religious beliefs

image from: http://www.kprf.ru/clipart/misc/astrology.jpg

III) Need for a Calendar, especially related to agriculture. The Nile Flood was an especially important, yearly event.

Early Western Cosmology

(models of the relation between the Earth and Celestial bodies)

I) Plato: Heavens were perfect and that the most perfect geometric object was the circle. Artists Rendering of Plato--stretched a bit and note quite true to form!

His beliefs were based on Socrates study of "forms".image of "Plato" a Plate, from: http://www.vidrioyarte.com/proddos.htm

II) Aristotle: Plato's student…demonstrated that the Earth was round:

Since

a) Earth's shadow on the moon was always circular

b) the altitudes of stars change with latitude

Favored "Geo-Centric" model of the Universe. Why?

• Observed no stellar parallaxes
• no winds
• spinning Earth would hurl its inhabitants into space.

Main difficulty with Geocentric Model: Retrograde motion.

Geocentric Model requires:

deference(large orbit) and epicycles (small circle to create the retrograde loops).

Ptolomey (pronounced Tolemy) more "accurate" model

Requires 80 different circles,

Aristarchus of Samos (300 B.C.):

"Heliocentric" arguments relative sizes of the Earth and the Moon, and incorrectly for the Earth and Sun.

Erostathenes (250 B.C.):

measured the circumference of the Earth "the shadow in the well" method.

Dark Ages-Aristotelian beliefs Mandatory:

Copernicus (1473 - 1534)tried to update the Ptolemaic model and realized the "Heliocentric" model was simpler since distant stars were so far that no parallax could be seen.

Galileo(1564 -1642)

Turned his telescope on the moon, the Sun, and the Planets

Provided the proof of Copernicus theories.

He observed that:

Venus had phases like the moon,

photo from: http://astro.ysc.go.jp/venus-phases.jpg

Conclusion: Venus orbited the Sun

--Jupiter has moons that Orbit Jupiter( not the Sun)

photo from: http://www.ladeltascience.com/astronomy/kisatchie04/jupiterandmoons.jpg

--The Sun has spots

photo from: http://solar.physics.montana.edu/canfield/ssu_images/sunspots.gif

--the Moon has craters (so celestial objects weren't perfect.)

Moon and Mars from NASA

--Saturn has "Ears"

Photo at left from the HST

at right: http://www.arizonausa.com/sky/solarsystem/saturn-proj-bw.jpg

Galileoattempted to prove that the Earth moves in several ways...

tides are due to a spinning, orbiting Earth-partically incorrect there. Galileo thought the Earth's motion about the sun would create an "inertial bulge" on the size of the Earth opposite the sun, but the bulge is not on the anti-solar side, and there are two "tidal bulges" each day...so what do you think is the real reason for the tides?

image of Tides on Earth from: http://www.angliacampus.com/public/sec/geog/coastln/page08.php

Galileo also developed the physics needed to understand orbital motion:

• The law of falling bodies ( distance object falls in a given time = 5 x (time)^2 where the units are meters per second. This decribes the acceleration of a falling object. (optional for experts: Actually, this law can also be described as h = 1/2 g t^2 where g is the acceleration of gravity at a particular point, and h is the distance something falls in a time t...since g = 10 m/s^2 at the earth's surface, the equation gives h = 5t^2 at the earth's surface. How far would something in one second if it were dropped from two Earth radii? What about 60 earth radaii? Answers: 1/4 of 10 m/s^2, and 1/3600 of 10 m/s^2. )
• The Law of Inertia (objects continue moving in a straight line at constant speed) unless a force acts on them
• The idea of Centriptal motion (an orbit results from an object falling downward while moving horizontally). Here is a shockkwave illustration to help demonstrate:

Galileo also found that the acceleration (a) and speed (v) of a planet or moon in its orbit and its orbital radius (R) is related by:

a = V^2/R

(optional for experts: This equation shows for example, that planets closer to the sun will move more rapidly than planets farther away, assuming that the acceleration is greater when they are closer--Newton would soon prove this to be the case!)

Galileo published many of these results in a book entitled:

Dialogue Concerning the Two Chief World Systems.

which resulted in house arrest...there he continued is work on motion of bodies...all of which was quite useful, especially for newton!

Tycho Brahe(1546-1601)

image from : http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.html

Tyco wished to solve "the problem" (geocentric vs. heliocentric) but felt that better observations were needed. Tyco was most like interested in proving that the "tyconic Universe" was correct

• Brahe developed instruments and made observations of the planets positions on the Celestial Sphere
• accurate to within 1 arc minute!
• 20 years worth of data-particularly orbit of Mars

Johannes Kepler ((1571 - 1630)

Mathematician...sought out Brahae for his famous data, and was hired by Brahe to fit data to the tyconic model universe. But...

Kepler was trying to fit data to the Kepler model Universe--the orbits of the six known planets fit into the largest spheres which could be inscribed into the six regular geometric solids--crazy by today's standards, but at least the orbits were centered on the sun!

Also, Brahae died and family wouldn't release data!

Eventually Kepler "acquired" Brahe's data and found that:

--the orbit of Mars just isn't a circle! Plato was wrong! This opened the door to a "true" understanding of the solar system.

Kepler's final Results:

1. All Planets orbit the sun in Elliptical orbits with the sun at one focus

http://www.mat.usach.cl/Memorias/LEMC/Diccionario/Image66.gif

2. A line joining a planet and the sun sweeps out equal areas in equal times. See http://www.calstatela.edu/faculty/kaniol/a360/keplers_laws.JPG

3. The square of a Planets orbital period is proportional to the cube of its semi-major axis. (P^2 = constant x a^3)..see: http://www.windows.ucar.edu/the_universe/uts/kepler3_small.gif

These three relations are now known as Kepler's three laws.

After Kepler Astronomers had:

• definitive proof that the Earth orbited the sun, and spun on its axis.
• an accurate description of the Solar system.
• Missing: an explanation of Why the planets orbited the sun and why Kepler's mysterious laws were true!

Issac Newton(1642 -1727)

image of Issac Newton from: http://www.sciences.univ-nantes.fr/physique/enseignement/tp/hist/newton.html

Newton realized that

• Gravity pulls apples and the moon to the Earth.
• Orbit is a compromise, between inertia, and the Earths gravity.
• Newton knew that the orbits must be eliptical...and new that a correct mathematical descriptioon of the way an object falls (due to a force) would result in the path of an object being elliptical (a basic ellipse is described by : (x/a)^2 + (y/b)^2 = r^2

This is slightly complicated since both objects move..check out this quicktime movie:

He also discovered:

• F = ma, (Newton's second law)
• Calculus!
• .....and he used Galileo's Centriptial motion law, and the law of falling bodies, together with the fact that the moons distance is 60 x the earth's radius to determine:

law of Universal gravitation :

F = G m1m2/d2

He realized that force is an interaction between two massive objects.

Also depends on the inverse square of the distance.

this law, together with Calcus Derives Kepler's laws.

-shows that the Orbits must be ellipses(Kepler's 1st law),

- planets must speed up as they approach perihelion (closest approach) (Kepler's 2nd law).

100 years later, Adams and Leverier Used basic laws to discover Neptune (with pencil and paper) (plus a new form of Calculus) so....

What does cause gravity?

--Einstein- gravity is due to the curvature of space time.

"marble in punch bowl"

predicts bending of light by massive objects, black holes

theory well verified

other interpretation: exchange of gravitons.

Also verified.

Will these pictures be unified one day?

Is this our mythology and superstition?