Ancient Astronomy and the Celestial Sphere

What do we see in the sky?

• Daily apparent motion of sky overhead

• Motion of Sun, Moon and planets against stars

• Seasonal change of Sun’s path– Different stars appear in the evening at

different times in the year

Some astronomical terms

• Celestial sphere

• North and South Celestial Poles

• Celestial Equator

• Ecliptic

• Direct Motion (eastward on ecliptic)

• Retrograde Motion (westward on ecliptic)

Celestial Sphere

Celestial Coordinates

The Ecliptic and the Celestial Equator

Declination and Right Ascension

Ecliptic

• The Sun’s apparent path through the sky over one year, through the constellations of the zodiac.

• At an angle of 23½0 to the celestial equator.• Summer solstice: June 21• Winter solstice: December 21• Vernal equinox: March 21• Autumnal equinox: September 21

Ecliptic

Eclipses• Lunar eclipses.

• Solar eclipses.

• Annular solar eclipses.

• Eclipse tracks.

Solar Eclipse

Solar Eclipse

“Diamond Ring” Effect

The Umbra of a Solar Eclipse

Solar Eclipse Paths

Annular Solar Eclipse

Lunar Eclipse

Lunar Eclipse-Curved Shadow of the Earth

Aristotle

• Born 384 BC (lived in Athens and Macedonia). Died 322 BC.

• Student of Plato.• Lectured and wrote

extensively on logic, rhetoric, poetry, ethics, economics, politics, physics, natural history, anatomy, physiology.

• Compared to Plato, relatively devoted to the study of the world.

The Nature of the World

• The world is composed of four elements: Earth, Water, Air and Fire, in order of lightness.

• Everything seeks its natural level.

• The heavens are made of quintessence.

• Everything in the heavens is spherical, and moves in a circular path around the Earth.

Impetus

• A property transmitted to an object by a mover (e.g. a throwing arm). In most medieval concepts, this property is “used up” as the object moves.

Ptolemy

• Lived in Alexandria c.140 AD.

• Observed the stars and planets.

• Attempted to fit the motions of the planets into a Geocentric system using circular motion.

Retrograde Motion: Jupiter and Saturn June 2000-May 2001

©Tunc Tezel, 2001

The Ptolemaic System

To match observed planetary motion, Ptolemy needed

• Deferent• Epicycle• Equant

Heliocentric Solar System of Aristarchus

Counterarguments to Heliocentric System

• No parallax observed.• No periodic

brightening of stars as Earth approaches and recedes.

• No sense of motion.• No physical context

for heliocentric theory.

Nicholas Copernicus

• Born 1473 (in Torun, Poland). Died 1543.

• Proposed heliocentric system, with planets moving in circular orbits.

• Author of De Revolutionibus (On the Revolutions).

Copernican System

• Planets move around the Sun in circular orbits.

• The Earth (and Moon) are third from the Sun.

• Simple explanation of retrograde motion.

Copernican Explanation of Retrograde Motion

                                                                                           

Tycho Brahe

• Born 1546 (in Denmark). Died 1601.

• Made extensive observations of the motions of the planets.

• Observed the supernova of 1572 and reasoned that the stars cannot be unchangeable.

Johannes Kepler

• Born 1571 (near Stuttgart, Germany). Died 1630.

• Assistant to Tycho Brahe.

• Originated three laws of planetary motion.

• Realized that planetary orbits must be ellipses.

Kepler’s First Law

• Planets move in ellipses, with the Sun at one focus.

How to Draw an Ellipse

Keplerian Orbital Parameters

• Semimajor axis: a (AU).

• Eccentricity: e = c/a.

• Sidereal Period: P (years).

• Inclination: angle to ecliptic plane ( 0 ).

Kepler’s Second Law

• The radius line from the Sun to a planet sweeps out equal areas in equal times.

Kepler’s Third Law

• The square of the sidereal period is equal to the cube of the semimajor axis, or

P2 = a3

Galileo Galilei

• Born 1564 (in Pisa, Italy). Died 1642.

• First to use a telescope for astronomical observations.

• Author of Dialogue Concerning the Two Chief World Systems.

• Originated concept of Galilean relativity.

Galileo’s Telescope Observations

• The phases of Venus.

• Mountains and craters on the Moon.

• Sunspots.

• The four bright satellites of Jupiter.

• The rings of Saturn.

• Neptune (although Galileo did not realize it was a planet).

Galileo’s Observations of Venus

Mountain and craters on the Moon

The satellites of Jupiter

Sunspots

Galileo’s Heresies

• Falling bodies move at the same speed, regardless of mass.

• The 1604 Supernova must be a star.

• Letter to Christina of Lorraine (1615)

• Dialogue Concerning the Two Chief World Systems (1632)

Isaac Newton

• Born 1642 (in Lincolnshire, England). Died 1727.

• Originated Three Laws of Motion

• Originated Law of Universal Gravitation.

• With Leibniz, invented Calculus.

• Author of the Principia.• Invented the first

reflecting telescope.

Mass and weight

• Mass is the amount of matter in an object. We measure it in kilograms (kg).

• Weight is the force exerted by gravity on an object. We measure it in newtons (N).

Your weight on various planets

Planet Weight (lbs)

Mercury 57

Venus 137

Earth 150

Moon 26

Mars 57

Jupiter 379

Saturn 161

Uranus 138

Neptune 177

Pluto 14

Newton’s First Law of Motion

• An object at rest tends to remain at rest. An object in motion moves at a constant speed in a straight line unless acted upon by a force.

Newtonian Orbits

Illustration from Pricipia, VII, Book 3, p. 551

Newton’s Second Law of Motion

• The acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass.

Force = mass × acceleration

F = m a

Newton’s Third Law of Motion

• For every action there is an equal and opposite reaction.

Law of Universal Gravitation

• The gravitational force between any two objects is proportional to the product of their masses and inversely proportional to the distance between them.

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Expanding our Solar System

• Uranus: discovered by William Herschel (1781).

Expanding our Solar System

• Neptune: position predicted by Adams and Leverrier; discovered by Galle (1846).

Expanding our Solar System

• Pluto: discovered by Clyde Tombaugh (1930).