The History of Astronomy

The Roots of Astronomy Already in the stone and bronze ages, human cultures realized the cyclic nature of motions in the sky. Monuments dating back to ~ 3000 B.C. show alignments with astronomical significance. Those monuments were probably used as calendars or even to predict eclipses.

Stonehenge

Stonehenge Constructed 3000 – 1800 B.C. in Great Britain Constructed 3000 – 1800 B.C. in Great Britain Alignments with locations of sunset, sunrise, moonset and moonrise at summer and winter solstices Probably used as calendar.

Amazon Stonehenge Constructed around A.D. 100 in Brazil

Other Examples around the World Caracol (Mexico); Maya culture, approx. A.D. 1000

Ancient Greek Astronomers Models were based on unproven “first principles”, believed to be “obvious” and were not questioned: 1. Geocentric “Universe”: The Earth is at the Center of the “Universe”. 2. “Perfect Heavens”: The motions of all celestial bodies can be described by motions involving objects of “perfect” shape, i.e., spheres or circles.

Ptolemy: Geocentric model, including epicycles Central guiding principles: 1. Imperfect, changeable Earth, 2. Perfect Heavens (described by spheres)

Introduced to explain retrograde (westward) motion of planets Epicycles a small circle whose center moves around the circumference of a larger one. Introduced to explain retrograde (westward) motion of planets

The Copernican Revolution Nicolaus Copernicus (1473 – 1543): Heliocentric Universe (Sun in the Center)

New (and correct) explanation for retrograde motion of the planets: Retrograde (westward) motion of a planet occurs when the Earth passes the planet. This made Ptolemy’s epicycles unnecessary. Described in Copernicus’ famous book “De Revolutionibus Orbium Coelestium” (“About the revolutions of celestial objects”)

Found a consistent description by abandoning both Johannes Kepler (1571 – 1630) Used the precise observational tables of Tycho Brahe (1546 – 1601) to study planetary motion mathematically. Found a consistent description by abandoning both Circular motion and Uniform motion. Planets move around the sun on elliptical paths, with non-uniform velocities.

Kepler’s Laws of Planetary Motion The orbits of the planets are ellipses with the sun at one focus. c Eccentricity e = c/a

Eccentricities of Ellipses 1) 2) 3) e = 0.02 e = 0.1 e = 0.2 5) 4) e = 0.4 e = 0.6

Eccentricities of planetary orbits Orbits of planets are virtually indistinguishable from circles: Most extreme example: Pluto: e = 0.248 Earth: e = 0.0167

A line from a planet to the sun sweeps over equal areas in equal intervals of time. Fast Slow Animation

Autumnal Equinox (beg. of fall) Summer solstice (beg. of summer) July Winter solstice (beg. of winter) Fall Summer Winter Spring January Vernal equinox (beg. of spring)

Astronomical Units (AU) 1AU = (about) 150 mil km

Kepler’s Third Law A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed: Py2 = aAU3 (Py = period in years; aAU = distance in AU) Orbital period P known → Calculate average distance to the sun, a: aAU = Py2/3 Average distance to the sun, a, known → Calculate orbital period P. Py = aAU3/2

It takes 29. 46 years for Saturn to orbit once around the sun It takes 29.46 years for Saturn to orbit once around the sun. What is its average distance from the sun? 9.54 AU 19.64 AU 29.46 AU 44.31 AU 160.55 AU

Isaac Newton (1643 - 1727) Major achievements: Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler Major achievements: Invented Calculus as a necessary tool to solve mathematical problems related to motion Discovered the three laws of motion Discovered the universal law of mutual gravitation

Newton’s Laws of Motion (I) Newton’s Laws of Motion (I) A body continues at rest or in uniform motion in a straight line unless acted upon by some net force. An astronaut floating in space will float forever in a straight line unless some external force is accelerating him/her.

Velocity and Acceleration Acceleration (a) is the change of a body’s velocity (v) with time (t): a a = Dv/Dt Velocity and acceleration are directed quantities (vectors)! v

Newton’s Laws of Motion (II) The acceleration a of a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force. a = F/m  F = m a

Newton’s Laws of Motion (III) Newton’s Laws of Motion (III) To every action, there is an equal and opposite reaction. The same force that is accelerating the boy forward, is accelerating the skateboard backward.

The Universal Law of Gravity A particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mm F = - G r2 (G is the Universal constant of gravity.)