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

● 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 AstronomersModels were based on unproven “first

principles”, believed to be “obvious” and were not questioned:

Geocentric “Universe”: The Earth is at the Center of the “Universe”.

“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 Earth2. Perfect Heavens (described by spheres)

Epicyclesa 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:

This made Ptolemy’s epicycles

unnecessary.

Retrograde (westward) motion of a

planet occurs when the

Earth passes the planet.

Described in Copernicus’ famous book “De Revolutionibus Orbium Coelestium” (“About the revolutions of celestial objects”)

Johannes Kepler (1571 – 1630)

Used the precise observational tables of

Tycho Brahe (1546 – 1601) to study planetary motion

mathematically.

Planets move around the sun on elliptical paths, with non-uniform velocities.

Found a consistent description by abandoning

both uniform motion & circular motion

Kepler’s Laws of Planetary Motion

1. The orbits of the planets are ellipses with the sun at one focus.

c

Eccentricity e = c/a

Eccentricities of Ellipses

e = 0.02 e = 0.1 e = 0.2

e = 0.4 e = 0.6

1) 2) 3)

4) 5)

Eccentricities of planetary orbits

Orbits of planets are virtually indistinguishable from circles:

Earth: e = 0.0167Most extreme example:

Pluto: e = 0.248

2nd Law: A line from a planet to the sun sweeps over equal areas in equal intervals

of time.Fa

stS

low

Animation

Autumnal Equinox (beg. of fall)

Winter solstice (beg. of winter)

Summer solstice (beg. of summer)

Vernal equinox (beg. of spring)

January

July

Fall

Winter Spring

Summer

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

3rd Law: A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed:

Py2 = aAU

3

(Py = period in years; aAU = distance in AU)

Orbital period P known → Calculate average distance to the sun, a:

aAU = Py

2/3

Average distance to the sun, a, known → Calculate orbital period P.

Py = aAU3/2

If it takes 29.46 years for Saturn to orbit once around the sun. What is its average distance from the sun?

A. 9.54 AUB. 19.64 AUC. 29.46 AUD. 44.31 AUE. 160.55 AU

Isaac Newton (1643 - 1727)

Major achievements:

Added physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler

2. Discovered the three laws of motion3. Discovered the universal law of mutual

gravitation

1. Invented Calculus as a necessary tool to solve mathematical problems related to motion

Newton’s Laws of Motion (I)

1. 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 AccelerationAcceleration (a) is the change of a

body’s velocity (v) with time (t):a = Δv/Δt

Velocity and acceleration are directed quantities (vectors)!

a

v

Newton’s Laws of Motion (II)2. 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)

3. 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.

F = - G Mmr2

(G is the Universal constant of gravity.)