The Origins of Modern Astronomy

Mesopotamian astronomers

• kept long term astronomical records.

• used the location of the Sun among the 12 constellations of the zodiac to keep keep track of seasons.

• noted the “wandering” of Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn.

• made predictions based on repeating patterns, including the saros cycle.

• showed no interest in building models.

• Observed that Mars, Jupiter, and Saturn periodically slow down, get brighter, reverse direction (from eastward to westward), and then resume their usual eastward motion.

• developed astrology

Retrograde Motion of Mars in 2001

February 15,2001

September 12, 2001

N

S

E W

As seen from Earth, the superior (outer) planets usually move eastward relative to the stars. However, they periodically slow down, get brighter, reverse direction and move westward for a while, slow down again, get dimmer, and then resume their eastward motion. This is called retrograde motion.

Aristotle (384-322 BC)

• All falling bodies fall straight down.

• The shadow cast by Earth on the Moon during a lunar eclipse is always circular.

• Different stars are seen from different locations on Earth.

• Therefore Earth is spherical

Concluded that Earth is spherical.

Concluded that Earth is the center of the universe and does not move.

Developed a geocentric (Earth –centered) model for the motions of the planets.

• If the Earth were moving, there would be a strong wind.

• Falling objects would fall to the west instead of vertically down.

• Our changing viewpoint as we orbit the Sun would cause the stars to look brighter and farther apart when we are on the part of our orbit closer to them.

Relationship Between the Vertical and the Direction to the Sun at Noon on the Summer Solstice

North Pole

South Pole

C

Z

S'

S

O

E

Angle ZOS = Angle ZCS' = Angle ZCE – Angle S'CE

Angle ZOS = Latitude - 23½º

Latitude 23½º

ZOS = ZCS' is the angle between the vertical and the direction to the Sun at noon at the summer solstice.

ZOS = 0º for observer at a latitude of 23½º

O'

O' is an observer at a latitude of 23.5o, and O at the same longitude, but farther north.

North Pole

South Pole

Z

S'

s

s = 5,000 stadia

Eratosthenes (276-195 BC) measured the circumference (C) of Earth using observations of the Sun at noon on the summer solstice at Alexandria (latitude 30.7º) and Syene (latitude 23.5º).

C 360

s

360C s

= 7.2º

C = 250,000 stadia

This is close to the correct value of 40,100 km if the stadium was about 1/6 km.

C360

7.25000 stadia

Ptolemy (127 - 151 AD)

• developed a geocentric model, (based on Aristotle’s model) that was accepted by scholars for almost 1500 years.

• compiled a catalog of more than 1000 stars, including celestial coordinates and brightness.

• expressed brightness as “magnitude”.

Contributions to Astronomy

• The center of a planet’s orbit moves along a circle called the “deferent”.

• The planet moves around that center in a circle called the “epicycle”.

• The center of the epicycle moves at a constant speed as viewed from a point called the “equant”.

The Ptolemaic Model

Retrograde Motion in the Ptolemaic Model(Mars, Jupiter, Saturn)

The center of a superior planet’s orbit moves in a circular orbit called the deferent. The planet itself moves around that center in a circle called the “epicycle”.

Deferent Epicycle

Earth Sun

Apparent Motion in the Ptolemaic Model(Mercury and Venus)

East

The center of the epicycle for these planets must always lie along a line from Earth to the Sun. This accounts for the fact we see them move back and forth, between east of the Sun and west of the Sun.

Renaissance Astronomy

Copernicus (1473-1543)

• Developed a heliocentric (Sun-centered) model of the solar system. Argued that such a model is simpler than the Ptolemaic model. Hoped that it could predict planet positions better.

Properties of Circular Orbits in Copernicus’ Heliocentric Model

Contributions to Science

• The planets move in circular orbits with the Sun as center.

• The farther a planet is from the Sun, the slower it moves.

• All of the planets move eastward around the Sun.

Retrograde Motion According to Copernicus

Earth, moves faster than a superior planet, so it catches up to the planet, and passes it.

Our line of sight usually moves eastward among the stars but, when we’re passing a superior planet, our line of sight moves westward.

West

EastSun

Measuring the Distance from the Sun to an Inferior Planet

E

P

e

e = greatest elongation(the maximum angle betweenThe Earth-Sun line and the Earth-Planet line)

SP = r SE = 1 AU

r sin e AU

1 AU = 1 astronomical unit = 1.496 x 108 km

The greatest eastern elongation of Mercury is 22.8o. Calculate its distance from the Sun.

r sin e sin 22.8 0.387 AU e = 22.8o

S

Tycho Brahe (1546 – 1601)

• Having measured the position of a new star (now known as Tycho’s supernova), and observed no parallax, he concluded that it was farther away than the Moon.

• This led him to question the Ptolemaic theory, according to which objects farther away than the Moon were celestial (therefore perfect) and could not change.

• was given an island to encourage his continuing his work in Denmark.

• built large metallic measuring instruments and measured positions of stars and planets with greater accuracy than his predecessors.

• proposed a model of the solar system in which the Sun and Moon orbit the Earth but the other planets orbit the Sun.

• hired Johannes Kepler.

Tycho’s Supernoiva Remnant

Johannes Kepler (1571 - 1630)

• Worked for Tycho Brahe.

• Acquired Tycho’s data after Tycho died.

• Studied the data on Mars and devised three laws of planetary motion, which are still accepted.

Galileo (1564 – 1642)

• Demonstrated that all bodies fall with the same acceleration: i.e., their speeds increase at the same rate (9.8 m/s every second).

• Built telescopes and used them to observe the Sun, Moon, and planets.

• Wrote a book that was influential in undermining confidence in the geocentric model of the universe, and got him into serious trouble with the Church.

Galileo’s Telescopic Observations

• Mountains and craters on the Moon.

• Spots on the Sun.

• Complete set of phases of Venus.

• 4 satellites orbiting Jupiter.

• Saturn’s “ears”.

• Many stars invisible to the naked eye.

Kepler’s Model of Planetary Motion

P

F1 F2

F1C = CF2 = c

F1P + PF2 = 2a

Properties of Ellipses

If F2 is the Sun and P is a planet, then A' is aphelion and A is perihelion.

Ellipse: a figure in which the sum of the distances from two fixed points is constant. Each of these points, labeled F1 and F2 in the diagram, is called a “focus”. The plural is “foci”.

CA' A

B

B'

rr'

a = CA = CA' = “semi-major axis”

b = CB = CB' = “semi-minor axis”

= c/a = the “eccentricity”

aphelion = farthest point from the Sun .perihelion = point of closest approach to the Sun

Kepler’s laws of Planetary Motion

• The orbit of a planet is an ellipse with the Sun at one focus.• The line from the Sun to a planet sweeps out equal areas in equal times.• The square of the sidereal period of a planet is proportional to the cube of the

semi-major axis of its orbit.

P2 = ka3

If P is in years and a in AU’s, then k = 1.I

Kepler’s Second Law

S

A

B

C

D

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

S is the position of the Sun (at one focus of the ellipse). A, B, C, and D mark positions of the planet. If area SAB = area SCD, then the time it takes the planet to go from A to B is the same as the time it takes the planet to go from C to D.

Since the distance AB is greater than the distance CD, the speed of the planet as it goes from A to B is greater than its speed as it goes from C to D.

The perihelion speed of a planet is greater than its aphelion speed.

Points Along the Orbit of Mercury at Two Day Intervals

Sun

The data shown above confirm Kepler’s third law for the 8 planets of our solar system. The same law is obeyed by the moons that orbit each planet, but the constant k has a different value for each planet-Moon system.

Planetsidereal period in

years

semi major axis in AU’s

a3/P2

Mercury 0.241 0.387 0.998

Venus 0.615 0.723 0.999

Earth 1.000 1.000 1.000

Mars 1.881 1.524 1.000

Jupiter 11.86 5.203 1.001

Saturn 29.46 9.54 1.000

Uranus 84.81 19.18 1.000

Neptune 164.8 30.06 1.000

Observational Evidence that P2 = ka3 for the Planets