The Origins of Modern Astronomy

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The Origins of Modern Astronomy
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Ancient Astronomy
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Mesopotamian astronomers

• began to build observatories about 6000 years
  ago.
• 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.
• 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 normal eastward motion. This is
  called retrograde motion
• developed astrology

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Retrograde Motion of Mars in 2001
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.
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Aristotle (384-322 BC)
Concluded that Earth is spherical.

• 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 the center of the
universe and does not move.

• 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.

Developed a geocentric (Earth centered) model
for the motions of the planets.
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Relationship Between the Vertical and the
Direction to the Sun at Noon on the Summer
Solstice
North Pole
O' is an observer at a latitude of 23.5o, and O
is farther north.
O
O'
ZOS ZCS' is the angle between the vertical and
the direction to the sun at noon on the date of
the summer solstice.
C
E
Angle ZOS Angle OCE - Angle O'CE
Angle ZOS Latitude - 23½º
South Pole
ZOS 0º for observer at a latitude of 23½º
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Eratosthenes (276-195 BC) measured the
circumference (C) of Earth using observations of
the sun at noon at the summer solstice at
Alexandria (latitude 30.7º) and Syene (latitude
23.5º).
North Pole
s
q 7.2º
q
s 5,000 stadia
C 250,000 stadia
This is close to the correct value of 40,100 km
if the stadium was about 1/6 km.
South Pole
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Ptolemy (127 - 151 AD)
Contributions to Astronomy

• developed a geocentric model, (based on
  Aristotles 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.

The Ptolemaic Model

• The center of a planets 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.

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Retrograde Motion in the Ptolemaic Model(Mars,
Jupiter, Saturn)
The center of a superior planets orbit moves in
a circular orbit called the deferent. The planet
itself moves around that center in a circle
called the epicycle.
Click to see animation
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Apparent Motion in the Ptolemaic Model(Mercury
and Venus)
The center of the epicycle for these planets must
always lie along a line from Earth to the Sun.
This accounts for the fact that they move back
and forth, from east of the sun to west of the
sun and back again.
East
Earth
Sun
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Renaissance Astronomy
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Copernicus (1473-1543)
Contributions to Science

• published a book on trigonometry
• 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

• 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.

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Retrograde Motion According to Copernicus
Earth
West
Mars
Vernal Equinox
Sun
East
Our line of sight usually moves eastward among
the stars but, when were passing a superior
planet, our line of sight moves westward.
Earth, moves faster than a superior planet, so it
catches up to the planet, and passes it.
Click to see animation.
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Measuring the Distance from the Sun to an
Inferior Planet
e greatest elongation (the maximum angle
between The Earth-Sun line and the Earth -Planet
line)
SP r
SE 1 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.
e 22.8o
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Tycho Brahe (1546 1601)

• Having measured the position of a new star (now
  known as Tychos 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.

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Johannes Kepler (1571 - 1630)

• Worked for Tycho Brahe.
• Acquired Tychos 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 disproving
  the geocentric model of the universe, and got him
  into serious trouble with the Church.

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Galileos Telescopic Observations

• Mountains and craters on the Moon.
• Spots on the Sun.
• Complete set of phases of Venus.
• 4 satellites orbiting Jupiter.
• Saturns ears.
• Many stars invisible to the naked eye.

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Keplers Model of Planetary Motion
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Properties of Ellipses
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.
P
B
r
r'
F1P PF2 2a
q
a CA CA' semi-major axis
A'
A
C
F1
F2
b CB CB' semi-minor axis
F1CCF2c
e c/a the eccentricity
B'
If F2 is the Sun and P is a planet, then A' is
aphelion and A is perihelion.
aphelion farthest point from the Sun
(Helios). perihelion point of closest approach
to the Sun
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Keplers 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
  equal to the cube of the semi-major axis of its
  orbit.

P2 ka3
If P is in years and a in AUs, then k 1.I
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Keplers Second Law
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.
B
C
S
D
The perihelion speed of a planet is greater than
its aphelion speed.
A
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Observational Evidence that P2 ka3 for the
Planets
The data shown above confirm Keplers 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.