Transcript Ancient Astronomy

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
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.
February 15,2001
September 12, 2001
N
W
E
S
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.
Relationship Between the Vertical and the Direction to the Sun at
Noon on the Summer Solstice
S
Z
North Pole
O
S'
O'
C
E
O' is an observer
at a latitude of
23.5o, and O at
the same
longitude, but
farther north.
ZOS = ZCS' is the angle between the
vertical and the direction to the Sun at
noon at the summer solstice.
Latitude
23½º
Angle ZOS = Angle ZCS' = Angle ZCE – Angle S'CE
Angle ZOS = Latitude - 23½º
South Pole
ZOS = 0º for observer at a latitude of 23½º
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
q
Z
North Pole
C
S'
s
q
q
360
s
q
q = 7.2º
s = 5,000 stadia
C
360
 5000  stadia
7.2
C = 250,000 stadia
South Pole
This is close to the
correct value of
40,100 km if the
stadium was about
1/6 km.
Ptolemy (127 - 151 AD)
Contributions to Astronomy
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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”.
The Ptolemaic Model
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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”.
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
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 we see them move back and forth,
between east of the Sun and west of the Sun.
East
Earth
Sun
Renaissance Astronomy
Copernicus (1473-1543)
Contributions to Science
• 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.
Retrograde Motion According to Copernicus
West
Sun
East
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.
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
S
r  sin  e  AU
P
The greatest eastern elongation of
Mercury is 22.8o. Calculate its
distance from the Sun.
e = 22.8o
e

r  sin  e   sin 22.8

 0.387 AU
E
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
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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
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”.
b = CB = CB'
= “semi-minor axis”
P
r
r'
F1P + PF2 = 2a
a = CA = CA'
= “semi-major axis”
B
q
A'
A
C
F1
F2
F1C = CF2 = c
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 .
perihelion = point of closest approach to the Sun
Kepler’s laws of Planetary Motion
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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
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
Points Along the Orbit of Mercury at Two Day Intervals
Sun
Observational Evidence that P2 = ka3 for the Planets
Planet
sidereal
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
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.