Transcript Stars

Ancient Cosmology
Monday, September 29
For 2000 years, geocentric model for
the universe was widely assumed.
Stars affixed to
celestial sphere
Moon, Sun, planets,
between Earth & stars
Spherical Earth at
center of universe
Most famous advocate of
geocentric model: the astronomer
nd
Ptolemy (2 century AD).
Developed elaborate
model to describe
motion of stars, Sun,
Moon, & planets.
Stars:
Circular motion around north celestial
pole (near the North Star, Polaris)
Time to complete circle = 23 hours, 56 min.
= 1 sidereal day
Stars look as if they were glued to
rigid spherical shell rotating once
every 23 hr, 56 min.
(You can’t tell, without a telescope,
that some stars are closer than others.)
Sun:
Circular motion
around celestial pole:
part of circle is below
horizon, so we say
Sun “rises” and “sets”.
Time to complete circle = 24 hours.
Observed motions of the Sun:
humanity’s first clock.
Noon
Sunrise
Sunset
1 solar day = time from one noon to
the next = 24 hours
IF the Sun
orbited the
Earth once
per day:
Midnight
Sunset
×
Observer
Noon
Sunrise
SINCE the
Earth rotates
once per
day:
×
×
Midnight
Sunrise
Sunset
Noon
×
×
Observed motions of the Sun can
be described if either
1) The Sun goes around the Earth
once per day, or
2) The Earth rotates about its axis.
Describing motions of stars and
Sun (and also Moon) was fairly
simple in the geocentric model.
Describing motion of
planets was difficult.
Planet = “Wanderer” in Greek
To naked eye,
a planet looks
like a star a tiny blob of
light.
Planets are distinguished by their
motion relative to stars.
↑ NORTH
Planets usually move west to east, but
sometimes east to west (retrograde),
relative to stars.
Ptolemy’s explanation of retrograde motion:
Planet (P) moves in a small
circle called the epicycle.
Earth
Center of epicycle (A)
moves in a large circle
called the deferent.
Combination of small and large circles
creates “loop-the-loop” retrograde motion.
Detailed structure of Ptolemy’s
geocentric model:
Earth
Complicated!
A bold minority opinion:
Aristarchus (3rd cent. BC)
proposed that the Earth
rotates on its axis & goes
around the Sun.
First heliocentric
(Sun-centered) model.
Heliocentric model was rejected by
the contemporaries of Aristarchus.
Aristarchus was accused of impiety.
Why did Aristarchus bother with a
heliocentric model, given the grief
he received?
Questions posed by Aristarchus:
How far away is the Sun?
How large is the Sun?
A sphere (like the Sun) will be 1/2° across
when its distance is 115 times its diameter.
How far away is the Sun?
Farther away than the Moon!
Moon comes between
Sun and Earth during
a solar eclipse.
Moon, like Earth, is an
opaque sphere, capable
of blocking light.
Phases of the Moon:
The Moon is an opaque sphere
illuminated by the Sun.
s
Half close
to Sun is
illuminated.
M
E
Half away
from Sun
is dark.
Gibbous, crescent shapes: result of perspective.
How Aristarchus found the relative
distances of Sun and Moon.
“First quarter” or “last quarter” Moon:
we see bright portion of Moon
as a perfect half-circle.
When we see the Moon as a half-circle,
Earth-Moon-Sun angle must be 90°.
90°
87°
When Aristarchus saw the Moon as
a half-circle, he measured the
Moon-Earth-Sun angle to be 87°.
A more accurate diagram:
M
E
90°
87°
S
3°
Get out your rulers:
Earth – Sun distance (E-S) is 19 times
Earth – Moon distance (E-M).
Aristarchus: Sun is 19 times farther away
(and thus 19 times bigger) than Moon.
(This is actually an underestimate
of the Sun’s immense size.)
Aristarchus: Earth is 3 times size of Moon
(from size of Earth’s shadow on Moon).
Despite the arguments of Aristarchus
(“Why should big Sun orbit tiny Earth?”),
heliocentric model ignored for 18 centuries.
Reviver of “heliocentrism”:
Nicolaus Copernicus
(Polish: 1473 – 1543)
Wednesday’s Lecture:
Renaissance Cosmology
Reading:
Chapter 2