Transcript Sun

From the Earth-centered to
the Sun-centered Model
Tuesday, January 8
For 2000 years, geocentric model for
the universe was widely assumed.
Stars affixed to
celestial sphere
Moon, Sun, planets,
between Earth & stars
Dante,
AD 1300
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.)
No sense of depth!
Comet Hale-Bopp:
10 light-minutes away
Andromeda Galaxy:
2 million light-years away
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
Sunrise
Noon
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.
Q: Why did ancient astronomers
believe the Earth is not moving?
A: Well, do you feel any motion?
Rotation speed at Earth’s equator =
circumference / rotation period =
40,000 kilometers / 24 hours =
1667 kilometers/hour
Describing motions of stars and
Sun (and also Moon) was fairly
simple in the geocentric model.
Describing motion of planets
was very difficult.
Planet = “Wanderer”
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.
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 110 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 halfcircle, he measured the Moon-Earth-Sun
angle to be 87°.
Trigonometry Alert!
x
θ
x
 cos 
y
y
x
y
 19 x
cos 87
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 huge Sun orbit tiny Earth?”),
heliocentric model ignored for 18 centuries.
Reviver of “heliocentrism”:
Nicolaus Copernicus
(Polish: 1473 – 1543)
Basic structure of Copernicus’ model:
Earth
Sun
Geocentric model (Ptolemy):
◦ Earth in central location
◦ Celestial sphere rotating about axis
◦ Sun orbiting around Earth
Heliocentric model (Copernicus):
◦ Sun in central location
◦ Earth rotating about axis
◦ Earth orbiting around Sun
Thursday’s Lecture:
Planets and Stars and
Galaxies (Oh my!)
Reading:
Chapter 1