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Admin. 9/6/16
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Class website http://www.astro.ufl.edu/~jt/teaching/ast1002/
Optional Discussion sections [THIS WEEK NO TUE. DISCUSSION OR
TUE./WED. OFFICE HR. - extra office hr on Thursday after discusson]
Tuesday ~11.30am (period 5), Bryant 3 (Basement level)
Thursday ~12.35pm (period 6), Bryant 3 (Basement level)
!
Office hr: Tuesday 12.30-1pm; Wed. 12.30-1.30pm, Bryant 302
3.
Homework 1: was due Mon. Sept. 5th 11.59pm via Canvas e-learning under
“Quizzes”
4.
Homework 2: is due Mon. Sept 12th 11.59pm via Canvas e-learning under
“Quizzes” (it will
5.
Reading for weeks 1 and 2: Chaisson & McMillan Ch. 0, 1, 2.1, 2.2, 2.3, can
continue Ch. 4.1, 5
6.
Observing project deadline: Thursday Oct. 27th 2016, however, you are
strongly advised to complete observing by Fri. Oct. 7th
7.
Email me Astro-news, jokes, tunes, images: [email protected]
Printed class notes? Name tags?
CAN TWO PEOPLE BRING SKATEBOARDS FOR THURSDAY’S CLASS?
1.
2.
8.
9.
Key Concepts: Lecture 7
Aristarchus and the relative distances to Moon and Sun
Parallax
Lecture 7 - Overview
• Ancient Greeks & Aristotelian Physics
– How did most of the early Greeks model the universe?
– What are the key physical ideals of Aristotelian
physics?
• Ptolemy - How did Ptolemy apply Aristotle’s physics to
model the cosmos?
• Copernicus - What were the main differences between his
model and those of most earlier Greeks?
Aristarchus of Samos (310-230 B.C.)
• Estimated relative sizes of the Moon & Earth
– timed duration of lunar eclipses
– compared the time it takes the Moon to enter the
Earth’s shadow with the time it takes the Moon
to cross the Earth’s shadow
Eratosthenes and the size of the Earth
• Estimated distance to Moon (relative to Earth’s diameter)
Precession
• Estimated distance to Sun (relative to Earth-Moon distance)
Aristotle, Hipparchus, Ptolemy - a geocentric model of solar system
Copernicus and the Heliocentric Model
– measured angular size of Moon & compared this to the
estimate of the Moon’s size relative to Earth’s diameter
– Assumed Moon’s orbit was circular & uniform
– Measured angle between Sun-Earth-Moon at 1st quarter:
estimated this to be 87 deg., so α=3 deg.
– Then Earth-Moon distance is about
= (3/360) x 2π x Earth-Sun distance
– But it was difficult to measure these angles: Aristarchus thought the
Sun was 20 times further away than the Moon, but it is really 400
times further.
Aristarchus of Samos (310-230 B.C.)
• Estimated size of Sun
– from total Solar Eclipse using
relationship between angular
size, physical size and distance
Angular size (measured in radians)
= Physical Size
Distance
Aristarchus estimated all these quantities in terms of the Earth’s diameter
⇒ Aristarchus found that the Sun was much bigger & much farther away
than the Moon
⇒ He therefore concluded that the Sun, not the Earth was at the center of
the Universe!
Parallax
• If Earth moves around Sun
then we should see parallax,
i.e., the displacement of
foreground stars with respect
to background stars.
• Parallax could not be seen by
early Greek astronomers: one
argument against the Suncentered model, e.g. by
Aristotle
• In fact parallax effects are real,
but very small as the stars are
very far away.
• We will see later in the class
how parallax is used to
measure distance to stars.
Eratosthenes (c. 200 B.C.)
Eratosthenes estimated the Earth’s diameter, and thereby took the relative
measurements of Aristarchus and placed them on an absolute scale
• On the summer solstice, at noon:
– the Sun was directly overhead in the city
of Syene, Egypt
– but in Alexandria, Egypt, the Sun was
displaced from the vertical
– Using a gnomon (i.e. a stick casting a
shadow) & basic trigonometry, he
determined that the angle from the vertical
was ~7.20
– thus ~7.20 = the angle between Syene &
Alexandria as seen from Earth’s center
– Alexandria was 5000 stadia from Syene,
and so the circumference of the Earth was
~250,000 stadia.
– But what is a stadium length?:
Modern estimates: 1 stadium = between 157.2
- 166.7 m. So how did Eratosthenes’
estimate of the Earth’s circumference
compare with the actual value?
7.200
5000
stadia
7.2
5000
stadia
=
0
360
Earth’s circumference
Hipparchus (c. 150 B.C.)
Erected an observatory on Rhodes & built instruments
to measure as accurately as possible the direction of
objects in the sky.
• Compiled a catalog of stellar coordinates - 850 entries
(perhaps inspired by seeing a Nova - “new star”)
• Discovered precession - direction of Earth’s axis of
rotation slowly changes, moving in a circle every
26,000 years
• Refined Aristarchus’ technique to measure Moon’s size
& distance
Scientific Models
•
– 29.5 earth diameters (actual distance = 30 earth
diameters)
•
•
•
•
Determined length of year to within 6 minutes
Carefully observed motions of Moon, Sun & planets
Predicted lunar and solar eclipses to within 1 hour
Developed a geometrical, geocentric model of the
universe
Precession of Earth’s Rotation Axis
• Earth’s axis
wobbles because it
is not quite perfectly
spherical and the
Moon and Sun’s
gravity act on these
imperfections.
• Effect is weak, so
period of wobble is
long: 26,000 years
• Our rotation axis,
i.e. the north
celestial pole, does
not always point at
Polaris.
• Conception of a physical model to explain the workings of
nature is a creative act of science.
• Models apply known laws of nature to explain observations.
• Key aspects of a scientific model
⇒ models explain what is seen
⇒ models predict observations accurately
⇒ simplify your understanding of nature
• Validity of models is tested by checking how well
predictions fit the best & newest observations.
• Scientific models are not necessarily static but can evolve
when new & better observations become available.
Modeling the Cosmos
• Key Observations to Explain
– Motion of Sun
• East to West in about 12 hours from sunrise to sunset
• West to East along ecliptic ~ 10 per day
• Small variation in speed along the ecliptic
• Variation of length of day & height of Sun with season
– Motion of Moon
• East to West in about 12 hours 25 minutes from moonrise
to moonset
• West to East within 50 of ecliptic
• Sidereal (relative to stars) & synodic (relative to Sun)
periods
Modeling the Cosmos
• Key Observations to Explain
– Motion of Stars
• East to West in ~ 12 hours
from star rise to star set
• star rise is ~ 4 minutes earlier
each day
• circumpolar stars
• stars in fixed position relative
to one another
• precession
• yearly motion relative to Sun
Modeling the Cosmos
• Key Observations to Explain
– Motion of Planets
• East to West in ~ 12 hours from rising to setting;
interval varies depending on rate of planet’s
motion with respect to stars
• West to East, within 70 of ecliptic
• Average speed varies along ecliptic
– fastest for Mercury
– slowest for Saturn
• Variation in speed along ecliptic for each planet
• Retrograde motion from East to West at a time
specific for each planet
Aristotle & Geocentric Model
• Geocentric - Earth at center - motionless
• Universe finite in size
• Motion of Sun, Moon, Planets & Stars
was
– circular
– uniform - constant rate of motion
• Model consisted of 56 spheres
• Did not fit observations well
• First to incorporate physical ideas or
concepts of motion
Aristotle’s View of the Cosmos
• Aristotle believed the Cosmos was
divided into two realms:
– Incorruptible Universe (the heavens):
• Eternal, unchangeable region in the heavens
• Natural Motions - No force required - Natural
motion of heavenly spheres was rotation at
uniform speed
– Corruptible Universe: a region of change near
the Earth made up of four basic elements:
• Earth, Water, Air, Fire
• Natural Motions
– Earthy material moved toward center of
cosmos
– Fire moved to highest heights
– Air below Fire
– Water between Earth & Air
• Forced Motions: motion of objects on Earth require
the application of a force, e.g. cart must be pushed
in order to move... and keep moving.
Hipparchus
Question
• In Aristotle’s Cosmos, the Earth was
stationary and at the center of the
universe.
• Imagine you lived at the time of
Aristotle. What observations or
evidence could you offer to support the
idea of a stationary Earth?
Aristotle’s Physics
• Aristotle believed Earth was
stationary and at the center of the
universe because:
– Natural motion of earthy material
appears to be toward the center of
the Earth.
– We do not feel the Earth moving.
– If Earth rotated then objects thrown
upward would not drop back to their
point of departure as they are
observed to do.
– If Earth moved about the Sun, then
one should observe stellar parallax,
yet this was not observed.
Parallax is the apparent
shift in the position of
an object compared to
background objects
because of the motion
of the observer
• Added geometrical devices to the basic
Geocentric model of Aristotle to explain
the detailed motions of the planets
• One example of these was the Epicycle:
the planet followed a small circle,
which itself went around the Earth. See
figure.
• Adding these complicated geometrical
devices made predictions of the
positions of the planets, Sun, Moon
more accurate, and could explain
retrograde motion, but at the expense of
abandoning the simplicity of uniform
circular motion about the Earth.
Ptolemy (125 A.D.)
• Designed a complete geometrical, geocentric model
of the universe that accurately predicted planetary
motions with errors within 5 degrees.
• Most of the geometric devices and basic foundations
of his model did not originate with him but were
based on the models of the early Greeks such as
Aristotle & Hipparchus
• Wrote the Almagest (Greatest)
– included his own original works & models
– included a compilation of past works of Greeks,
especially Hipparchus
– 13 volumes
“Well do I know that I am mortal, a creature of one day.
But if my mind follows the winding paths of the stars
Then my feet no longer rest on Earth, but standing by
Zeus himself I take my fill of ambrosia, the divine dish.”
Copernicus (1473-1543)
• Developed a Heliocentric (Sun centered)
model of the cosmos
• Why? Ptolemy’s geocentric model lasted for
centuries mainly because it accurately
predicted celestial motions so there was little
reason to discard it
• Copernicus studied the works of Aristotle,
Pythagoras & Plato
• Copernicus objected to the complicated
geometrical devices that Hipparchus and
Ptolemy had had to use. This judgement was
based on aesthetics - these geometrical
devices, such as epicycles, were not faithful
to the ideal of uniform circular motion - i.e.
they make the models too complex.
Copernicus’ Heliocentric Model
• Copernicus worked on his new Heliocentric
model for 20 years
– Sun was placed at center of cosmos
– Earth no longer static, but revolved
around Sun once a year & rotated on axis
once a day
• His work was published in De revolutionibus
in the year of his death
• De revolutionibus took after the Almagest in
outline and basic intention - to explain
planetary motions
• Even though it took 20 years to develop this
model did not predict celestial motions any
better than Ptolemy’s geocentric model!
Heliocentric Model
of Copernicus
• Cosmos finite in size
• Assumed no forces for heavenly motions
– physics of Aristotle
• Assumed uniform, circular motions
– done for aesthetics - followed Aristotle
• All heavenly spheres revolve around the Sun & the Sun is at the
center of the cosmos
– chosen based on aesthetics and simplicity
• The distance from the Earth to the sphere of stars is much greater
than the distance from the Earth to the Sun
– accounts for lack of observed stellar parallax
Heliocentric Model of Copernicus
• The daily motion of the heavens relative to the horizon
results from the Earth’s motion on its axis
– aesthetic appeal since only 1 sphere is rotating not
many
– however, he did not account for the objection that
if the Earth rotated, objects should be flung from
the surface
• The apparent motion of the Sun relative to the stars
results from the annual revolution of the Earth around
the Sun
• The apparent retrograde motions of the planets occur
because of the motion of the Earth relative to the other
planets
– retrograde explained as a natural result of the
planet’s revolutions about Sun - what we observe is
an illusion
Retrograde Motion Explained
•
•
Comparison of Ptolemaic & Copernican Models
When the Earth passes
any of the outer planets
retrograde motion
occurs.
Also explains why
planet is brighter when
undergoing retrograde
motion... because it is
closer.
Geometrical devices,
e.g. epicycles
Copernican Model
• Copernicus eliminated epicycles to explain
retrograde motion
• However, to account for variations in
planetary speeds he was forced in the end to
resort to using many epicycles, i.e. smaller
circles on circles.
• The complete model became more
complicated than Ptolemy’s - larger total
number of circles
• Violated Aristotelian physics & did not
offer new physical ideas to support his
model
• Didn’t predict motions any better than
Ptolemy’s model
Comparison of Ptolemaic & Copernican Models
A bit worse that
Ptolemy