Transcript chart_set_2 - Physics and Astronomy

The “Geocentric Model”
Ancient Greek astronomers knew of Sun, Moon, Mercury, Venus, Mars,
Jupiter and Saturn.
Aristotle vs. Aristarchus (3rd century B.C.):
Aristotle: Sun, Moon, Planets and Stars rotate around fixed Earth.
Aristarchus: Used geometry of eclipses to show Sun bigger than Earth
(and Moon smaller), so guessed Earth orbits Sun. Also guessed Earth
spins on axis once a day => apparent motion of stars.
Difficulty with Aristotle's "Geocentric" model: "Retrograde motion of the planets".
However, Ptolemy (c. A.D. 140) invented a model where planets circle
in “epicycles” that orbit the Earth. This helped to explain retrograde
motion for a long time, until astronomical observations became more
precise. The Ptolemaic Model.
"Heliocentric" Model
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Rediscovered by Copernicus in 16th century.
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Put Sun at the center of everything.
Much simpler. Almost got rid of retrograde
motion.
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But orbits circular in his model. In reality,
they’re elliptical, so it didn’t fit the data well.
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Not generally accepted then.
Copernicus 1473-1543
Galileo (1564-1642)
Built his own telescope in 1609.
400 years ago.
Discovered four moons orbiting Jupiter =>
Earth is not center of all things!
Co-discovered sunspots. Deduced Sun
rotated on its axis.
Discovered phases of Venus, inconsistent
with geocentric model.
Johannes Kepler
• (1571 - 1630)
• Born near Stuttgart
• Studied philosophy and theology at Tubingen
• Developed love for astronomy as a child
• Showed high level of mathematical skill
• Had a reputation as a skilled astrologer
• Wanted to be a minister; became instead a
teacher of astronomy and math in Graz, Austria
• Became assistant to Tycho Brahe in 1601
• Developed Laws of Planetary Motion
Kepler's First Law
The orbits of the planets are elliptical (not circular)
with the Sun at one focus of the ellipse.
eccentricity = e =
CIRCLE
e=0
distance between foci
major axis length
ELLIPSE
moderately so
ELLIPSE
highly elliptical
Kepler's Second Law
A line connecting the Sun and a planet sweeps out equal areas
in equal times.
Translation: planets move faster
when closer to the Sun.
slower
faster
Kepler's Third Law
The square of a planet's orbital period, P, is proportional to the cube of
its semi-major axis, a.
P2 α a3
(for circular orbits, a=radius).
Translation: the larger a planet's orbit, the longer the period.
With the scale of the Solar System determined, can rewrite Kepler’s Third Law as:
P 2 = a3
So compare Earth and Pluto:
Object
a (AU)
Earth
Pluto
1.0
39.53
as long as P is in years and a in AU.
P (Earth years)
1.0
248.6
Newton (1642-1727)
Kepler was playing with mathematical shapes and
equations and seeing what worked.
Newton's work based on experiments of how
objects interact.
His three laws of motion and law of gravity
described how all objects interact with each other.
Newton's Correction to Kepler's First Law
The orbit of a planet around the Sun has the common
center of mass (instead of the Sun) at one focus.
x
Star
center
of mass
planet
Center of mass is not at the geometric center of the star, but because stars are so much more massive than
it’s usually beneath the surface of the star.
Timelines of the Big Names
Galileo
Copernicus
1473-1543
1564-1642
Brahe
1546-1601
Kepler
1571-1630
Newton
1642-1727
The Celestial Sphere
An ancient concept, as if all
objects at same distance.
North Celestial pole
But to find things on sky,
don't need to know their
distance, so still useful today.
Features:
- Does not rotate with Earth
- Poles, Equator:
Celestial Equator
Projections of Earth’s Pole’s and
Equator out onto the sky
South Celestial pole
The Year
Earth’s rotation axis is inclined (tilted)
23 1/2 degrees to the plane of its orbit.
Spring
Sun
Winter
Summer
N. Hemisphere
tilted towards
the sun
Fall
Direction of
Earth’s motion in orbit
N. Hemisphere
tilted away from
the Sun
Inclined view of the Earth’s orbit
The Earth revolves around the Sun in 365.256 days (“sidereal year”).
Note: the projection of Earth’s orbital plane onto the sky
(the Celestial sphere) is called the Ecliptic
The "Solar Day" and the "Sidereal Day"
Solar Day
How long it takes for the Sun to return to the same position
in the sky (24 hours).
Sidereal Day
How long it takes for the Earth to rotate 360o on its axis.
These are not the same!
The Motion of the Moon
The Moon has a cycle of "phases", which lasts about 29 days.
Half of the Moon's surface is lit by the Sun.
During this cycle, we see different fractions of the sunlit side.
Which way is the Sun in each case?
Cycle of phases slightly longer than time it takes Moon to do a complete orbit around Earth.
Cycle of phases or
"synodic month"
29.5 days
Orbit time or "sidereal
month"
27.3 days
Eclipses
Lunar Eclipse
When the Earth passes directly between the Sun and the Moon.
Sun
Earth
Moon
Solar Eclipse
When the Moon passes directly between the Sun and the Earth.
Sun
Moon
Earth
Solar Eclipses
Diamond ring effect - just before or
after total
Total
Partial
Annular - why do these occur?
Lunar Eclipse
Q: Why don't we get eclipses every month?
Q: How can there be both total and annular eclipses?
A: Look at Moon's orbit tilted compared to Earth-Sun orbital plane:
Sun
Moon
Earth
5.2o
Side view
Also, moon's orbit slightly elliptical:
Moon
Distance varies by ~12%
Earth
Top view, exaggerated ellipse
Types of Solar Eclipses Explained
Sun
Moon
Earth
Total
Annular
Partial
Certain seasons are favorable for eclipses. Solar “eclipse season”
lasts about 38 days. Likely to get at least a partial eclipse
somewhere.
It's worse than this! The plane of the Moon's orbit precesses, so
that the eclipse season occurs about 20 days earlier each year.