Download Lecture 5 Motions of the Planets

Lecture 5
Motions of the Planets;
Geometric models of the Solar System
Motion of Planets
Opposition, Conjunction
Retrograde Motion
Scientific Method and "Models"
Size of the Earth
Geocentric vs Heliocentric Solar System
Jan 27, 2006
Astro 100 Lecture 5
1
Motions of the Planets
• Apparent motion is quite uneven, but paths are
near ecliptic ("planet" is Greek for "wanderer")
• Due to combination of apparent motion of Sun and
actual motion of planets around Sun
• First, definitions of angular position relative to
sun:
– Elongation: angle from sun
– Conjunction: ~0 deg elongation
• Inferior between Earth and Sun
• Superior other side of the Sun
– Quadrature: 90 deg elongation
– Opposition: ~180 deg elongation (opposite sun)
Jan 27, 2006
Astro 100 Lecture 5
2
1
Loops
• Two classes of apparent motions:
URL for this demo: http://www.mhhe.com/physsci/astronomy/applets/Retro/frame.html
• Inferior planets: Mercury, Venus
– Always near sun in sky, do both direct and retrograde
(E to W) among stars
– Never reach quadrature, largest angle (maximum
elongation) = 28 deg (Mercury), 47 deg (Venus)
– When W of sun, only seen in morning sky, when E,
only seen in evening.
• Superior planets: Mars, Jupiter, Saturn, (Uranus,
Neptune, Pluto)
– Generally direct motion, slower than sun, but near
opposition, do retrograde loops
Jan 27, 2006
Astro 100 Lecture 5
3
Handy Summary Table
Solar System Apparent Motions: Summary
What
Due to
Path
Direction
Sidereal
Period
Synodic Event
Diurnal:
Stars
Earth Rotation
about celestial
poles
E to W
23h 56m
solar day = 24h
Annual:
Sun
Orbit of Earth
around Sun
"ecliptic", tilted
23.5 deg to equator
W to E
(direct)
365.2422
solar days
solar year,
seasons
Moon
Orbit of Moon
around Earth
tilted 5 deg to
ecliptic
W to E
27d 8h
phases,
eclipses
Planets
Orbits of planets
around Sun
tilted up to 17 deg
to ecliptic
direct,
0.39 - 248
retrograde years
conjunction,
opposition
How apparent motions were explained is a good illustration
of the "Scientific Method" . . .
Jan 27, 2006
Astro 100 Lecture 5
4
2
Scientific Method
Experiment
Theory
Raw Data
Calibrated data
Analyzed data
Speculation
Hypothesis
Prediction
Model/Theory
• Most Useful Theories:
Law ("reality"??)
– Predictive Power: can predict the result of some experiment
which has not yet been done
– Falsifiable: can suggest an experimental result which would
be impossible with this theory
– "Simplest": given two theories making same prediction,
choose the simplest.
In Astronomy, where you can't do experiments, only make
observations, the culture is:
Instrumentalist
Jan 27, 2006
Observer
Analyst
Pure Theorist
Astro 100 Lecture 5
5
Example: Greek's size and shape of Earth
• The Greeks already had a sufficiently scientific outlook and
enough data (purely visual!) to estimate the sizes and
distances of the Earth, Moon, and Sun based on hypothesis
that Earth and Moon are spherical
• Eratosthenes (-200 BC) observes: Vertical object casts
no shadow in one location at noon on a certain day, while
shadow is never shorter than 7 deg at the same time 5000
"stades" north
– vertical not same direction in different places (Earth
curved)
Jan 27, 2006
Astro 100 Lecture 5
6
3
Size of Earth
• If Earth spherical, it is 5000 stades x 360 deg /7
deg in circumference
– This is close to correct answer if "stade" – 1/6 km:
Earth circumference = 250,000 stades = 40,000 km
Earth diameter = circumference/ pi = 13000 km
• Ultimate verification: circumnavigation of Earth
So, let’s apply this method to the motions of the
planets:
Jan 27, 2006
Astro 100 Lecture 5
7
Geocentric Model of Solar System
• (most elaborate: Ptolemy, 125 AD)
– Moon and Sun motion consistent with real (almost
uniform) circular motion around stationary Earth.
– So associate Sun, Moon, and planets with spheres in
uniform rotation with Earth at center.
– Nonuniform apparent motion is allowed by attaching
planets to little uniformly rotating spheres (epicycles)
whose centers are attached to object's main sphere.
Spheres do not overlap. Except for having Moon closer than
Sun (to get solar eclipses), the size of each sphere is
arbitrary. Can be made as exact as you like by adding
epicycles to epicycles. Basically, Real = Apparent
Jan 27, 2006
Astro 100 Lecture 5
8
4
Jupiter & Saturn Movie
W
Jan 27, 2006
E
Astro 100 Lecture 5
9
Eratosthenes Observation
Figure 1.19, p41, Arny
Jan 27, 2006
Astro 100 Lecture 5
10
5
Geocentric Model
Figure 1.23, p45, Arny
Jan 27, 2006
Astro 100 Lecture 5
11
Geocentric Epicycles
Figure 1.24, p45, Arny
Jan 27, 2006
Astro 100 Lecture 5
12
6