Reminders
• Homework 1 (Introduction to Mastering
Astronomy) is due TODAY at 5 pm.
• Only 8 people have registered for Mastering
Astronomy. All information needed is on class
website:
http://www.ifa.hawaii.edu/users/clhung/Astro
110.html
• Homework 2 (Scales in Astronomy) is due
Tuesday at 5 pm.
New Discoveries: Higgs Boson!
• The Large Hadron Collider (LHC) is
the world’s largest and highestenergy particle accelerator
• Located near Geneva, Switzerland
• Running since 2010
Main goal: Search for the Higgs
Boson!
But, other discoveries are sure
to be made.
Video link at: http://www.phdcomics.com/comics.php?f=1489
July 4, 2012
What does it mean?
• Confirms the current
theoretical model of physics
• Our predictions were right!
• Need to do more tests to
determine that it really is the
Higgs Boson.
• Next up: Search for more
particles!
Planetary Motions
Geocentric Models of the Solar System
• “Geo” = Earth
• Primary model of solar
system from Ancient
Greeks (like Aristotle)
until 1600 AD
• Explains rise and setting
of sun, constellations,
and some planets
• BUT, could not explain
retrograde motion of
Mars, Jupiter & Saturn.
Retrograde Motion
Ptolemaic Model
Heliocentric Model
• Nicolaus Copernicus
developed the first
heliocentric (sun centered)
model in 1543.
• Explains general motion of
planets (including
retrograde motion), rising
& setting sun
• Problems – planets orbited
in circles with uniform
speed - wasn’t actually any
more accurate than
Ptolemaic system.
Kepler’s Theory of the Solar System
• In 1605 AD, Johannes Kepler
perfected the heliocentric
model by introducing elliptical
orbits.
• Very accurately predicts rising
& setting sun, moon, and
motion of planets & stars.
• Kepler used the orbit of Mars
(measured by his boss Tycho
Brahe)
– He hit upon the idea of an
ellipse after 40 (!) failed
attempts to calculate the orbit
of Mars.
What is an ellipse?
An ellipse looks like an elongated circle.
Eccentricity = Amount
of flattening
Class Action!
Eccentricity, e
•how squashed or out
of round the ellipse is
•a number ranging from
0 for a circle to 1 for a
straight line
e = 0.02
e = 0.7
e = 0.09
Kepler’s 1st Law
The planets, including Earth, revolve around the sun in elliptical
orbits. The sun is at one focus of the ellipse, the other is empty.
What is the shape of Earth’s orbit
around the Sun?
Earth, e = 0.016
Kepler’s 2nd Law
The line joining a planet to the Sun sweeps out equal areas in equal times as the
planet travels around the ellipse.
It takes as
much time
to go from A
to B as from
C to D
Planets
move faster
closer to the
sun
Speed
Note: If you drive at higher
speeds, you will cover a larger
distance in the same amount of
time.
OR: If you drive at higher speeds, you
will cover the same distance in less
time.
Class Action!
If you cover 100 miles in 7 hours, then your
speed would be
(a) Greater than 11 mph
(b) Less than 11 mph
(c) Equal to 11 mph
Kepler’s 2nd Law
The line joining a planet to the Sun sweeps out equal areas in equal times as the
planet travels around the ellipse.
Class Action!
Class Action!
Class Action!
Lecture Tutorial
• Break up into groups of 2-3
– NO MORE THAN 3
• In your group, work through the following:
– Kepler’s 2nd Law (pages 21-24)
– Discuss the answers – don’t be silent!
• I will be roaming around if you need help…
• If your group finishes, check your answers
with another group & begin Newton’s Law &
Gravity (pages 29-31)
Class Action!
Kepler’s second law says “a line joining a planet and the Sun
sweeps out equal areas in equal amounts of time.” Which of
the following statements means nearly the same thing?
A) Planets move fastest when they are moving toward the Sun.
B) Planets move equal distances throughout their orbit of the Sun.
C) Planets move slowest when they are moving away from the Sun.
D) Planets travel farther in a given time when they are closer to the
Sun.
E) Planets move the same speed at all points during their orbit of
the Sun.
Summary
Kepler’s 1st Law:
The orbits of planets are ellipses with the sun at one focus
Kepler’s 2nd Law:
A line drawn from a planet to the sun sweeps out equal areas in equal
intervals of time.
A planet must move rapidly when it is close to the sun and more slowly
when it is far from the sun.