Transcript PPT

Planetary Orbits: Kepler’s Laws
PTYS/ASTR 206
Kepler’s Laws / Gravity
1/18/07
Announcements
• The correct link for the course webpage
http://www.lpl.arizona.edu/undergrad/classes/spring2007/Giacalone_206-2
• The first homework due Jan 25 (available for download on website).
• Starry Night Backyard software program – blue CD that comes with
textbook
• Preceptors
– Please fill out a preceptor application.
– Please also give me your schedule on the back of the form
• Mission update volunteers?
• LPL Public Lecture Series next Tuesday
PTYS/ASTR 206
Kepler’s Laws / Gravity
1/18/07
Today’s Topics
• Finish discussion on Copernican revolution
– A long-standing Earth-centered view of the solar
system is turned on its head with the invention of the
telescope
– Phases of Venus
• The modern view of the solar system and the
epiphany that gravity is important!
– Kepler’s revision to the system devised by Copernicus
• Kepler’s Laws
– Galileo’s experiments on gravity
– Newton’s law of universal gravitation
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The Ptolemaic
System
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Nicholas Copernicus
• 1473-1543, Polish
• Re-proposed heliocentric
theory
• Put the Sun at the center, but
still believed the orbits of the
planets were circles +
epicycles
• He felt that this was a more
natural explanation of the
solar system
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Tycho Brahe
• 1546-1601, Danish
• Nose cut off in duel by a fellow student
• Observed a supernova, and periodic
comets
– Proof that the stars and planets are not
constant, as the ancient astronomers
believed
• Best pre-telescope observer
– Given island of Hven to build an
observatory
– Best, most observations
– Still no parallax
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Galileo Galilei
• 1564-1642, Italian
• Used telescope
– Jupiter’s moons
– Lunar mountains, sunspots
– Phases of Venus
• Experiments on motion
– Including attempts to measure
the speed of light
– Famous gravity experiment
using the leaning tower of Pisa
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• Galileo also discovered
four moons, now called
the Galilean satellites,
orbiting Jupiter
• The positions of these
moons change rapidly
and can be seen during
the course of one
evening
– Especially Io and
Europa, the two closest
to Jupiter
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Jupiter and 3 of the Galilean
satelites (only Callisto is
missing from this amateur
photograph)
This is what Jupiter looks
like through a standard
amateur telescope. Galileo
probably saw it similarly
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Phases of Venus
Galileo’s observations of Venus’s gibbous (“full-ish”)
phase definitively ruled out Ptolemy’s geocentric
model !
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The phases of
Venus in the
Ptolemaic Model
only a crescent
Venus is possible
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The Phases of Venus in Heliocentric
Model – including the gibbous phase of
Venus, as observed
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Conclusion
• The 1000-year-old paradigm of a
Earth-centered solar system, was
proved incorrect as the result of
simple observations made by a new
technology -- the telescope.
• New technologies often lead to rewriting of textbooks.
• Current “new technologies” include
– Space age
– Super computers
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Johannes Kepler proposed elliptical paths
for the planets about the Sun
•
Using data collected by
Tycho Brahe, Kepler
deduced three laws of
planetary motion:
1. the orbits are ellipses
2. a planet’s speed
varies as it moves
around its elliptical
orbit
3. the orbital period of a
planet is related to the
size of its orbit
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Kepler’s First Law
• The planets move about the sun in elliptical orbits with the
Sun at one foci of the ellipse
Aphelion
Perihelion
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Semi-major axis
The Semi-major axis
is ½ the “long” width
of the ellipse
Planetary fact sheets
usually quote the
semi-major axis of the
orbit
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Ellipses
• Eccentricity – a measure of how oblong an ellipse is.
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• Here are two elliptical orbits with the Sun at one
focus. The orbits of most of the planets are nearly
circles. But other objects, especially comets, have
orbits with high eccentricities.
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Kepler’s Second Law
• The Planet sweeps
out equal areas of
the elliptical orbit, in
equal time intervals
• The planet moves
fastest when it is
closest to the Sun
and slowest when it
is farthest away
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Kepler’s Third Law
The square of a planet’s period (P) is proportional
to the cube of its semi-major axis (a).
or
The farther a planet is from the sun, the longer it
takes to go around the sun
P = the period (in years)
a = semi-major axis (in AU)
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A warning about this formula !
It only applies to planetary motion about the
Sun! Also, the units must be P in years, and a in
AU. Otherwise you will NOT get the correct
result
P = the period (in years)
a = semi-major axis (in AU)
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• Galileo discovered that the
higher an object is dropped, the
greater its speed when it
reaches the ground
• All falling objects near the
surface of the Earth have the
same acceleration (9.8 m/s2)
Acceleration
Due to Gravity
• The acceleration of gravity on
the surface of other solar-system
bodies depends on their mass
and radius
– Mars and the Moon have a smaller
acceleration of gravity
– Saturn is about the same as Earth
– Jupiter is more than Earth
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Objects fall at the same rate – independent
of mass !
• Galileo’s famous experiment
– Showed that objects of different
masses dropped from the same height
arrive to Earth at the SAME time
– Disproved Aristotle’s “theory”
– Did he really do it ?
• The experiment was also
performed by an astronaut on the
moon?
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Astronaut Alan Bean
Did Galileo’s experiment on the Moon
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Isaac Newton (1642 – 1727)
• Developed the Laws of
Motion
• Discovered the law of
gravity
• Used physics to derive
Kepler’s 3rd Law
– (see page 81 and box 4-4
of the textbook)
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Newton’s Law of Universal Gravitation
• Gravitation force between two bodies
• G = Gravitational Constant = 6.67x10-11 N • m2 / kg2
• m1 and m2 = the masses of the two objects
• r
= the distance between the two (more precisely,
the distance between the two centers)
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Galilean Satellites and Kepler’s Laws
• Newton derived Kepler’s third law using physics
and his universal law of gravitation. His form of
Kepler’s 3rd law for the orbits of the planets
about the Sun is:
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Today’s in-class activity
• You may work together in small (2-3 people) groups
– You must hand in your own work
• Please remain in your seats until we collect all of the
finished activities
• After the activity is turned in, we will toss a coin to decide
if it will be graded
– Heads – it is graded
– Tails – it will not be graded
• If time permits, we will go over the activity afterwards
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Reading for next class
• Chapter 4
– Box 4-2 (p. 67)
– Section 4-6, 4-7, 4-8 (pp. 76-85)
• Chapter 2
– Section 2-3, 2-4, 2-5 (pp. 22-31)
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Kepler’s Laws / Gravity
1/18/07