Transcript Models of the Solar System - Londonderry School District

Historical Models of our Solar System
and
Kepler’s Laws of Planetary Motion
Geocentric Model
• Earth is center of our
Solar System
• Aristotle- Over 2000
years ago,
• Unexplained on how
planets appear to move
backwards
• Ptolemy- Planets move in
small circles or epicycles
Heliocentric Model
• Sun is center of our
Solar System
• Copernicus- Over 450
years ago (1543 ad)
• First to suggest
heliocentric theory
and vaguely mapped
out the planets
orbiting the sun in a
circular orbit.
Galileo
• Supporter of
Copernicus’s
Heliocentric theory
• House arrest
• Observed moons
orbiting Jupiter and
theorized objects can
revolve around other
planets not just Earth
Solar System precisely measured
• Tycho Brahe- studied
Solar System and
made very accurate
recordings of his
observations
• Tycho’s assistant,
Kepler, used
information for the
details of orbits
Kepler’s Laws of Planetary Motion
1st Law - Law of Ellipses
Each planet orbits the sun in a path called an ellipse or elongated
circle
An ellipse is a closed curve whose path is determined by 2 points
or foci within the ellipse
Focus 1 is the Sun and Focus 2 is a mathematical imaginary point
Semi-major axis = ½ major axis or average distance from sun (AU)
Eccentricity
• Degree of elongation
or shape of planet’s
orbit
• Ratio between the
foci and length of
major axis
• Circular = 0
• Very elongated = 1
2nd Law – Law of Equal Areas
• An imaginary line between the Sun and a planet
sweeps out equal areas in equal times as the
planet travels around the ellipse.
• Perihelion (P) – a planet is closer to the sun
• Aphelion (A) – a planet is further from the sun
3rd Law – Law of Periods
• Mathematical relationship P2 = a3
• a= semi-major axis (planets average distance
from Sun measured in AU’s)
• p= planet’s orbital period (time)
Newton
• Used Kepler’s Laws of
planetary motion and
published Principia for
short. In this publication,
considered to be the
greatest piece of scientific
literature ever written.
•
Contains Newton’s laws
of motion including
universal gravitation.
Einstein (1879-1955)
• Changed Newton’s
gravitational theory based
on findings of Mercury’s
orbit.
• Developed Theory of
Relativity. It completely
changed the way we
study gravity and even
changed our
understanding of the
universe.
Kepler’s Laws Simulations
Click
http://www.physics.sjsu.edu/tomley/kepler.html
Law of Ellipses– Change the size of the ellipse
with the scrollbar
Describe the eccentricity (number and shape)
when you move scrollbar to the right.
______________________________________
______________________________________
Describe the eccentricity (number and shape)
when you move scrollbar to the left.
________________________________________
______________________________________
Law of Equal Areas –What happens to the
speed and distance for the planet?
Set eccentricity to be between .5 and .6
Describe the speed as the planet orbits the sun
at eccentricity between .5 & .6.
____________________________________
Why does speed change when it approaches the
sun? __________________________
__________________________________
Describe the distance a planet covers when
it orbits the sun at A) .0P to .1P and
compare it to B) .4P to .5P.
__________________________________
Why is the distance different?
___________________________________
Why is Kepler’s 2nd law called Equal Areas
in Equal Time?
___________________________________
__________________________________
Law of Equal Periods –
Click on last option “different a, same e”
(AU’s, eccentricity) Move the scrollbar to
the right for two different a’s or AU’s
Hint: 3.5 AU and 1 AU
The larger a planet’s AU amount the
______________________ they are to the
Sun and the __________________ their
period of revolution (orbit) around the Sun.
Bibliography
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http://www.astro.umass.edu/~myun/teaching/a100/images/geocentric.jpg
http://www.physics.hku.hk/~nature/CD/regular_e/lectures/images/chap04/heliocentric.jpg
http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/galileo5.jpg
http://galileo.rice.edu/sci/brahe.html
http://www.asu.cas.cz/~had/tycho.jpg
http://cseligman.com/text/history/ellipse2.jpg
http://www.windows.ucar.edu/the_universe/uts/kepler3_small.gif
http://library.thinkquest.org/27585/frameset_intro.html
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/imgrel/merc.gif
http://zebu.uoregon.edu/~soper/Orbits/eccentricity.gif
http://www.physics.hku.hk/~nature/CD/regular_e/lectures/images/chap04/geocentric.jpg
http://outreach.atnf.csiro.au/education/senior/cosmicengine/images/cosmoimg/keplerellipse.gif