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INTRO TO ASTRO
Lesson 6
Kepler and the Laws of Planetary Motion
ANOTHER THOUGHT
EXPERIMENT
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Imagine you have made a discovery that
changes the scientific world view, but
goes against everything that has been
TRUE for 1400 years.
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Would you feel compelled to reveal it?
Despite repercussions? Even if it changed
the way YOU view the world?
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Kepler mastered, like the best scientists, the
most complicated technical issues,
especially in astronomy, but he always
emphasized his philosophical, even
theological, approach to the questions he
dealt with: God manifests himself not only
in the words of the Scriptures but also in the
wonderful arrangement of the universe and
in its conformity with the human intellect.
Thus, astronomy represents for Kepler, if
done philosophically, the best path to God
(see Hübner 1975; Methuen 1998 and 2009;
Jardine 2009).
JOHANNES KEPLER
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Worked as an assistant of Tycho Brahe
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Closely studied the orbit of Mars under Brahe
which lead to his formation of the laws of planetary
motion
Observed and documented supernova of 1604
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Meticulous observer and recorder of the cosmos,
in particular our solar system
KEPLER
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Kepler endorsed Copernican model of
solar system
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Copernican model still couldn’t accurately
predict period and speed of the planets
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Why?
Why would this matter?
ELLIPSES
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Properties of ellipses:
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Ellipses have two foci which determine its shape, the
further apart the foci, the flatter the ellipse
ELLIPSES
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The amount of "flattening" of the ellipse is termed the
eccentricity.
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Ellipses have eccentricities lying between zero and one
ELLIPSES
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The long axis of the ellipse is called the major axis, while the
short axis is called the minor axis (adjacent figure). Half of
the major axis is termed a semimajor axis.
DATA DRAMA
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After Brahe’s death, Kepler was able to obtain his data.
However, he did so by less than legal means, thwarting
Brahe’s family out of their inheritance
And it was fortunate for the development of modern astronomy
that he did!
Kepler was able to determine the orbits of each planet using
triangulation
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1ST LAW
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The orbits of the planets are ellipses, with the Sun at one
focus of the ellipse.
http://astro.unl.edu/classaction/animations/renaiss
ance/kepler.html
2ND LAW
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The line joining the planet to the Sun sweeps out equal areas
in equal times as the planet travels around the ellipse.
Hence, by Kepler's second law, the planet
moves fastest when it is near perihelion and
slowest when it is near aphelion.
3RD LAW
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Kepler's 3rd law is a mathematical formula. It
means that if you know the period of a planet's
orbit (P = how long it takes the planet to go
around the Sun), then you can determine that
planet's distance from the Sun (R = the
semimajor axis of the planet's orbit).
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It also tells us that planets that are far away
from the Sun have longer periods than those
close to the Sun. They move more slowly
around the Sun.
THIRD LAW EXPLAINED
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Kepler's Third Law implies that the period for a
planet to orbit the Sun increases rapidly with
the radius of its orbit. Thus, we find that
Mercury, the innermost planet, takes only 88
days to orbit the Sun but the outermost planet
(Pluto) requires 248 years to do the same.
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http://astro.unl.edu/classaction/animations/rena
issance/kepler.html
SAMPLE PROBLEMS
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Using years as our unit of time and AU as our unit of
distance:
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As an example of using Kepler's 3rd Law, let's calculate the
"radius" of the orbit of Mars (that is, the length of the
semimajor axis of the orbit) from the orbital period. The time
for Mars to orbit the Sun is observed to be 1.88 Earth years.
Thus, by Kepler's 3rd Law the length of the semimajor axis
for the Martian orbit is
3RD LAW SIGNIFICANCE
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If you knew the period of orbit of a planet
you could calculate it’s distance or
semimajor axis
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Vice Versa
YOU TRY
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An asteroid orbits the sun at a distance of 2.7 AU. What is its
orbital period?
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A dwarf planet discovered out beyond the orbit of Pluto is
known to have an orbital period of 619.36 years. What is its
average distance from the sun?
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Chiron is a dwarf planet that orbits the sun between Saturn
and Uranus, and has an average distance from the sun of 14
AU. What is its orbital period?