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Kepler’s Three Laws of Planetary Motion
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From Celestial North, this is IT’S OVER YOUR HEAD, a look at what’s up in
the sky over Puget Sound.
In the 16th century, many important discoveries were made about the
Universe, and particularly about our solar system. Two astronomers of the time,
Danish nobleman Tycho Brahe and German mathematician Johannes Kepler,
pooled their talents to attempt to unravel the mystery of exactly how the planets
moved. The prevailing belief at the time was that they moved in perfect circles
with the Sun at the center, but this mathematical explanation did not match what
was seen in the sky.
Kepler studied how the planets moved and ultimately
formulated three laws to describe their motions.
referred to in planetary discussions.
You may have heard them
But what exactly are Kepler's Laws of
Planetary Motion? In this week's show, we will discuss these elegant tools for
understanding the heavens.
When Kepler and Brahe were working on solving the problem of the
planets' orbital shapes, Brahe was slightly mistrusting of Kepler. He felt that the
young German might actually surpass him as the premier astronomer of the time.
Therefore, he only permitted Kepler to see portions of his vast collection of data.
In the ultimate irony, Kepler used what he was given and still eclipsed Brahe,
brilliantly devising his laws of planetary motion.
Copyright © 2006 Celestial North, Inc. All rights reserved.
060809.doc
Kepler’s Three Laws of Planetary Motion
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The first of Kepler's laws is fairly simple, although it was very difficult to
figure out and was actually documented second.
The first law is:
A planet
moves around the Sun in an ellipse with the sun at one focus. While a circle has
only one central point, an ellipse has two foci. In a planetary orbit, the Sun is
located at one of these foci. Kepler figured this out by using observations of the
orbit of Mars. Mars, he noticed, does not quite move in a circle but rather in a
more elongated, eccentric path. In fact, the orbit of Mars is more elongated than
that of most other planets in our solar system. When he applied the equation for
an ellipse, it fit the data perfectly. The other planets in the solar system obey the
ellipse pattern also, and so does every other body in the cosmos that orbits
another.
Kepler didn't simply discover something that worked for Mars; he
discovered an equation that worked for the entire Universe. His insight, using
geometry pioneered by the Ancient Greeks, is often mentioned as an example of
the power of applying pure mathematics to real world situations to help us
understand what's going on.
Copyright © 2006 Celestial North, Inc. All rights reserved.
060809.doc
Kepler’s Three Laws of Planetary Motion
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Kepler's second law of motion was actually figured out first, based on his
observation that planets orbit more quickly when they are near the Sun, and
move more slowly when they are farther away. Kepler's Second Law is: If a line
is drawn from a planet to the Sun, this line sweeps out equal areas in equal
times. Imagine this—with the Sun at one focus of a planet's planar elliptical orbit,
the point at which the planet is closest to the Sun is called perihelion, and the
point at which it is farthest away is called aphelion. When a planet orbits for, say,
ten days around the Sun near its perihelion, it will sweep out the same area in
space as if it were moving for ten days through its distant aphelion point. This is
because as the planet gets closer to the Sun, the Sun's gravity pulls on it harder,
causing it to move faster. Far away from the Sun, at aphelion, the planet is still
pulled by gravity, but not as strongly. It slows down, but the area it sweeps out is
quite large due to the great distance. In the end, the two areas, one short and
wide, the other long and skinny, are equal to one another for the same time
frame. As with Kepler's first law, this elegant truth holds not just for planets of
our solar system, but also for all other celestial bodies.
Copyright © 2006 Celestial North, Inc. All rights reserved.
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Kepler’s Three Laws of Planetary Motion
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Kepler's third law is a little more complicated than the first two, but it is the
one that is used most for calculations. Kepler's third law says that the square of
a planet’s orbital period is proportional to the cube of the semimajor axis of its
orbit. What? Well, the semimajor axis—sometimes called the orbital "radius"—is
one half the length of the longest dimension of the ellipse. This distance, if
cubed (that is, multiplied by itself 3 times), is proportional to the square of a
planet's orbital period. This is a useful law to know, because in applying it, we
see that the "radius" of a planet's orbit can be calculated from the orbital period,
and vice versa. This can be especially helpful when trying to find the orbital
period of planets around other stars. If we know the radius, we can find out.
You can learn more about Kepler's Laws of Planetary Motion on the web.
We’re on the web at CelestialNorth.org. Until next time, this is ________
and _________, with a reminder that the night is large and full of wonders.
Copyright © 2006 Celestial North, Inc. All rights reserved.
060809.doc
Kepler’s Three Laws of Planetary Motion
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REFERENCES:
http://csep10.phys.utk.edu/astr161/lect/history/kepler.html
1.
2.
http://observe.arc.nasa.gov/nasa/education/reference/orbits/orbit
3.
_sim.html
http://mathpages.com/rr/s8-01/8-01.htm
Copyright © 2006 Celestial North, Inc. All rights reserved.