November 9, 2019 0

Kepler’s First Law of Motion – Elliptical Orbits (Astronomy)


In 1609, Johannes Kepler published Astronomia
Nova, a book containing ten years of his efforts to understand the orbit of the planet Mars.
He was using state-of-the-art astronomical observations from his mentor and employer,
Tycho Brahe, who was famous for generating an enormous amount of high-quality data, and
he needed to find the best explanation for the motions of Mars – a very tricky problem! There were three models of the solar system
out there at the time, but none of them worked very well for Mars. First, the Ptolemaic system
put the Earth at the center, with the Sun and planets orbiting it in perfect circles.
There was also Copernicus’s heliocentric model, which set the Earth among the planets,
revolving around the Sun. And finally, Tycho had his own system to propose, which combined
aspects of both: he put the Earth at the center with the Sun and moon orbiting it, but let
the other planets orbit the Sun. All three systems relied upon circular orbits,
because the circle was accepted as an ideal shape. Copernicus, Tycho, and Galileo all
believed that planets should travel along circular paths, but the data just didn’t
fit. Instead, Kepler found that another shape,
the ellipse, works a lot better. An ellipse is sort of like a flattened circle, and it
has some special properties. You can draw one by taking a loose string… …attaching both ends to the paper, and using
a pencil to keep the string taught while moving all the way around the perimeter… The result
is an ellipse! The length of the string never changed, meaning that the sum of the distances
between each endpoint, or focus, and any point on the ellipse is constant. In Astronomia Nova, Kepler states that Mars
travels in an elliptical orbit around the Sun, which is at one of the foci of the orbit.
Later on, he expanded this first law to include all of the planets and demonstrated that this
shape fit the available observations. The further apart the two foci are, the longer
and skinnier the ellipse, and this “skinniness” parameter is called “eccentricity.” Comets
can have very eccentric orbits, coming in quite close to the Sun before traveling back
to the outer reaches of the solar system. On the other hand, In a perfect circle, the
two foci would lie right on top of each other right at the center. The orbits of the planets
in our solar system are not very eccentric at all. They’re really very close to circular,
which is partly why perfectly round orbits seemed like a natural thing to expect in the
first place. It wasn’t easy to abandon a central idea
like that, but with his first law of planetary motion, Kepler rejected circular orbits and
showed that an ellipse could better explain the observed motions of Mars. Generalized
to all planets, it states that the orbit of a planet follows an ellipse with the Sun at
one focus.

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