Explained In 5 Questions: Kepler’s Law of Planetary Motion | Encyclopaedia Britannica


SPEAKER 1: Kepler’s first law
of planetary motion states that all planets move about the
Sun in elliptical orbits having the Sun as one of the foca. But what does that actually mean? Well an ellipse is a shape that
resembles a kind of squashed circle. Its foci are two points within the
ellipse that describe its shape. For any point on the ellipse, the sum of that
points distances to the two foci is the same. The further apart the foci are,
the more squashed the ellipse is. If the foci become so close that they are
only one focus, you just have a circle. In reality orbits are never perfectly circular. But we do know that the Sun will always be one
of the foci of the elliptical path of an orbit. Knowing that the Sun is a
focus of the planet’s orbit can tell us a lot about the shape of that orbit. Kepler tells us that orbits are ellipses, which
are like circles with some added eccentricity. But what is eccentricity? How do you figure it out? Eccentricity measures how flattened
an ellipse is compared to a circle. We calculate it using this equation. So what does that mean? Well, a is the semi-major axis, or half the
distance along the long axis of the ellipse. And b is the semi-minor axis, or half the
distance along the short axis of the ellipse. The equation is a way to compare these axes
to describe how squashed the ellipse is. An ellipse with zero eccentricity
would just be a regular old circle. As eccentricity increases, the
ellipse gets flatter and flatter until it just looks like a line. An orbit with an eccentricity greater than
one is no longer an ellipse but a parabola if e is equal to one a hyperbola
it e is greater than one. For example, the giveaway that
Oumuamua, the first interstellar comet, was not from around here was
that its eccentricity was 1.2. The eccentricity of Earth’s
orbit is only 0.0167. Kepler’s third law states that the squares
of the sidereal periods of revolution of the planets are directly proportional to
the cubes of their mean distances from the Sun. Which what does that mean? Basically it’s saying that how long a planet
takes to go around the Sun, its period, is related to the mean of
its distance from the Sun. That is the square of the
period divided by the cube of the mean distance is equal to a constant. For every planet, no matter its period or
distance, that constant is the same number. Kepler’s second law tells us that a planet moves
more slowly when it’s further from the Sun. But why should that be? Well, as a planet orbits the Sun
it may not keep a constant speed but it does maintain its angular momentum. Angular momentum is equal to the mass of
the planet times the distance of the planet to the Sun times the velocity of the planet. Since the angular momentum doesn’t
change, when the distance increases the velocity has to decrease. That means when the planet gets
further from the Sun it slows down. Kepler’s second law deals with the
speed of planets orbiting the Sun. So does it tell us at what point
the Earth is moving at top speed? The second law tells us that the Earth
moves fastest when it’s closest to the Sun, or at its perihelion. That happens in early January. At that point Earth is about
92 million miles from the Sun. Meanwhile it’s at its slowest in early July, at
its furthest point from the Sun, or aphelion. That greatest distance is
about 95 million miles. That difference of 3 million
miles might sound like a lot but Earth’s orbit is so vast that
it’s actually merely circular.

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