Page 18 - GALIET PHYSICS BLOSSOMS II+

orbital path. From these, many other figures can be derived, such as the two most significant ones:
- the planet’s perihelion (its closest point to the sun), and
- the planet’s aphelion (its furthest point from the sun).
From these definitions, it follows that if the planet’s orbit has a semi-major axis “a” and eccentricity “e”, the planet’s
perihelion is at a distance a (1 - e) from the Sun, while its aphelion is at a (1 + e), as shown below:
Our solar system’s orbits are so eccentrically small that we cannot distinguish them from circles, which made Ptolemy and Copernicus’ model feasible. When Kepler swaps circular orbits with elliptical ones, he does away with the Grecian fascination over the circle’s perfection (Parmenides, Plato, Aristotle) and with Galileo’s theory. Galileo, too, had defended circular planetary motion rejecting elliptical motion.
Kepler’s 2nd Law9
Kepler’s second law deals with the speed at which a planet traverses different parts of its orbit:
The radius vector of the orbit (connecting the sun to the planet) sweeps out equal areas of the ellipse in equal times.
As seen below, while orbiting the sun, a planet traces the arcs A, B, and C in equal times.
However, in the same amount of time, the planet travels a greater distance along arc C than along arcs A or B, showing variation in speed given that the time is the same, and the distance is different. When a planet is close to
9 Drawing and study summary of Kepler’s Second Law from class notes and slides and from Chaisson, McMillan. Astronomy Today. 44-45. •18•