Orbits and Planetary Motion: Tycho Brahe and Johannes Kepler

Vocabulary flashcards focusing on the key astronomical figures, geometric properties of orbits, and Kepler's Three Laws of Planetary Motion based on the lecture text.

Tycho Brahe

A pre-telescopic Danish astronomer ($1546\text{--}1601$) born to nobility who made continuous, precise records of the positions of the Sun, Moon, and planets for almost $20\,\text{years}$ from his observatory on Hven.

Johannes Kepler

A German mathematician and astronomer ($1571\text{--}1630$) who served as an assistant to Tycho Brahe in Prague and analyzed Brahe's data to discover the three fundamental laws of planetary motion.

Hven

The North Sea island where Tycho Brahe established an astronomical observatory at age $30$ under the patronage of Danish King Frederick II.

Orbit

The path of an object through space.

Conic Sections

A family of curves formed by the intersection of a plane with a cone, consisting of the circle, ellipse, parabola, and hyperbola.

Ellipse

A closed curve forming a somewhat flattened circle, where the sum of the distances from two special fixed points inside (foci) to any point on the curve is always constant.

Foci

The two special points inside an ellipse (singular: focus) such that the sum of the distances from any point on the ellipse to both points is constant.

Major Axis

The widest diameter of an ellipse, denoted as $2a$.

Semimajor Axis

Half the major axis of an ellipse ($a$), representing the distance from the center to one end, which specifies the size of the ellipse and equals a planet's average distance from the Sun.

Eccentricity

The ratio of the distance between the two foci of an ellipse to the length of its major axis, measuring shape elongation on a scale from $0.0$ (a circle) to a maximum of $1.0$ (a flat line).

Kepler's First Law

The principle stating that the orbits of all planets are ellipses with the Sun located at one focus.

Kepler's Second Law

The Law of Equal Areas, which states that an imaginary line connecting a planet to the Sun sweeps out equal areas in equal intervals of time ($t$), causing the planet's orbital speed to increase when closer to the Sun and decrease when farther away.

Kepler's Third Law

The mathematical relationship stating that a planet's orbital period squared ($P^2$) is proportional to the semimajor axis of its orbit cubed ($a^3$), expressed as $P^2 = a^3$ when period $P$ is in Earth years and semimajor axis $a$ is in astronomical units.

Orbital Period ($P$)

The time it takes for a planet or other object to travel once completely around the Sun.

Astronomical Unit (AU)

A unit of distance equal to the average distance between Earth and the Sun, approximately equal to $1.5 \times 10^8\,\text{kilometers}$.