History of Earth's Shape

• Oblate describes the shape of the Earth.
• Solstice refers to the highest or lowest point of the sky at noon.
• An eclipse happens when a celestial body passes between two others, blocking light.
• Heliocentrism: An astronomical model where celestial bodies revolve around the Sun.
• Geocentrism: A theory where Earth is the center of the universe.
• Around 500 BC, there was a belief the Earth was round and not flat.
• In 430 BC, Anaxagoras supported Pythagoras' proposal of observing the Earth during eclipses.
• In 340 BC, Aristotle theorized the Earth was spherical.
• The North Star has a fixed position in the sky.
• Greeks traveled to places nearer the equator using the North Star.
• The shape of the Moon is evidence that the Sun is spherical.
• Disappearing ships are used as an argument that the Earth is flat.
• Anaxagoras explained what causes the phases of the Moon.
• Eudoxus believed the Sun and Moon were attached to spheres.
• Aristotle was a student of Plato and thought that Earth was spherical.
• Aristarchus was the first Greek to profess the heliocentric view.
• Eratosthenes was the first to successfully attempt to determine the size of the Earth.
• Hipparchus was one of the greatest Greek astronomers.
• Claudius Ptolemy theorized that the Earth was the center of the universe.
• The Ptolemaic model describes the Sun, Moon, and other planets in circular orbits around the Earth.
• Astronomy is the science of the universe outside our planet.
• Moons are natural objects which orbit larger objects.
• An eclipse occurs when a celestial body, like a moon or planet, moves into the shadow of another celestial body.
• A solar eclipse occurs when the Moon passes between the Sun and Earth, blocking light from the Sun fully or partially.
• Lunar phase refers to the cyclically recurring apparent forms of the Moon.
• A gibbous moon is a form of the Moon that is more than half full and appears swollen on one side.
• The crescent moon is a figure of the Moon that appears curved, with pointed ends.
• Waxing describes the Moon when the illuminated portion is increasing.
• Waning describes the Moon when the illuminated portion is decreasing.
• A solar planet is a large, round object in a solar system that orbits the sun and has cleared out most other objects in its orbit.
• The solar system includes the Sun, planets, comets, and other objects that revolve around it.

Astronomical Units & Eccentricity

• An astronomical unit (AU) is 1.5 x 10^8 kilometers or 1.5 x 10^11 meters.
• Eccentricity is the ratio of the distance between foci to the major axis of an ellipse.
• Foci are points inside an ellipse where the sum of distances from any point on the ellipse is constant.

Kepler's Laws

• First Law: Each planet moves around the Sun in an elliptical orbit with the Sun at one focus.
• Second Law: A line joining a planet and the Sun sweeps equal areas during equal intervals of time.
• Third Law: The square of a planet's orbital period is directly proportional to the cube of the semi-major axis of its orbit.

Tycho Brahe

• Tycho Brahe was a Danish astronomer and nobleman.
• He made accurate observations of the movements of celestial bodies.
• King Frederick II of Denmark built an observatory for Brahe.
• By 1576, Brahe had an established observatory.
• Brahe invented different astronomical instruments with the help of his assistant.
• He made extensive studies of the solar system.
• Brahe was able to determine the position of 777 fixed stars accurately.

Johannes Kepler

• King Frederick II died.
• Kepler's successor did not fully support Brahe's work.
• Kepler moved to Prague in 1599.
• Emperor Rudolf II supported Kepler and he became an imperial mathematician.
• Emperor Rudolf II recommended Johannes' work for him as an assistant.
• Kepler was born into a German family and studied as a scholar at the University of Tubingen in 1589.

Brahe/Kepler Collaboration

• Brahe and Kepler had an unsteady working relationship.
• Kepler was an assistant to Brahe.
• Brahe mistrusted Kepler, shadowed by the fear of losing his work.
• Brahe assigned Kepler the task of interpreting observations of Mars, whose movement did not match Brahe's calculations.
• Kepler was tasked to figure out the path Mars followed as it revolved around the Sun.
• Brahe gave this task to Kepler to keep him occupied, leaving Brahe to develop his laws of planetary motion.