Chapter 3 Analyzing Scales and Motions of the Universe

Eratosthenes and Aristarchus Using simple tools and basic geometry to measure: the size of the Earth Moon and Sun and the distances to the Moon and Sun

The Greek Geocentric Model An Earth-centered, or geocentric, model of the universe

The Problem of Retrograde Motion The “merry-go-round” model doesn’t explain retrograde motion―periods when the planets appear to move backwards in the constellations.

The Ptolemaic System To explain retrograde motion, Ptolemy created a complicated system of spheres on spheres.

The Heliocentric Model and Retrograde Motion

Nicolaus Copernicus Introduced the heliocentric model of the solar system and deduced that Mercury and Venus had interior orbits and Mars, Jupiter, and Saturn had exterior orbits compared to Earth.

Copernicus and the Orbits Elongation: the angle between the Sun and a planet, as viewed from Earth. Conjunction: a planet and the Sun lining up, as viewed from the Earth. Elongation can be used to determine the size of the orbit.

Galileo Galilei Used the newly invented telescope to observe the heavens. He discovered: Mountains on the Moon Sunspots on the Sun Rings around Saturn Phases of Venus Moons in orbit around Jupiter That the Milky Way was innumerable stars

The Phases of Venus Galileo’s discoveries of moons orbiting Jupiter and phases of Venus strongly supported a heliocentric model.

Phases of Venus could not occur in the Ptolemaic system.

The Moons of Jupiter Observations of Jupiter and its moons showed that there are objects that do not orbit Earth.

Elliptical Orbits and Kepler’s First Law The orbit of a planet about the Sun is an ellipse with the Sun at one focus. Mercury has the most eccentric orbit at 0.207.

Orbital Speeds and Kepler’s Second Law A line joining a planet and the Sun sweeps out equal areas in equal intervals of time. A planet moves fastest when closest to the Sun.

Orbital Periods and Kepler’s Third Law The greater the distance between the Sun and planet, the slower the planet travels. P2 = a3 P: planet’s period, in years a: planet’s semimajor axis, in AU

Newton’s Laws An object remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force. F = ma Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

Gravity Explains Kepler’s Laws

Newton’s Law of Universal Gravitation F : gravitational force between two objects m1 : mass of first object m2 : mass of second object r : distance between objects G : universal constant of gravitation

An Explanation of Orbits A: A ball dropped from a great height falls straight down. B & C: A ball thrown with some horizontal speed. E: A ball thrown with the “right” speed orbits in a perfect circle. D & F: Balls thrown with speed a little too slow and a little too fast orbit in an ellipse.