Key Ideas and Terms

3-1 Astronomers of antiquity used observation and reasoning to develop astonishing advances in the study of astronomy

• Ancient Greeks knew Earth was round because of Earth’s curved shadow on the Moon during a lunar eclipse.
• Eratosthenes estimated the size of Earth by comparing noontime shadow lengths at different locations on Earth.
• Aristarchus determined relative distances to the Sun and Moon by carefully measuring the speed of Earth’s shadow during an eclipse and the angle between the Sun and a first quarter moon.
• Powers of ten are used to express large and small numbers where 10³ is the same as 1000 and noted using the prefix kilo-.
• An astronomical unit is the average distance between Earth and the Sun.
• A light-year is the distance light travels in one year in empty space.
• A concept of Earth at the center of the universe with planets, the Sun, and stars orbiting around Earth is known as a geocentric model.
• Retrograde motion is the apparent westward movement of planets normally traveling from west to east against the apparently stationary background stars.
• Ptolemy imagined a universe where planets could change apparent direction of motion by moving in tiny circular orbits attached to larger and larger circular orbits.

3-2 Nicolaus Copernicus devised the first comprehensive Sun-centered model

• The idea that the most simple and most straightforward explanation of observations in nature is most likely to be correct is called Occam’s razor.
• Copernicus advocated a conception of the universe with our Sun at the center of the universe and Earth orbiting the Sun, just like the other planets, known as the heliocentric model.
• Viewed from Earth, greatest eastern elongation is the farthest a planet can be observed from the setting Sun.
• Viewed from Earth, greatest western elongation is the farthest a planet can be observed from the rising Sun.
• Planets are at inferior conjunction when they are between Earth and the Sun.
• A planet is at superior conjunction when the Sun is between Earth and the planet.
• Planets are at opposition when Earth is between the planet and the Sun.
• The length of time for a planet to orbit the Sun is known as its period.
• The synodic period is the time that elapses between two successive identical configurations as seen from Earth—from one opposition to the next, for example, or from one conjunction to the next.
• The sidereal period is the true orbital period of a planet, the time it takes the planet to complete one full orbit of the Sun relative to the very distant background stars.

3-3 Galileo’s discoveries of moons orbiting Jupiter and the phases of Venus strongly supported a heliocentric model

• Galileo used his telescope to observe moons orbiting Jupiter, demonstrating Earth was not the center of all orbits.
• Galileo’s telescope observations of the phases of Venus demonstrated Venus could not be orbiting Earth, but must be orbiting the Sun instead.

3-4 Johannes Kepler proposed that planets orbit the Sun in elliptical paths, moving fastest when closest to the Sun, with the closest planets moving at the highest speeds

• Kepler’s first law is that the orbit of a planet about the Sun is an ellipse with the Sun at one focus.
• Eccentricity is a measure of the relative roundness of an elliptical shape.
• The semimajor axis, a, of a planet’s orbit is the average distance between the planet and the Sun.
• The closest an orbiting planet gets to its central star is its perihelion distance, while the farthest an orbiting planet gets from its central star is its aphelion distance.
• Kepler’s second law is that a line joining a planet and the Sun sweeps out equal areas in equal intervals of time and is also known as the law of equal areas.
• Kepler’s third law says that the larger a planet’s orbit—that is, the larger the semimajor axis, or average distance from the planet to the Sun—the longer the sidereal period, which is the time it takes the planet to complete an orbit and is sometimes written as P² = a³.

3-5 Isaac Newton formulated three laws relating force and motion to describe fundamental properties of physical reality

• Newton’s first law of motion is that an object remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force.
• Newton’s second law of motion says that in order to give an object an acceleration (that is, to change its velocity), a net outside force must act on the object and is often written as F = ma.
• Newton’s third law of motion is the famous statement about action and reaction, which states whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

3-6 Newton’s description of gravity accounts for Kepler’s laws and explains the motions of the planets

• Newton’s law of universal gravitation is that any two objects attract each other with a force that is directly proportional to the mass of each object and inversely proportional to the square of the distance between them.
• Planets do not fall into the Sun during their orbits because they have a sufficiently high velocity moving them forward.