Title your notes: Models of the Solar System https://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=7783 Title your notes: Models of the Solar System 1

Models of the Solar System What is the Center of the Solar System? The early scientists, in their attempt to answer this fundamental question created various models of the solar system. Models, which placed Earth at the center, are called Earth-centered, or geocentric, models.

Models of the Solar System The Geocentric Model The early philosopher and astronomer believed that everything in the universe is “perfect”; and that the planets are perfect spheres circling in perfect circular orbits. They believed the Earth was the most important object in space and therefore assumed it to be the center of the universe. 3

Models of the Solar System The Geocentric Model Aristotle, a Greek philosopher reasoned that if Earth circled around the sun, then the relative positions of the stars would change as Earth moves. This apparent change in the position of an object when viewed from different angles or locations on Earth is known as parallax. What Aristotle did not take into account is the fact that stars are very far away. At such great distance parallax cannot be observed without a telescope. 4

What is Parallax? nearby star appears to move back and forth compared to more distant stars parallax depends on distance  use it to measure distance

Trigonometry Use basic trigonometric relations. Used by modern surveyors to measure great distances (also called surveyor's method). d : distance b : baseline p : angle b p d February 14, 2006 Astronomy 2010

Parallax  Distance measure angular shift p know baseline distance (1 AU) trigonometry  star distance d February 14, 2006 Astronomy 2010

Parsecs Distances to the stars in units of astronomical units are huge, a more convenient unit of distance called a parsec is used abbreviated “pc”. parsec = distance of a star that has a parallax of one arc second using a baseline of 1 astronomical unit. 1 parsec = 206,265 AU = 3.26LY. Nearest star (Alpha Centuri) is ~1.3 parsecs from the Sun.

The astronomical unit (AU) is roughly the distance from the Earth to the Sun. However, that distance varies as the Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, it is now defined as exactly 149,597,870,700 meters (about 150 million kilometers, or 93 million miles).

Models of the Solar System The Geocentric Model The geocentric model of the solar system became a very important part of ancient Greek Astronomy beginning in the sixth century B.C.E. The Greek philosopher Aristotle (384–322 B.C.E.) was among the first scholars to put forward an Earth-centered model of the Solar System. His model positioned the moon, sun, planets, and stars on a series of circles that moved around Earth. 10

Models of the Solar System The Geocentric Model Aristarchus, a Greek astronomer and mathematician, is believed to have proposed a sun-centered model of the solar system. Ptolemy an astronomer, geographer, and mathematician, exploited Aristotle’s Earth-centered view and developed a complex geocentric model that was used by astronomers over the next thousand years. 11

Historical Models of the Solar System The Geocentric Model According to Ptolemy’s model, the planets moved on small circles that in turn moved on larger circles. 12

Historical Models of the Solar System The Geocentric Model Ptolemy’s “wheels-on-wheels” model seemed to make sense since it very well illustrated observations made at the time going back hundreds of years. Scientist for many centuries used Ptolemy’s model to make predictions of the motions of planets years into the future. 13

Historical Models of the Solar System The Heliocentric Model (Sun-Centered) 14

Models of the Solar System The Heliocentric Model The model which placed the sun at the center is called the heliocentric or sun-centered model. The Polish astronomer Nicolaus Copernicus adopted Ptolemy’s idea that planets’ orbits are perfect circles, he however developed Aristarchus’s primitive sun-centered model into a well thought out heliocentric model. Copernicus’s model is known as the most influential of modern astronomy. 15

Tycho Brahe made accurate measurements of planetary motion. Tycho Brahe (1546-1601): Danish astronomer

Tycho’s contributions to astronomy Tycho discovered ‘new star’, or ‘nova’, upsetting ancient notion of perfect, unchanging heavens. Made very accurate measurements of planetary positions.

Johannes Kepler (1571-1630): German Was Tycho’s assistant. Used Tycho’s data to discover Three Laws of Planetary Motion.

Kepler’s First Law of planetary motion The orbits of planets around the Sun are ellipses with the Sun at one focus.

Ellipse = an oval built around two points, called focuses (or foci). SIZE of ellipse: Major axis = longest diameter of ellipse. Semimajor axis = half the major axis.

SHAPE of ellipse: Eccentricity = distance between foci divided by major axis. Foci close together: ellipse nearly circular, eccentricity close to zero. Foci far apart: ellipse very flattened, eccentricity close to one.

Example: Mars Semimajor axis = 1.524 A.U. Eccentricity = 0.093 (much smaller than one)

(3) Kepler’s Second Law of planetary motion A line from the Sun to a planet sweeps out equal areas in equal time intervals.

Consequences of Kepler’s Second Law: Planets move fastest when closest to the Sun. Example: Mars Perihelion: 206,600,000 km (1.381 A.U.) Max. Orbital Speed: 26.5 km/s Aphelion: 249,200,000 km (1.666 A.U.) Min. Orbital Speed: 22.0 km/s

Kepler’s Third Law of planetary motion The square of a planet’s orbital period is proportional to the cube of its average distance from the Sun*: *A planet’s average distance from the Sun is equal to the semimajor axis of its orbit.

Kepler’s Third Law in mathematical form: P = orbital period (in years) a = semimajor axis (in A.U.) Example: The orbit of Mars

Galileo made telescopic observations supporting the heliocentric model. Galileo Galilei (1564-1642): Italian Galileo was among the first to observe the sky with a telescope (1609).

Models of the Solar System The Heliocentric Model Galileo Galilei was a scientist who conducted his experiments in the manner of moderns scientists. He actually used a very systematic approach very similar to the scientific methods. Galileo’s observations showed that they are other celestial objects beside Earth with orbiting satellites. 28

Models of the Solar System The Heliocentric Model His discovery best fit the heliocentric model. Galileo also observed that Venus went through phases similar to the phases of Earth’s moon. The observation of these phases was more in line with the idea that planets revolve around the sun rather than the Earth. 29

Phases of Venus in the geocentric model of Ptolemy. Only new and crescent phases.

Phases of Venus in the heliocentric model. The Phases of Venus Phases of Venus in the heliocentric model. All phases; smaller angular size when full than when new.