ASTR 1101-001Spring 2008

Joel E. Tohline, Alumni Professor

247 Nicholson Hall

[Slides from Lecture12]

Contrasting Models of Planetary Motions

• Greek Geocentric Model (Ptolemaic System) – §4-1– Originated by Apollonius of Perga &

Hipparchus in 2nd century B.C.– Expanded upon by Ptolemy in 2nd century

A.D.

• Copernican Heliocentric Model – §4-2– Proposed in 1543 by Nicolaus Copernicus– (Also considered in 3rd century B.C. by

Aristarchus)

Contrasting Models of Planetary Motions

• Geocentric Model– Underlying hypothesis: Earth is unmoving

and at “center of the universe”

• Heliocentric Model – Preferred (by Copernicus) initially because of

its relative simplicity– Eventually proven correct by new

observations made possible by the aid of telescopes (see Galileo’s discoveries §4-5)

Naked-Eye Observations“explained” by both Ptolemy and Copernicus

• Stars (and Sun, Moon, etc.) rise in east and set in west once every 24 hours

• Remove 24-hr diurnal motion; Sun and Moon both move steadily west-to-east at different rates (Moon = month period; Sun = year period)

• Superior planets [Mars, Jupiter, Saturn] usually wander slowly east-to-west (observed periods greater than 1 year) but periodically display retrograde (west-to-east) motion

• Inferior planets [Mercury, Venus] never wander very far (in angular separation) from the Sun; only seen shortly before or shortly after sunrise/sunset

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Revolutionary discoveries not especially relevant to the “geo-” versus “helio-” centric debate:– Mountains and Craters on the Moon– Sunspots on the Sun (ouch!)– Rings of Saturn– The “Milky Way” is “a mass of innumerable

stars”

Galileo Galilei (1564-1642)

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Revolutionary discoveries not especially relevant to the “geo-” versus “helio-” centric debate:– Mountains and Craters on the Moon– Sunspots on the Sun (ouch!)– Rings of Saturn– The “Milky Way” is “a mass of innumerable

stars”

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Revolutionary discoveries not especially relevant to the “geo-” versus “helio-” centric debate:– Mountains and Craters on the Moon– Sunspots on the Sun (ouch!)– Rings of Saturn– The “Milky Way” is “a mass of innumerable

stars”

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Revolutionary discoveries not especially relevant to the “geo-” versus “helio-” centric debate:– Mountains and Craters on the Moon– Sunspots on the Sun (ouch!)– Rings of Saturn– The “Milky Way” is “a mass of innumerable

stars”

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Revolutionary discoveries not especially relevant to the “geo-” versus “helio-” centric debate:– Mountains and Craters on the Moon– Sunspots on the Sun (ouch!)– Rings of Saturn– The Milky Way is “a mass of innumerable

stars”

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Discoveries useful in resolving the “geo-” versus “helio-” centric debate:– Venus exhibits phases like those of the Moon– The apparent size of Venus was related to the

planet’s phase (as well as to the planet’s angular distance from the Sun)

– Jupiter has four “Galilean satellites”; their orbital behavior is like a Copernican system in miniature

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Discoveries useful in resolving the “geo-” versus “helio-” centric debate:– Venus exhibits phases like those of the Moon– The apparent size of Venus was related to the

planet’s phase (as well as to the planet’s angular distance from the Sun)

– Jupiter has four “Galilean satellites”; their orbital behavior is like a Copernican system in miniature

Phases of Venus

Phases of Venus expected in theCoperican Heliocentric model

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Discoveries useful in resolving the “geo-” versus “helio-” centric debate:– Venus exhibits phases like those of the Moon– The apparent size of Venus was related to the

planet’s phase (as well as to the planet’s angular distance from the Sun)

– Jupiter has four “Galilean satellites”; their orbital behavior is like a Copernican system in miniature

Angular size “” expressedin arcseconds.

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• Discoveries useful in resolving the “geo-” versus “helio-” centric debate:– Venus exhibits phases like those of the Moon– The apparent size of Venus was related to the

planet’s phase (as well as to the planet’s angular distance from the Sun)

– Jupiter has four “Galilean satellites”; their orbital behavior is like a Copernican system in miniature

Galileo’s New Observationsmade with the aid of a telescope (~ 1610)

• First fundamentally new astronomical data in almost 2000 years!

• Contradicted prevailing opinion (and religious belief) and strongly suggested a heliocentric (Copernican) structure of the “universe”

Scientific utility of theCopernican Heliocentric Model

• Can deduce the true “sidereal” (as opposed to readily measured “synodic”) orbital periods of each of the planets [see textbook BOX 4-1 and Table 4-1]

• Can deduce the distance that each planet is from the Sun, relative to the Earth’s distance from the Sun (1 AU); [see textbook discussion associated with Table 4-2]

Synodic versus SiderealPlanetary Orbital Periods

• When two systems that have different natural oscillation periods (Plong & Pshort) start out “in alignment” with one another, they will return to an aligned arrangement after a time that is identified by their so-called “beat” period, “B”.

Synodic versus SiderealPlanetary Orbital Periods

• For two planets:

Sidereal periods

Synodic versus SiderealPlanetary Orbital Periods

• For two planets:

Synodic period