Lecture 12: The Wanderers

Key Ideas

• "Wandering stars" that follow complex paths near the Ecliptic.

• Inferior Planets
• Superior Planets
• Conjunction & Opposition

The Naked-Eye Sky

Sun:

Bright disk ~1/2° across

Moon:

Pale disk ~1/2° across that goes through monthly phases.

Stars:

Pinpoints of light that appear fixed relative to each other on the Celestial Sphere.

Planets: (Greek: planetai = "wanderers")

Points of light that move relative to the "fixed" stars.

Stay within a few degrees of the Ecliptic

Follow complex paths that take between 88^d (Mercury) and 30^y (Saturn) to complete a circuit through the Zodiac.

Five Classical Planets:

Mercury, Venus, Mars, Jupiter, & Saturn

Inferior & Superior Planets

Inferior Planets: Mercury & Venus

• Appear to follow the Sun across the sky.
• <28° for Mercury, and <47° for Venus.

Superior Planets: Mars, Jupiter, & Saturn

• All move along the Ecliptic on paths seemingly independent of the motions of the Sun.
• All can appear in the sky any time (e.g., around midnight)

Inferior Planet Configurations

Inferior Conjunction

Planet is between the Earth and the Sun.

Superior Conjunction

Planet on the other side of the Sun from Earth.

During either conjunction, the inferior planet appears to rise and set with the Sun.

Maximum Eastern Elongation

• Planet is at its furthest East of the Sun as seen from the Earth (28° for Mercury, 47° for Venus)
• Rises & sets after the Sun ("evening star")

Maximum Western Elongation

• Planet is at its furthest West of the Sun as seen from the Earth (same angles as Eastern Elongation).
• Rises & sets before the Sun ("morning star")

Superior Planet Configurations

Opposition

• Planet is opposite the Sun in the sky.
• Rises as the Sun sets
• Highest in the sky at midnight.

Conjunction

• Planet is on the same side of the sky as the Sun.
• Rises with the Sun
• The planet does not appear in the the night sky.

Eastern Quadrature

• Planet at right angles to the Earth-Sun line.
• Planet rises at noon, sets at midnight.

Western Quadrature

• Planet at right angles to the Earth-Sun line.
• Planet rises at midnight, sets at noon.

Retrograde Motion

• Called "Direct Motion".
• Motion is non-uniform (not at the same speed).

Sometimes, however, the planets appear to

• Slow down & stop!
• Start moving westward, or RETROGRADE,
• Slow down & stop again,
• Resume moving eastward again.

Apparent retrograde motion is observed in all planets.

Inferior Planets (Mercury & Venus):

Undergo retrograde motion around inferior conjunction.

Superior Planets (Mars, Jupiter, & Saturn):

Undergo retrograde motion at around opposition.

[Click Here to see an montage (18Kb) of the recent (1998-2000) retrograde motions of Mercury, Venus, Mars, Jupiter, and Saturn. Note that Jupiter & Saturn, currently visible after sunset high in the Eastern sky, are just now (Jan 18) ending a period of retrograde motion that started back in October of last year.](Graphic by R. Pogge)

Who Ordered That?

The struggle to understand these motions took nearly 3000 years:

• The motions are subtle and defy poetic or metaphorical description.
• Their complexity similarly defies simple geometric description.

A Question of Approach

Two approaches have been taken:

Phenomenological Description

• Find a way to compute the motions without worrying about the details of why they work this way.
• Goal is to "preserve appearances" (i.e., make reliable predictions)

Physical Description

• Discover the underlying physical principles behind the planetary motions (i.e., ask "why" they move).
• Predictions of the motions should then follow from first principles

From Myth to Science

Internal Consistency

Must follow the same basic rules, no special cases or special pleading is allowed.

Predictive Power

Must provide measurably accurate predictions of future behavior.