Planetary Motion

Dr. Bill Pezzaglia

Updated 2014Jan21

VI. Planetary Motion (& Gravity)

A. Cycles of Planets

B. Greek Geocentric Model

C. Heliocentric Model

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A. Cycles of Planets

1) The Wanderers

2) Superior Planets

3) Inferior Planets

3 1a. The Wanderers 4

• The Babylonians discovered that the 5 brightest stars wandered the sky.

• Mercury, Venus, Mars, Jupiter & Saturn• They followed the ecliptic (like sun and

moon), but had erratic paths.

1b. Retrograde motionBabylonians had noted “wandering” motion of planets. Here in 1997 Mars moves “direct” (normal eastward motion) most of the time, but then moves “retrograde ”(westward) for awhile, then returns to direct motio n.

5 1c. Synodic Period

Babylonians note retrograde pattern repeats every “synodic period”, but in a different part of sky.

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Planet Synodic (days) Note

Mercury 116

Venus 584 Mayan Calendar

Mars 780

Jupiter 399

Saturn 378

2. Superior Planets

• Superior Planets: (Mars, Jupiter, Saturn)• They go retrograde when they are opposite the

sun

• Different than “Inferior Planets” which are never seen far from the sun.

• Ancients have no explanation for this behavior

7 2a. Superior Planet Configurations

•Further from sun than earth•Opposition is 180 degrees elongation, best time to view (closest, transits at midnight)

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2b. Synodic Period of MarsHere from July 2005 through February 2006, Mars moves across the constellations Pisces, Aries, and Taurus. Mars's motion is direct (from west to east, or from right to left in this animation) most of the time but is retrograde (from east to west, or from left to right in this animation) during October and November 2005.

9 2c. Synodic Period of Mars

• Every 780 days (synodic period) the retrograde motion repeats, but in a different part of the sky.

• Two periods later, in late 2009, Mars moves across the constellations Gemini and Cancer.

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3a. Inferior Planets

• Inferior Planets: (Mercury, Venus) are never seen far from the sun. They go retrograde at “inferior”conjunction with the sun.

• In “modern”heliocentric model, we can see why the inferior planets never can be opposite the sun.

11 3b. Venus Diaries 12

Omen texts, first Babylonian Dynasty (1900-1660 BC), Venus is both the morning and evening star. Tablets of Ammizaduga1650 BC were lost, but copied at Nineveh 650 BC, show 21 years of Venus data, including an 8 year cycle.

Note 5 synodic periods is exactly 8 years, matches 13 orbits of Venus around the sun. Hence Venus will be in the same constellations, repeating the same patterns every 8 years!

3c. Venus Cycles 13

Invisible for 66 days around superior conjunction,

evening star for 254 days

invisible for 9 days (on average) at inferior conjunction

morning star for 254 days

cycle repeats in 584 days

Mayan Indians discovered similar cycle (much later).

3d. Mayan Calendar 14

They identified Venus with the godQuetzalcoatl.

Chichen Itza, Yucatan (1000 A.D.)

B. Geocentric Models

1) Early Greek Models

2) Epicycles

3) The Geocentric Universe

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“The School of Athens”

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1. Early Greek Models

a) Plato’s Academy

Plato (427-348 BC) leaves the problem of planetary motion for his students to solve. He insists it must be done with circles

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“Let none but geometers enter here”

1b. Eudoxus (408-355 BC)

introduces “Homocentric Spheres”, a complex system of axes and balls. It generates a retrograde path.

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The “hippopede” path

extends model, has over 55 spheres to explain retrograde motion of 5 planets

1c. Aristotle (384-322 BC) 19 1d. Heraclides of Pontus (388-315 BC) 20

• Student of Plato and Aristotle (?)

• First to propose that the earth rotates (to explain motion of stars and sun)

• Resistance to this idea: wouldn’t falling objects fall sideways due to spin?

2. Epicycles(a) Appolonius of Perga (262-190 BC) proposes

epicycle concept to explain retrograde motion (also introduces idea of eccentric)

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2c. Hipparchus of Rhodes (190-120BC)

extends epicycle ideas for sun (to explain seasons not being same length) and moon’s change in orbital speed. Had include idea that earth is not at center but “eccentric”

23 3a. Claudius Ptolemy

• Claudius Ptolemaeu (87-150 A.D.).

• Refines the epicycle theory.• “Geocentric Model” the earth

is at the center of the universe

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3b. Ptolemy’s Geocentric Universe 25

One of the “flaws” is trying to explain why Mercury a nd Venus are never seen very far from the sun. The da shed line represents some unexplained connection that ke eps them all in line.

3c. Ptolemy’s Geocentric Universe 26

The Ptolemaic system is used for over 1500 years!