Geocentric and Heliocentric View of the Universe

Retrograde Motion - End to the Geocentric Cosmic View

• A historically well known astronomical phenomenon: An astrological view


• Like the Sun and the Moon, the planets generally appear to move slowly eastward through the zodiac (OK for a geocentric model as well).


• Occasionally, some planets appear to move westward relative to the stars! (a challenge for a geocentric model)


• As shown by the diagram on the right side, this can be explained by the projected locations of planets in a heliocentric solar system model.


• See this Java applet demonstration at UIUC as well.

Stellar Parallax

• Apparent Shift in the position of a nearby star as we look at it from different places in the Earth's orbit.


• Parallax should not exist in a geocentric model.


• Aristotle reasoned that we should see the stars' location change by parallax if the Earth moved around the Sun.


• The more distant the star, the smaller the parallax -- a method to derive distances to stars!

Quiz 5: How large is the stellar parallax?

Astronomy vs. Astrology

• Scientific Process: observation, question, hypothesis, prediction, test, evaluation


• Example: numerical sequences


• 1, 2, 4, 8, 16, 32, .....
• 1, 2, 3, 5, 8, 13, .....
• 1, 2, 2, 3, 4, 6, 9, .....


• Powerful influences of celestial bodies on life:
  
  • Sun as the source of energy and life
  • Moon's phases and tides
  • needs and temptations for predictive power
  • monetary rewards?
  
  
• Putting astrology to a test

"Copernican Revolution"

• Nicholas Copernicus (1473-1543): found Ptolemaic model wrong and developed a heliocentric theory of the solar system (also credit Aristarchus [310-230 BC]). - a giant leap in the cosmological view!


• Tycho Brahe (1546-1601): conducted accurate naked-eye observations


• Johannes Kepler (1571-1630): developed the laws of planetary motions using the accurate data by Brahe


• Galileo Galilei (1564-1642): found observational proof against Earth-centered universe
• discovery of Jupiter's moons
• discovery of phases of Venus (see the movie)

Kepler Laws

• Kepler's First Law
The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

• A circular orbit is a special case of a more broadly possible elliptical orbits
• Circular orbits cannot predict the observations of Brahe


• Kepler's Second Law
As a planet moves around its orbit, it sweeps out equal areas in equal times.

• A planet moves faster in the deeper gravitational potential of the Sun near perihelion
• A planet moves slower in the shallower gravitational potential away from the Sun, near aphelion
• Conservation of angular momentum (R₁V₁ = R₂V₂)




• Kepler's Third Law
The amount of time a planet takes to orbit the Sun is related to its orbit's size, such that the period P squared is proportional to the semi-major axis, a cubed.

• 1 AU (astronomical unit) = distance between the Sun and the Earth (about 150 million km)

"Weighing" Celestial Bodies using Orbital Motion

• Q1: What is the orbital period of a planet located 10 AU away from a Sun-like star?


• Q2: A planet is found around a nearby star X, located only 1 AU away. It takes the planet only 2 months to go around the star once. How much heavier is this star compared with the Sun?

Reading assignment for next lecture: Units 14 & 15