Chabot College Astronomy

Scott Hildreth

Geocentric vs. Heliocentric Theory Comparison Study Sheet Sample Answers & Comments


Introduction

This worksheet is intended to help you understand and review the observed motions of the sky, and how the two different models of our solar system accounted for or explained those motions. A second benefit of completing this worksheet may also be to help you see how any science progresses, by developing theories and models to explain phenomena, and revising those theories as new observations are made. Answers will be posted (and discussed in weekly sections).

Instructions

For each of the observations listed below, note how each model explained why the observation occurred. The first has been completed for you as an example. You might want to answer these on a separate piece of paper.

 Observations
 Geocentric Explanations  Heliocentric Explanations  Comments
 1. Stars rise in the East, and set in the west, over 24 hours. The sky is a fixed celestial sphere that rotates over Earth below in about 24 hours. The Earth rotates on its axis once per day circling the earth  Geocentric observers felt the sky moved around the Earth. Since it does not appear the Earth is spinning, the only other option is that the sky must move. The Heliocentric theory accounted for this observation by having the Earth spin on its axis once per day.
 2. The sky seems to revolve around Polaris, the North Star. Polaris was "special" - it didn't seem to move, and therefore was different than other stars.   And the stars around it (in constellations we call "circumpolar", like Cassiopeia, and Ursa Major and Ursa Minor) were also deemed to be special, because they stayed above the Horizon all night (for observers in mid-northern European latitudes.)

 Some myths held Polaris to be a spike that held the sky up over Earth.  Many observers - reportedly as early as the 4th century BCE - recognized Polaris was not *exactly* at the pole.  In some Arabic cosmologies, the sky was seen to be held up with a tent pole, extending to the North Star.  And Polaris itself was regarded by some cultures as an evil star, and others as a guardian of that hole.

The Earth's rotation axis points in the direction of the North star, so that point doesn't seem to move. One of the key tenets of science is that explanations of Nature should be as simple as possible (but not TOO simple!) 

Note how the geocentric theory had to explain why the sky has some stars that move differently than others, with some moving fast and others moving slow, and some changing during the year and others always visible,

 3. The Sun moves east slowly during the year among a select group of stars (the zodiac constellations). The sun must be moving across the sky - the celestial sphere - drawn by special forces.  In some Greek myths, the Sun was a golden chariot, pulled across the sky by Helios (or Helios was the sun himself.)  At night, after setting in the West, Helios must have continued *below* earth, through the underworld, to emerge again to rise in the East the next day.

The sun was clearly the most powerful object in the sky, giving us light and heat and melting the ice that gave us water.  So if the sun moves in front of only certain stars - the zodiac constellations - they must clearly have special powers.  Thus is born the beginnings of astrology - that the sun, AND the constellations it moves in front of, have powers that influence human lives and events.

As the Earth slowly circles the Sun on our orbital path (the "ecliptic"), we see the Sun in front of different constellations each month - but *only* in front of those along that same orbital plane.  Imagine circling a friend while both of you stand in a park - they will appear to be in front of trees and benches and gates and other park features as you move around them, but they will never be seen in front of the sky above you or below your feet. The zodiac (the "zoo" of animals of the key constellations) is a band about 18 degrees wide centered on the ecliptic.  There are really 13 constellations that the Sun appears to move in front of during the year, but the 13th, regarded typically as Ophiucus, the Serpent Bearer, near to Scorpius, was considered unlucky.  Having 12 zodiac constellations was easier to manage (and coincidentally matched the apparent period of Jupiter in the sky much better than 13 would.)
 4. The Sun rises at different points along the eastern horizon, reaches different max. heights, and sets at different points in the west, during the year. (Seasons) The sun, as a god or independent being, could move north or south as he rose - as he might want to do on his own. 

In the fear that after rising farther and farther southeast from October through mid-December, many cultures held ceremonies that marked and celebrated the Sun's decision to "turn around" on December 21 - the winter solstice.  Even though it marked the first day of winter, with cold weather to come, the turning of the Sun also promised that Spring would eventually come.

The Earth's rotation axis stays tilted towards Polaris year round as we orbit the Sun, meaning that for part of the year the northern hemisphere is tilting away from the Sun, creating winter with the Sun appearing to move lower across the sky, and up fewer hours in a day (winter).  And six months later, when we on the opposite side of the sky, but still tilting towards Polaris, the northern hemisphere was now also tilting *towards* the sun, resulting in it appearing higher in the sky for more hours in a day (summer).

The fixed tilt angle and orbit of Earth resulted in the apparent drift of the sunrise/sunset positions back and forth between the summer and winter solstices.

Many cultures around the world developed rather sophisticated "horizon astronomy" observatories or monuments that used the Sun's apparent motions along the horizon at sunrise or sunset, marking the key points of the solstices and equinoxes.  Stonehenge in England  is regarded as one of the most famous, but there are stone circles across the British Isles, and similar sites across North America, in Africa, and Southeast Asia.
 5. The Moon goes through phases. Like the Sun, the moon was considered powerful and special, and its phases were considered illustrations by some cultures of its power to appear as it might want. 

Most geocentric theories had the Moon clearly orbiting Earth as one of the closest celestial bodies to us, and correctly recognized that it was illuminated by sunlight, which creates phases based on how much of the moon's lit surface we see.  

The moon orbits Earth, as we both orbit the sun.  Except during the occasional, temporary lunar eclipses, the moon is always lit by the sun, and the phases we see are a result of what portion of its lit surface was can see from Earth.  This is an example where both geocentric and heliocentric theories shared the same general answer for an observed phenomena. Note though that the heliocentric theory had to account for WHY the moon stayed with Earth as we orbited the Sun. 

Before Galileo's work on mechanics, and Newton's formulation of the universal law of gravitation, it was argued by geocentrists that IF the Earth  did move in a heliocentric model, THEN we would lose our moon.  Since the moon does stay with us, then the Earth must not be moving!  (The logic here seems sound, but is based on the faulty assumption that something physical had to bind the Moon in place to the Earth.)

 6. The planets show retrograde motion, appearing sometimes to move backwards in the sky. In later Greek geocentric theories, the planets were imagined to be orbiting on circular paths around the Earth, and then on smaller circular loops (epicycles) that moved atop the larger circles. 

(Later theories accounted for even smaller variations in the planets' observed orbits by placing the center of the planets circular orbits not exactly at the center of Earth.)

Planets like Mars, Jupiter, and Saturn showed retrograde motion as Earth, in its smaller and faster orbit around the Sun, caught up to and then passed the slower-moving outer planets. 

And Mercury and Venus, orbiting in even smaller orbits, showed retrograde motion as they moved first in one direction coming out from behind the sun, then reaching their  maximum angular distance from the sun, and then turning around to sweep between us and the sun. 

One way to picture the motions of the inner planets is like a racing car on a track, seen from the grandstands first moving to the left along the back straight, then later moving the right along the start-finish line on the near side of the track.

One of the key difficulties presented by retrograde motion was that each planet did it differently, and in front of different constellations, at different times and in different ways.  Ptolemy's brilliance in developing and refining the geocentric model until it "saved the appearances" that we saw in the planets motions from earth was good science - but his model was nonetheless wrong.
 7. The stars do not seem to shift positions ("Parallax"). In geocentric models, everything orbited around Earth, and you wouldn't see parallax because the Earth didn't move. In heliocentric models, if the Earth DID orbit the sun, we should see a slight difference in the positions of stars from one side of our orbit to the other.  This wasn't observed until 1838, because the stars were so far away that even the enormous distance from one side of Earth's orbit to the other - spanning 186,000 miles - wasn't enough to create an angle that was detectable in smaller telescopes. The lack of parallax was used as one of the key arguments AGAINST heliocentrism.  Few could conceive of the truly astronomical distances to the stars that was necessary to make our motion around the sun inconsequentially small in comparison.
 8. Venus shows different phases and sizes (in a telescope). In geocentric models, this could NOT be explained adequately.  That Venus could appear larger or smaller could be rationalized with it orbiting on a large epicycle while orbiting Earth, so that it would come closer and look larger, and then move farther and look smaller.  But the fact that its sized changed in addition to and synchronized with its phases in Galileo's observations was a nail in the coffin of the geocentric theory - this could not be explained. Venus had to orbit the Sun, and at times was seen very near to the sun on the *back* side of its orbit, when its distance from us was about 160 million miles away.  It would appear almost full in phase, but very small.

Then, almost 9 months later, Venus had caught up to Earth and was about to pass (or "lap") us on its inner orbit, and was only about 20-25 million miles away, appearing much  larger - but with most of its lit surface now facing inward towards the sun - not towards Earth.

Note that this observation does NOT prove Earth orbited the Sun, and Galileo did not claim that to be case either with this one fact.  It did prove Venus orbited the sun, and obviously ruled out that Venus orbited Earth.  So the heavens were not geocentric.  But it remained to be shown that Earth orbited the Sun with a different set of observations, made by James Bradley who discovered stellar aberration - a change in the path of the light from stars due to our motion in our orbit.
 9. Jupiter shows four moons that stay with the planet as it moves in the sky (with a telescope). In geocentric models this could NOT be explained adequately.  If the moons orbited Jupiter, then everything did not orbit the Earth!  This was a key observation on many levels - not only disproving geocentrism, but also hinting at the idea that the Earth COULD move in orbit around the Sun and not lose our moon, either. Galileo's observations of the moons of Jupiter also confirmed Kepler's third law of planetary orbits - that the distance of an orbiting body from the body it orbits is related mathematically to the amount of time it takes to orbit, according to the relationship

P^2/a^3 = constant.
 10. Polaris was not always the north star in our sky. ("Precession") That Earth was the center of all motion meant that any changes in the orientation of the sky were a result of the sky slipping, or being held up in a slightly different place above us. It wasn't until Newton that the physics of rotation caught up to this observation - that was recognized by not explained.  That Earth is in essence a very fast spinning, but very heavy, top, results in a very LONG period of precession - 26,000 years long.  So the wobble is going to be very slow. While records of stars thousands of years ago were difficult to find, it is known that the celestial pole around which the stars moved was not exactly at Polars - about 7,000 years ago it was much closer to the star Thuban in the constellation Draco.

 


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