The planets in our solar system and their moons are not independent sources of visible light like stars. They appear as bright objects in the sky, because they are illuminated by the Sun. Only the side of a planet or moon facing the Sun is bright. It is usually possible to see only part of the bright side of a planet or moon at any given time. For example, as our Moon moves through its roughly 29 day orbit, its appearance changes as shown in Figure 1. The balance of light and dark is called the phase of the Moon. The other planets and their moons are distant enough from us that they appear to the naked eye to be comparable in size to stars, but it is possible to observe their phases with the aid of a telescope.
Figure 1 : The phases of the moon. The cycle of phases is divided into quarters. In the first quarter, only a bright crescent is visible. In the second quarter, the bright portion of the Moon grows (waxes) from a half to a full circle. The bright portion then decreases in size (wanes) through the latter two quarters. The completely dark phase is called the new moon.
The phase of a planet or moon depends on its position relative both to the Sun and the observer. Hence, any model of the solar system can be used to make predictions regarding the phases of the planets and moons. From our perspective on Earth, Mercury and Venus are inner planets. That is, they are closer to the Sun than we are. The Ptolemaic and Copernican models of the solar system make different and incompatible predictions regarding the phases of the inner planets viewed from Earth. Hence, observations of the phases of the inner planets lead us to reject one or both of these models. In 1613, in his Letters on Sunspots [Dr57], Galileo Galilei reported that Venus displays a full set of phases similar to those of the Moon. He later presented these observations as evidence in his Dialogue on the Two Chief World Systems [Dr67].
The animations discussed below show the motions of the Sun, Earth, and Venus according to the Ptolemaic and Copernican models. They also show Venus from the vantage point of the Earth, displaying the phases predicted by each model. Snapshots of one of the animations appear in Figure 2. Based on your own observations of these animations, you should be able to make your own judgment as to whether Galileo's observation of the phases of Venus favored one model over the other.
Figure 2 : Snapshots of an animation showing the Sun, Earth, and Venus from "above" and from Earth.
The animations below with file names ending with the suffix .py are written in the Python programming language with the Visual Python 3D graphics library. Both the Python language and the Visual Python package are open-source software - they are available for free. You can download both from the Visual Python Web site :
http://www.vpython.orgFollow the "Downloads" link followed by the link for your operating system, and follow the instructions. It is important to install Python before Visual Python.
To save local copies of the the animations, right-click on each of the following animation links
and use Save Target As... to save a copy of each file. The files ptolemy.py and copernicus.py are the animations of the two models. You should not run planet.py itself, but it must be present in order to run ptolemy.py and copernicus.py.
If you have installed Python and Visual Python, double-clicking on your local copy of an animation program will run it. You can control the speed and direction of the animations and exit the programs with the following keyboard commands:
v : toggle view
f : faster
s : slower
r : reverse
q : quit
Compare the two views of each animation to get a sense of the two models. Carefully describe any differences you see. You may want to add to your response as you make further observations.
Use the view from Earth to observe the phases of Venus over a few orbits. Make a sketch of the progression of phases predicted by each model. Galileo reported observations of a complete cycle of Moon-like phases of Venus. Does Galileo's observation of the phases of Venus favor one model over the other? Explain.
Planets are observed to move relative to the fixed stars. Sometimes their motion is in the same direction as the apparent motion of the stars, and at other times they move in the opposite direction. The opposing motion is called retrograde motion. Use the view from Earth in each animation to determine whether or not each model predicts retrograde motion. Does the empirical observation of retrograde motion favor one model over the other? Explain.
The angular distance of a planet from the Sun in the sky is called its elongation. The inner planets, Mercury and Venus, are observed to have bounded elongation. That is, they each seem to have a maximum elongation, whereas the outer planets are observed to move through all possible angular separations from the Sun. Use the view from Earth in each animation to determine whether or not each model predicts bounded elongation. Does the empirical observation of bounded elongation favor one model over the other? Explain.
The Ptolemaic model places the Earth at the center of the solar system, while the Copernican model places the Sun at the center. What kind of observation(s) would settle this specific dispute? Explain.
The following discussion of absolute distances has nothing to do with the phases of Venus. However, if you are curious about the absolute scales of the models, read on.
If you observe a distant object (a planet, the Moon, a star, e.g.) in the sky with a telescope, it is not very difficult to measure its angular position, which can be expressed as two angles, similar to the latitude and longitude angles used to identify geographic locations on the Earth. However, the distance between the object and the Earth is not at all easy to measure directly.
The distance of an object from the Earth can be determined indirectly by measuring its parallax. The parallax of an object is the difference in its angular position in the sky when viewed from two different locations. If the both the parallax and the distance between the locations of the observations are known, trigonometry can be used to calculate distance from the Earth to the object. The parallax of a planet viewed from opposite sides of the Earth is illustrated in Figure 3.
Figure 3 : The parallax of a planet viewed from two different locations is the difference between its apparent angular positions at these locations relative to the "backdrop" of very distant stars. In this illustration, the two locations are on opposite sides of the Earth. (The diameter of the Earth and, and hence the resulting parallax, is greatly exaggerated in the diagram.)
Despite many attempts, a reliable measurement of the Earth-Sun distance was not made until much later than one might suspect. The solar parallax was first measured with reasonable precision during subsequent transits of Venus across the Sun in 1761 and 1769. Measurements of the apparent angular positions of Venus at its time of alignment with the Sun, viewed from many different locations on Earth, yielded high-precision values for the solar parallax [VH85].
The measurements of the solar parallax in 1761 and 1769 led to an astonishing result. The Earth-Sun distance is about 20 times those proposed by Ptolemy and Copernicus. The fact that an error of this magnitude survived for so many centuries illustrates the difficulty of determining absolute distances between objects in our solar system, and how irrelevant those distances are in predicting the angular positions which we can measure directly.
Crowe, Michael J., Theories of the World from Antiquity to the Copernican Revolution, New York : Dover Publications, Inc., 1990.
[Dr57] Galilei, Galileo (1613), Letters on Sunspots, In Discoveries and Opinions of Galileo, Stillman Drake, Trans. and Ed., New York: Doubleday, 1957.
[Dr67] Galilei, Galileo (1632), Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican, Stillman Drake, Trans., Berkeley : University of California Press, 1967.
[NSSDC] Williams, David R., "Planetary Fact Sheets," National Space Science Data Center, 13 April 2004 <http://nssdc.gsfc.nasa.gov/planetary/planetfact.html>.
[VH85] Van Helden, Albert, Measuring the Universe, Chicago : The University of Chicago Press, 1985.
[Go67] Goldstein, Bernard R., "The Arabic Version of Ptolemy's Planetary Hypotheses," Transactions of the American Philosophical Society, 57(1967): 1-55.
