The Phases of Venus

Venus through telescope on July 10, 2013
Taken by Samer Hariri @ OCC-OR

One of the many observations that Galileo made in support of a heliocentric model of the solar system was on the phases of Venus. One might ask, how can you conclude from observing and recording the phases of Venus over a period of time that the Sun is at the center and that Earth along with all the other planets are orbiting it? Galileo had an understanding of moving bodies, and by using simple geometry he was able to confidently support a heliocentric model once his observations matched his predictions. To truly understand this thought process, one must attempt to draw out what the phases of Venus would look like to Earth in both a heliocentric and a geocentric model. Of course to create such an attempt requires an understanding of how planetary bodies like Venus or the moon can have phases in the first place.

The phases of Venus as drawn by Galileo.
Galileo Galilei, Il Saggiatore [The Assayer] Rome, 1623.
Image obtained from http://brunelleschi.imss.fi.it/

Full Moon during the Oct 18, 2013
partial lunar eclipse. (aka Hunter Moon)
Taken by Samer Hariri

On October 18, 2013, there was a partial lunar eclipse visible here in Michigan. During that eclipse, the Moon was in it's full phase, and was passing through the penumbra of the Earth. The difference in brightness was hard to depict for this partial eclipse but with high quality imaging techniques, one would surely see a difference (click here for example). So why do eclipses happen, and how are they related to the phases of the Moon? When we look at the diagrams showing how the phases of the Moon occur, we notice that during a full phase, the Earth is in between the Sun & Moon. During a new phase, the Moon is directly between the Earth & Sun. When this happens, we are unable to see the moon in the sky because the side that is lit by the Sun is facing away from us. During these two phases (full & new) is when lunar (due to full) & solar (due to new) eclipses are possible. A crescent phase occurs when the Moon is waning into a new phase, or waxing out of a new phase. This occurs when it's location is almost in between the Earth & Sun but not completely. The Moon is either a waning or a waxing gibbous when it is closer to it's full phase location. We know that the Moon orbits the Earth, and by understanding its motion about the Earth we can predict its phases quite accurately.

Diagram showing the location of the Moon and its corresponding phases as it orbits the Earth.
Note how the location of the Moon is different from new phase to new phase (green shaded area).
One would expect it to start and end in the same location as it cycles through its phases but it doesn't. Why?
Image obtained from Wikipedia.

      

Phases of Venus in relation to its orbit
around the Sun as seen from Earth.
Image obtained from Wikipedia.

Similarly, if we were to draw Venus along its orbit about the Sun, we can predict the phases we would see of it. As you look at the diagrams showing the location of Venus in relation to what phase we see of it here on Earth, think about how similar that is to the phases we see of the Moon, but more importantly what difference there are. For example, the possibilities of locations in this case can never have the Earth be in between Venus and the Sun. This means that we can never see a full phase of Venus on Earth. However, if we were to base our prediction on a geocentric model then would we expect to see a full phase of Venus, if any? The answer is yes we would since the orbits would eventually have an order where the Earth is now between the Sun and Venus, and we would be able to see a full phase of Venus, and possibly a Venusian (or Venerian if you'd like) eclipse! When Galileo realized that he is not able to witness a full phase of Venus, he immediately knew that the Sun was at the center of our solar system. In addition, the apparent size of the phases indicated that Venus was indeed orbiting the Sun inside the orbit of the Earth. Think about where Venus is during each phase, and what the size of that phase is as drawn by Galileo and if that makes sense or not.

Images of the phases of Venus taken through the Jaicoa Observatory. The image
shows the phases of Venus over a period of time and depicts nicely how the size and shape changes.
Image was taken by Efrain Morales Rivera and was obtained from http://www.jaicoa-observatory.com

Finally, think about the other planets and what phases of those planets we are able to see. What phases do you think Mercury would exhibit? What about Mars? Would we ever see Mars as a crescent here from Earth? It's amazing how by simply observing the various phases of planetary bodies here from Earth, we are able to explain accurately the location of these planetary bodies with relation to Earth. We were able to construct a fairly accurate representation of our solar system some 400-500 years ago by simply looking up at the night sky and "reverse engineering" what we saw into models and diagrams that make sense. The best out of a lot of these early models of our solar system were the ones that explained a lot of the phenomenon (like phases of Venus, retrograde motion, etc..) in the most simplistic manner possible. I sometimes wonder if I would have had the capacity to come to the same conclusions Galileo, Copernicus, or the various others came to about our solar system simply based on the observations they made. It makes sense to me today, and it seems to be relatively elementary, but I'm not sure if I would be as brilliant to initially think of something that is so simple, yet so profound if I had lived in the times of Galileo Galilei...