Copernicus' On Planets

Copernicus' theory of a rotating and orbiting Earth manages to explain the daily motion of the sky and the annual motion of the Sun just as well as Ptolemy, but no better.  If that was all he had, his theory probably would have died right there.  But Copernicus had an ace up his sleeve: epicycle-free retrograde motion for the planets.

The first thing to note about Copernicus' theory of the planets is that by making Earth and the other planets orbit in circles (roughly) about the Sun, Copernicus automatically creates two different categories of planets.  First there are planets whose orbits are enclosed within Earth's orbit (ie, planets that are closer to the Sun than is Earth).  These planets will always be seen near the Sun from Earth's perspective, so clearly these must be the inferior planets (Mercury and Venus).  The other category is the planets whose orbits enclose Earth's orbit (those farther from the Sun than is Earth).  These planets can at times be opposite the Sun from Earth's perspective, so clearly these are the superior planets (Mars, Jupiter, Saturn).

This is nice - the division between inferior and superior has a very natural explanation in the Copernican system.  But you ain't seen nuthin' yet.  In order for an inferior planet to undergo retrograde motion as seen from Earth, that planet must move along its orbit faster than does Earth.  In that case, the planet will appear to retrograde (as seen from Earth) when it passes Earth on the inside.  Of course, if it is passing Earth on the inside then it must be between the Earth and the Sun.  In other words, it just be in conjunction as seen from Earth.  And we already know that the inferior planets do, in fact, retrograde only when in conjunction.

For superior planets to retrograde they must move slower than Earth.  In that case, they will appear to retrograde when Earth passes them on the inside.  If Earth is passing them on the inside, then Earth must be between the planet and the Sun.  So as seen from Earth the planet and Sun will be in opposition.  And we know that the superior planets do, in fact, retrograde only when in opposition.  What is more, when Earth is passing the planet it will be as close as possible to that planet.  This explains why superior planets are brightest during retrograde/opposition - that is when they are closest to Earth.

So Copernicus gets retrograde motion without having to use epicycles (although he does, in fact, use epicycles for something else as we will see later).  Moreover, his simple theory automatically achieves all of the links we find observationally: retrograde is linked to brightness and also to conjunction/opposition.  No special tweaking necessary.  In the Copernican theory it CAN'T BE ANY OTHER WAY.  This is a severe constraint on the Copernican theory and it makes it much more likely that the Copernican theory would conflict with observations if the theory were not, in fact, true.  But it doesn't conflict with observations.  Pretty cool.

But there is a complication.  In the Copernican theory we cannot directly observe the periods of the planetary orbits.  This is because while the planets are moving, WE are also moving.  So the cycles we observe (synodic periods, zodiacal periods) are really a mixture of the motion of the planet we are observing and our own motion.  My class spent much of today's class period working to disentangle those motions.  We succeeded in determining the orbital periods of all five visible planets, but in order to do so we had to do a bit of geometry and some calculation. 

Next week we will finish up our discussion of Copernicus by determining the sizes of the planetary orbits.  This will help us to see the overall coherence of the Copernican system, and why Copernicus felt that Ptolemy's system was a monster.