Why the Apparent Motion of the Sunspots Supports the Copernican Model

Galileo's Dialogue, Day 3, Part 3

As I wrote in a recent post, I intend to write posts for each of the four days in the Dialogue Comparing the Ptolemaic and Copernican Systems¹, the book that got Galileo in trouble with Rome. This is the third post about Day Three in the Dialogue. Here are the previous posts:

• Day One: Galileo Dismantles Aristotle's Separation of Earth from the Heavens.

• Day Two, Part 1: Galileo Attacks Aristotle’s Followers.

• Day Two, Part 2: Galileo Insists the Earth is Spinning on its Axis.

• Day Two, Part 3: Galileo on the Acceleration of Falling Bodies.

• Day Two, Part 4: Galileo Channels Plato.

• Day Three, Part 1: Galileo Calls Out Chiaramonti’s Manipulation of Data.

• Day Three, Part 2: Galileo Praises Aristarchus and Copernicus.

One of my readers wished to know more on how the apparent motion of the sunspots, as seen from the earth, supported the Copernican model. I therefore decided to write a separate post on this topic. I wrote in the previous post:

Salviati then moves on to discussing sunspots, which were unknown to each of Aristarchus and Copernicus, and only became known with the introduction of the telescope. It turns out that the apparent motion of sunspots on the surface of the sun is another argument in favor of the earth orbiting around the sun.

The argument is as follows. Assume that the sun rotates on its axis, which itself is at an angle to the ecliptic (the name, derived from the word eclipse, for the equatorial plane of the solar system). The earth’s axis is also at an angle to the ecliptic, but a different one. This assumption can be verified by the fact that sunspots move across the solar disk, and can disappear off to one side and then reappear on the other side sometime later. As the earth orbits the sun, for half of the year, the apparent motion of the sunspots should be a slight curve upwards, while for the other half of the year, the apparent motion should be a slight curve downwards. And that is exactly what happens.

Observation of sunspots by Galileo

My reader is not the only one who wants to know more. So does Simplicio:

For who is there to assure me that such peculiarities might not also be seen in a sun moving along the ecliptic, by inhabitants of an earth stationary in its center? [p.352]

Salviati initially responds by stating that for the Peripatetics, this is a non-problem, since for them the sunspots either do not exist or are not attached to the sun:

[T]he true pure Peripatetics, laughing at anyone who employs himself in what (to their thinking) are empty fooleries, will pretend that all these appearances are vain illusions of the lenses, and will thus free themselves with little trouble from the obligation of thinking any more about it. [p.353]

But Salviati does address the problem seriously, stating that noöne has proposed a solution:

But as for scientific astronomers, after having given very careful thought to what might be said on this matter, we have not found under the ancient system any reply adequate to harmonize the course of the spots with human reason. [p.353]

So what is the problem? Salviati states that everything will have to be explained in terms of motion of the sun:

Assuming that the visible motions of the sunspots are as we have declared above, and assuming the earth to be immovable in the center of the ecliptic, on whose circumference the center of the sun is placed, it is necessary that all the diversity which is perceived in these movements shall have causes residing in the motions of the solar body. [p.353]

Salviati makes three points. First, the sunspots must move with the sun; this Galileo had previously argued. Second, the axis of rotation of the sun must be tilted with respect to the ecliptic, otherwise the sunspots would always appear to be moving in a straight line from the point of view of an observer on earth. Third, this axis of rotation of the sun must itself vary over time, i.e., the sun must wobble, allowing the sunspots to appear to move up or down, depending on the time of year. Salviati then explains two necessary motions:

And since such states would be continually altering, making the tilting and the curvature now greater and now less, the former being sometimes reduced to complete equilibrium and the latter to perfect straightness, this axis of monthly revolution of the spots would have to be supposed to possess a rotation of its own, by which its poles would describe two circles around the poles of another axis (which would thereby be assigned to the sun), the radius of which circles would correspond to the degree of tilt of this axis. And it would be required that its period should be one year, since that is the time in which all the appearances and diversities in the paths of the spots are repeated. That the rotation of this axis should be made about the poles of another axis parallel to that of the ecliptic, and not around any other points, is clearly indicated by the maximum tilts and the maximum curvatures, which are always of the same magnitude. [p.354]

Hence finally it will be necessary, in order to keep the earth fixed in the center, to attribute to the sun two movements around its own center, on two different axes, one of which would complete its rotation in a year, and the other in less than a month. [pp.354-355]

But those two motions would not be sufficient, because the sun would need two further motions, in order to rotate around the earth, the first on a daily basis for the day-night cycle, and the second on an annual basis for the seasons:

To my mind, such an assumption seems very difficult, almost impossible; this arises from having to attribute to the same solar body two other movements about the earth on different axes, tracing out the ecliptic in a year with one of these, and with the other forming spirals or circles parallel to the equinoctial plane, one a day. [pp.355]

So Salviati concludes that the apparent motion of the sunspots is a serious argument in favor of the revolution of the earth around the sun:

Now if these four motions, so incongruous with each other and yet necessarily all attributable to the single body of the sun, could be reduced to a single and very simple one, the sun being assigned one inalterable axis; and if with no innovations in the movements assigned by so many other observations to the terrestrial globe, one could still easily preserve the many peculiar appearances in the movements of the solar spots, then really it seems to me that this decision could not be rejected.

---

If you wish to donate to support my work, please use the Buy Me a Coffee app.

1. Galileo Galilei. Dialogue concerning the two chief world systems — Ptolemaic and Copernican. Translated by Stillman Drake, foreword by Albert Einstein. University of California Press, 2nd ed., 1967.