page_title: Letters on Sunspots
section_title: Galileo's Second letter – 14 August 1612
hierarchical_section_title: Letters on Sunspots / Galileo's Second letter – 14 August 1612
caption_attribution_description: English: Geometrical diagram of differential foreshortening on the surface of the Sun and above it
context_page_description: Letters on Sunspots was a pamphlet written by Galileo Galilei in 1612 and published in Rome by the Accademia dei Lincei in 1613. In it, Galileo outlined his recent observation of dark spots on the face of the Sun. His claims were significant in undermining the traditional Aristotelian view that the Sun was both unflawed and unmoving.
  The Letters on Sunspots, was a continuation of Sidereus Nuncius, Galileo's first work where he publicly declared that he believed that the Copernican system was correct. This was the first work where Galileo used a ship, which would later become famous in Dialogue Concerning the Two Chief World Systems.
  Galileo often mentions how he does not know or understand some things. He mentions that the Sun might not be revolving, or that the spots might look different if they were viewed in different parts of the world. However, in one passage, he states that the Sun does have a motion, and he wonders what causes this motion. This is where his work established a connection between cosmology and mechanics. Galileo wrote, "I seem to have observed that physical bodies have physical inclination to some motion."
context_section_description: Galileo's second letter restates the key propositions from his first letter, and is otherwise mostly concerned with geometric proofs that the spots are on the surface of the sun rather than above it. To accompany these proofs Galileo provides 38 detailed illustrations, which allow the reader to see how his observations relate to his calculations.
  Further observations confirm what Galileo originally believed – that the spots were on or very close to the Sun, which carries them round as it rotates on its own axis.
  He notes that as sunspots approach the limit of their movement cross the visible field of the Sun, at the point where they are seen 'sideways on' from Earth, they sometimes appear as thin as a thread; if, as Apelles maintained, the spots were satellites, they would be clearly set apart from the surface of the Sun at this point.
  The apparent acceleration of the spots as they approach the centre of the Sun and their slower speeds towards the edges, are perfectly consistent with a circular rotation on the surface. The growth in apparent size of the gaps between spots as they approach the centre, and their apparent diminution towards the edges of the Sun, likewise confirm this.
  He uses a geometrical diagram to demonstrate the effects of foreshortening, showing how if the sunspots were removed from the surface of the Sun by even a twentieth part of its diameter, there would be a very observable difference in the visible foreshortening effect. The apparent distance to the observer from C to F is seven times smaller than the actual distance on the surface of the Sun from C to H; however, if the spots are just a small way above the surface of the Sun, the apparent distance from C to F corresponds to the actual distance from R to N, which is less than a third the length of C to H.  Thus by measuring the differences in the apparent distances between spots as they move across the Sun, it is possible to know with certainty whether the foreshortening corresponds to the proportion CF:CH or to some other proportion.  The changes in apparent distance observed leave no doubt on this question.
  He uses a second diagram to demonstrate the gaps between sunspots which can be seen right up to the point where they disappear at the limb of the Sun.  This, he says, means they must be low against the sun and thin, rather than high above its surface and thick.
  Galileo then counters a number of arguments that might be put forward to show that sunspots are an effect in the Earth's atmosphere. These were not arguments Apelles had advanced; rather, he had also argued against them.  Galileo's points were made for the sake of completeness, although, as he argues 'it is not necessary to waste time in re-examining every other conceivable position [for the sunspots], for anyone will immediately encounter manifest impossibilities and contradictions himself, so long as he has understood the phenomena I have recounted above.'.
  He says that because the spots change shape, it is difficult to be certain whether some complete a full revolution and reappear in changed form after disappearing round to the dark side of the Sun for fourteen or fifteen days. However he believes that this does in fact happen. 'I am inclined to this belief upon seeing a very large one appear and grow continuously while the visible hemisphere turns; since it is credible that it was generated long before its arrival, so it is reasonable to believe that it can last after its departure, such that its duration will be much longer than the time of half a revolution of the Sun. Therefore, some spots can doubtless, or rather necessarily, be seen twice by us.
  He considers arguments about the natural inclination of bodies for different kinds of motion in order to judge whether the spots are on the surface of the Sun or in its atmosphere, and concludes that the regularity of sunspot motion argues that they 'originate in a solid and firm body where the motion of the whole and of the parts is a single one.' (However, in his Third Letter he argued, against Scheiner, that 'there is no one so si
caption: Geometrical diagram of differential foreshortening on the surface of the Sun and above it
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