Sunspots from the past

  Jean-Dominique Cassini (1625–1712), also known as Giovanni Domenico Cassini, was an Italian–French mathematician, astronomer, and engineer. Cassini's observations are also referred in La Hire.

   11 – 20 August 1671

  The series of sunspot observations recorded from 11 August to 15 September 1671 was analyzed by Hayakawa et al. (2021a). They got an average latitude of 10 ± 1^o for the observations by Cassini on 11 – 13 August 1671 and 7.5 ± 2.5^o for Siverus on 18 August – 15 September 1671, proposing that both observers documented the same long-lived active region. Below, we expand upon these findings by analyzing sunspot longitudes and rotation rates.

  The observations by Cassini were published in two French monographs: one covering 11 – 13 August (Cassini, 1671a), and the other spanning 14 – 20 August 1671 (Cassini, 1671b). On the same year, these monographs were also reprinted in English in the Philosophical Transactions (Cassini, 1671c, 1671d) allowing a comparison of engraving accuracy between the French and English editions.

  Apparently, Cassini used an equatorial-mounted telescope invented by Christoph Grienberger (Daxecker, 2003). For detailed observations of the fine structure of sunspots, Cassini employed a seventeen-foot telescope. A three-foot glass was used for measuring the penumbra's position on the solar disk. His goal was to estimate the rotational velocity of the sunspot, which he stated as the main objective of his research.

  Cassini referred to the penumbra as a "misty crown" or "coronet". Only objects sharing this common crown were classified as spots, while tiny objects beyond the crown's boundary were described as “black points” rather than spots. Cassini noted that some barely visible points were so small that the engraver had to represent them as much larger than they actually were. On the image of the solar disk, the engraving discrepancy in the crown’s position is up to 1^o, and for the small black points, it is up to 2◦. Once, there is a discrepancy in the number of black points recorded in the French and English monographs. Both monographs depict the solar disk as slightly (5%) vertically elongated, which contrasts with Picard's measurements (Le Monnier, 1741) indicated that the horizontal diameter slightly exceeded the vertical diameter.

  Cassini made twelve detailed drawings of the sunspot group, but only the first four were transferred to the solar disk. He recorded the solar semi-diameter (15' 55''), measured the linear size of the sunspots, and regularly noted the time elapsed between the active region and the solar limb as they crossed the same "horary circle". This data allows us to map the detailed sunspot drawings onto the solar disk with accuracy up to the orientation of the sunspot group. The uncertainties in Cassini's measurement were approximately one hour for time and a few degrees for sunspot position.

  A typical observation was accompanied with the following notation: From six at night to seven, the time between the Sun's center and coronet is one time eight seconds, and another time seven seconds and half. During the initial days, Cassini measured the distance to the center of the spot, then to the inner edge of the penumbra, and finally to the front outer edge of the penumbra.

  Figure 1a shows our reconstruction of the sunspot group's positions and areas. Sunspot-group areas are, on average, 30% larger than those estimated from the original solar disk engraving (see Electronic Supplementary Materials). Between 11 and 16 August 1671, the sunspot group follows a latitude of 9.9 ± 0.5^o. However, on 17 and 18 August the latitude increases, reflecting growing uncertainty in the observations.

  The observations on 11 August and in the morning of 18 August lack details about the fine structure of the sunspot group; thus, these positions are represented schematically. The final observation on 19 August is a product of suggestion based solely on a brief note indicating that the spot was approximately its own breadth away from the solar limb. Clouds prevented Cassini from taking precise measurements that day.

  Figure 1b illustrates the derived longitudes. The black points represent the longitude of the largest leading sunspot, while the green points denote longitude of the entire sunspot group. From 15 August 1671 onward, there is a noticeable decline in the longitude values, which likely results from the observational uncertainties. This has a significant impact on the calculated rotation rate.

  From 11 to 15 August, the rotation rate is determined to be 14.1 ± 0.6^o d^-1 for the largest leading sunspot and 14.3 ± 0.6^o d^-1 for the entire group. When including data up to 18 August, the rate for the largest spot decreases to 13.9 ± 0.6^o d^-1. For the complete set of data, the rotation rates are 14.3 ± 2.1^o d^-1 for the largest spot and 14.4 ± 1.5^o d^-1 for the entire group. Continued here...

   18 October – 22 November 1672

  This series of observations was published by Cassini (1672) and Bion (1751, reprinted from 1699). However, originally the observations were carried out by Roemer and Picard.

   8 – 14 August 1676

  Analyzing the sunspot's rotation, Cassini (1676a) concluded that the sunspot (Macula) observed in August and the one from late June were distinct objects. He noted that the late-June sunspot was located farther from the Equator than the August sunspot. Hook (1677) also observed this active region and wrote that, on 8 August 1676, he counted "about six greater and smaller [spots] in one knot with their proper Nubecules".

  Figure 2(a) illustrates the position of the sunspot (la tache) as retrieved from the measurements by Picard and/or Cassini at the Paris observatory using quadrants with radii of 3 foot and 32 inches, recorded from 9 to 14 August 1676 and later published by Le Monnier (1741). Additionally, we embed sunspot drawings from Cassini (1676a, 1676b) in green. The sizes of these spots are chosen arbitrarily, and the observation times were not noted. The latitudinal position of the sunspots (3' from the disk center, as stated by Cassini) align well with the measurements of Flamsteed and Halley (Fig. 2 therein).

  To derive the heliographic coordinates of the sunspot, we assume the angular size of the solar disc to be 31' 46'' based on Picard's measurements. The resulting latitudes range from −4.6 to −9.6^o, with an average of −7.6 ± 1.8^o. Figure 2(b) shows the corresponding longitudes with a derived rotation rate of 14.2 ± 0.3^o d^-1, which aligns with Flamsteed's and Halley's measurements. This result is considered more reliable due to small scatter in longitudes (less than 1^o).

   18 November – 30 November 1676

  This sunspot group was reported by Flamsteed (Fig. 3 therein) and Picard (Fig. 3 therein). Cassini also documented this October–December sunspot. Figure 3 reprints the colored modification of the original engraving from Cassini (1730) with an overlaid heliographical grid. The image size is small, while the sunspots themselves are enlarged. Consequently, the engraving is coarse and not suitable for calculations. However, it serves as a useful illustration of the uncertainties inherent in such engravings. Further, we process more accurate engravings.

  First, we would like to present a loose translation from Cassini (1730), who tested his method of predicting the trajectory of the sunspot that appeared on 18 November 1676. He wrote: astronomers have so far depicted the position of sunspots day by day, but never described the line of their motion. This is the third sunspot to appear this year, a year in which they are more frequent than in the 20 previous years. It is the same sunspot that we saw at the end of last month [October], though we had not observed it earlier due to clouds. Mr. Picard observed it while taking the altitude of the Sun for clock correction on the morning of 30 October. Although, we cannot be certain about the duration of this type of spot (de cette sorte de Taches), which often dissipate in a few days when they form again, I believe, however, based on their size — which is larger than other spots this year — that they may reappear. To ensure the sunspot could be observed by multiple astronomers in different locations, I wrote to Mr. Oldenburg (Oldemburg in French) urging readiness for the observations. Having calculated the time of the sunspot's return and sketched the path it should follow based on my method, I searched for it on the morning of the 18th through a 20-foot telescope. I found it so close to the