The coordinates for this episode point to Castor, which is one of the two brightest stars in the constellation Gemini. Castor is located at the very precisely measured distance of 49.152 light years (15.070 pc) [1], which means that it's fairly close in astronomy terms, and it has a magnitude of 1.6 [2], so it's easily visible without a telescope and even relatively easy to find in urban areas with light pollution. The star is also known as Alpha Geminorum, but because even the professional astronomers call it Castor, I will also use the name Castor. As an additional note, the "alpha" star in a constellation is usually the brightest, but Pollux, which is labelled Beta Geminorum, is actually slightly brighter [3].
Both Castor and Pollux are very famous twins in Greek mythonology, but they were actually known individually as Kastor and Polydeukes and together as Dioskouroi [4]. Castor and Pollux are the Latinized versions of their names, and Gemini is the Latin name for the twins together [4]. Anyhow, according to the myths, the twins had the same mother, who was Queen Leda of Sparta, but different fathers. To maintain the "safe for kids" rating for this podcast, I will, without going into detail, say that Leda was first visited by Zeus in the form of a swan, and then she spent time with her husband, King Tyndareus, later in the day [4]. As a result, nine months later, she gave birth to Castor, who was Tyndareus's son and therefore mortal, and Pollux, who was Zeus's son and therefore immortal [4].
When they grew up, Castor was apparently a good horseman, while Pollux was a good boxer, and they went on a lot of adventures together [4]. Their most famous adventure was their trip with Jason and the Argonauts' in their quest for the Golden Fleece [4], but a lot of references also mention their participation in the Calydonian Boar Hunt with Meleager [5]. Later, in a clash with two other men over their fiancees, Castor was killed [4, 5]. The bereaved Pollux then pleaded with Zeus to make his brother immortal, and thus, Castor and Pollux were placed in the constellation Gemini [4, 5].
That's a really brief summary of the Greek mythology of Castor and Pollux. The stars in this constellation are not always identified as "twins" by other cultures, but, rather interestingly, they are treated as twins in ancient Babylonian astrology [6], which is probably the origin of the Greek and Roman versions of the constellation.
Now, in terms of science, the main thing that can be said about Castor is that it is not just a single star. A large portion of this description of the Castor system was taken from a paper published in 2022 by Guillermo Torres et al. [1], so if you really want to read a detailed analysis of this system, go check out that paper. I also hope I don't confuse anyone with the sheer number of numbers I am going to be using.
Anyway, people originally thought that Castor was just one star, but in very early telescope observations in 1718 and 1719, James Pound and James Bradley were able to see what they thought were two separate stars [7]. These objects were given the designations Castor A and Castor B. This was the first time that anyone had been able to identify what was a physically bound pair of stars in the sky. So, at this point, people know that the Castor system contained two stars.
In 1897, Aristarkh Belopolsky identified that the spectrum of Castor B was being Doppler shifted in a periodic way that was consistent with two stars orbiting each other [8]. Hence, Castor B was labelled a spectroscopic binary system. In 1906, Heber D. Curtis discovered that Castor A was also a spectroscopic binary [9]. That's four stars so far.
Next, around 1916, a much fainter star named YY Geminorum was identified by Walter Adams and A. H. Joy as being at the same distance and as moving in the same direction as Castor [10] This led people to conclude that YY Geminorum was actually orbiting Castor A and Castor B, so it was given the new name Castor C. Additional analyses of those data revealed that Castor C was also an eclisping binary, which means that the orbits of the stars are aligned so that one will pass in front of the other while they go around each other [11]. That now gives us six total stars in the Castor star system.
OK, so just to review everything, Castor is basically a star system with six stars. Two of the stars are part of a binary object (or subsystem) called Castor A, another two stars are in Castor B, and the final two stars are part of Castor C. Let's now talk about each of those subparts of Castor. Castor A consists of a whitish hydrogen-burning star larger than the Sun with a red dwarf orbiting it. The two stars are separated by a distance of 0.12 AU (or 0.12 times the distance from the Sun to the Earth, or closer than Mercury is to the Sun) and orbit each other once every 9.2 days [1]. Castor B looks very similar to Castor A except that the two stars are separated by a distance of 0.052 AU and orbit each other once every 2.9 days [1]. Castor C contains two red dwarfs, so it looks much fainter. These two red dwarfs are separated by roughly 1.4 million km (or about 3.5 times the distance from the Earth to the Moon) and orbit each other once every 19 hours and 33 minutes [12]. As a side note, a couple of these red dwarfs in Castor A, B, and C apparently experience a lot of starspot activity and flares because they produce a notable amount of X-ray emission that seems associated with this type of thing [13, 14, 15].
Castor A and Castor B are separated by a distance of 101 AU and orbit each other once every 459 years [1]. Castor C, on the other hand, is really far away from everything else. It is separated from Castor A and B by a distance of about 1100 AU and orbits Castor A and B approximately once every 14000 years [12]. That's slow.
One of the interesting things about all of this is that the stars do not orbit each other in the same plane [1]. In other words, the plane of the orbits of the two stars in the Castor A system, the plane of the orbits of the two stars in the Castor B system, the plane of the orbits of the two stars in the Castor C system, the plane of the orbits of Castor A and Castor B around each other, and the plane of the orbit of Castor C around everything else are all misalighned. I didn't see any discussion about this, but it might be possible that this messy six-star system did not form out of a nice, flat disk of gas like the Solar System did but instead formed out of multiple disks of gas that produced stars that became gravitationally bound later. Alternately, all six of the stars did form out of a single flat disk of gas, but then gravitational interactions between these stars and other stars changed the orbits of the stars in the Castor system.
One important point about Castor is that, because it is so close and because the orbits of the stars in this system have been measured so accurately, it has been possible to make really precise measurements of the masses of the stars in this system. That is particularly important, as it means that when astronomers see any other individual stars that look similar to any of the stars in the Castor system, they will be able to assume that those stars have masses matching the similar-looking stars in the Castor system.
Anyway Castor is indeed a very complicated star system. It kind of makes the entire mythological story about Castor, including why he is mortal while his brother is not, seem very straightforward.