Tin is Jupiter in the alchemical scheme. Its symbol resembles the numeral four, and in Latin texts the metal is frequently called simply Jupiter or Jove.
Of the seven correspondences this is the one for which the reasoning is least evident, and the honest thing is to say so. Gold and the Sun, silver and the Moon, mercury and Mercury, iron and Mars, lead and Saturn all have an obvious hook in colour, speed, name or weight. Tin and Jupiter has none that the sources make explicit. The usual reconstructions appeal to position in the ordering: the seven metals were mapped onto the seven planets in their classical sequence of distance or of apparent speed, and tin falls where Jupiter falls. Some accounts associate the whiteness and brightness of tin with Jupiter's brilliance as the second-brightest planet. Neither explanation is documented as the original rationale.
What is documented is the association itself, which is stable across the corpus from late antiquity onward and appears alongside the other six in medieval and early modern texts alike. The word jovial, meaning cheerful, comes from the astrological character of Jupiter rather than from anything about the metal, and the two should not be run together.
Tin's practical role in the tradition was as a component of alloys and as a source of its oxide. Tin oxide is a white opacifier, and tin-glazed earthenware, the white surface on which maiolica, delftware and Islamic lustreware are painted, depends on it. That technology reached Europe through the Islamic world from around the ninth century.