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In astrology and alchemy (for gold), a variant with a face, 🌞︎, is sometimes seen. This does not occur in astronomy, botany or (obsolete) chemistry.
Etymology
The shield of the sun god Apollo, with a boss in the center. Medieval replacement of ⟨🜚⟩, the sun with a single ray, which in ancient times had replaced a sun orb surrounded by multiple rays.
Compare the Egyptian hieroglyph ⟨⟩ and the Chinese character ⟨⟩, both of which mean 'sun' and 'day'.
A subscript to variables in mathematical equations, such as π☉ (solar parallax).
1803, Robert Patterson, The Papers of Thomas Jefferson, volume 40 (in English), Princeton University Press, published 2013, page 71:
Suppose the apparent angular distance of the sun & moon's nearest limbs [...] to be 110°.2′.30″ the app. alt of ☉'s lower limb measuring 20°.40′ and that of ☽'s lower limb 35°.24′