This is a remake of the song by Hy Zaret And Lou Singer, performed by folk singer Tom Glazer on the album Space Songs (Motivation Records, 1959). The album has been restored, in high fidelity, by Argosy Music. Information on Space Songs, as well as a free PDF songbook and links to purchase the album and its five science-themed counterparts can be found here.
The origin of the chorus and of the facts in the song come from a book titled "Stars: A Guide to the Constellations, Sun, Moon, Planets and Other Features of the Heavens" written by professors Herbert Zim and Robert Baker, copyright 1951 by Simon and Schuster.
The original melody to this song is taken from The Girl I Left Behind Me, a traditional military folk song sung for departing troops. A midi file and lyrics are available here.
The song states that the sun is so hot that everything in it is a gas; however, this is incorrect. The sun is so hot that all gases are ionized and turned into plasma, which is a very highly-charged state of gas considered a state of matter separate from gas. To address this misinformation, TMBG wrote the song "Why Does The Sun Really Shine?" for the album Here Comes Science.
TMBG have been performing their version since at least 1985, with a performance from that year appearing on the television show Nick Rocks.
A performance of the song, from an April 6, 2002 concert at Newport Music Hall, Columbus, OH (with tour manager Brendan Hoffman as fire-eater), appears as a bonus video on the Direct From Brooklyn DVD.