Amos wrote this song while going through a breakup with Eric Rosse, who co-produced her first two albums with her. There was a specific incident that triggered her to write it: Amos in a hotel room in Phoenix, Arizona, in April 1994 on tour for her second album, Under The Pink, when she couldn't get in touch with Rosse and went through an intense bout of anger and self-loathing. This explains the opening lines:
No one's picking up the phone
Guess it's me and me
And this little masochist
She was living her dream, playing sold-out shows, but felt tormented when she wasn't on stage - heartbreak will do that to a person. Amos realized she needed a new perspective and went on a quest to find it. She ended up in Hawaii, where with the help of a friend she did some heavy psychological lifting and realized she needed to claim her own energy instead of taking it from men. This became a these of her next album, Boys For Pele, which is named for the Hawaiian goddess of volcanos. "Hey Jupiter" was a key step on this journey; Amos wrote that the song was her "trying to step into womanhood from girlhood."
Jupiter comes into the picture because when Amos conceived this song in that Phoenix hotel room, she went into the bathroom and steamed it up, leaving markings on the mirror that she interpreted as Earth and Jupiter, who were once in love but have been separated for billions of years. She decided it was a love song from Earth to Jupiter.
This is the kind of curious song that made Amos one of the biggest online draws in the early days of the worldwide web. Internet access was slow and limited in 1996, so web surfing was a bit of a commitment. Many of Amos' fans looked her up as soon as they got their first modems, so her record company, Atlantic, used her page on their website as a marketing tool, posting exclusive photos and news on her latest developments. They also posted a 30-second sample of "Hey Jupiter" on December 15, 1995, about five weeks before the album was released. This was novel at the time because it gave fans a sneak peek right on the internet.