Sigh. Where's Neil deGrasse Tyson when you need him?
But actually, this one's not as complicated as it sounds. Finch tells Violet a story about an April Fool's Day hoax played by a famous astronomer, Sir Patrick Moore. (Yup, this happened in real life.)
"[Moore] told viewers that they could experience the phenomenon by jumping in the air at the exact moment the alignment occurred. If they did, they would feel weightless, like they were floating." (34.17)
The public bought it hook, line, and sinker, and soon enough Moore was getting calls from all sorts of people who said they floated across their backyards like balloons. The phenomenon wasn't real, of course; it was just a joke. What's important is that it felt real.
Finch considers the Jovian-Plutonian effect to be a symbol for romantic love. He even calls Violet "my Jovian-Plutonian gravitational effect" (45.18). (Talk about nerdy pet names.) What can we say? Sometimes people make their own magic in this world.