Spaceman Jax: Lost in Spaaaace!
With more than 170 billion galaxies in the observable universe, it's more than likely that Jax is causing trouble in some other galaxy altogether. Neither the show nor the comics ever mention the Earth, and no planet is shown with our distinctive arrangement of continents. With the exception of the Space Cadet fan club pins, no reference is ever made to any of the planets in our solar system or any stellar body humans have observed.
Considering that the show was created during the atomic age of the early 1960s, with fears of the destructive power of the H-bomb running high, it's possible that in the show's timeline the Earth was destroyed - just as Spaceman Jax's home planet Tiberion 3 had been destroyed in a tug-of-war over its previous resources. In that case, perhaps the Earth's absence in storylines is simply because after four thousand years, the rest of the galaxy has simply forgotten this piece of history.
Another theory explaining where the Earth is in the Spaceman Jax Galaxy, is that it is there all along, just going under another name. Tarloc, the show's greedy industrialist bad guy, uses the profits from his Tarloc Industries to buy up planets to exploit their resources. Each planet that he buys, he renames after himself (Tarloc XVII or Tarloc XIX, for example). It sounds a little self-centered, but it's pretty darn cost-effective. So perhaps the Earth was swallowed up in his galactic land grab, and by 6354 ¾ we're known as Tarloc XXVII.