The first settlers of New Jupiter were a handful of humans, with androids to help make the planet habitable. Many generations down, the New Jupitan President, John E Hoover, faces a challenge to his hereditary role. His popularity is threatened by the Association of New Jupitan Independence – ANJI – who want to establish New Jupitan Independence. So Hoover has set up an Earth Theme Park – Earthworld. It is nearly complete and will enormously boost the planet's income from off-worlders – and thus the President's popularity. So Hoover has no intention of telling anyone that there are people entering Earthworld who are mysteriously never seen again.

Meanwhile, the president has triplet daughters to succeed him in his hereditary role. Unbeknownst to him, they have been tampering with Earthworld's androids – but why? And can the Doctor find out before the problems of New Jupiter get out of control?