The one where Hepesh leads a revolt against the royal house of Peladon...
The first few scenes of episode four feel like one huge info-dump on the part of writer Brian Hayles, who tries to have his characters (principally the Doctor) explain everything that's happened in one long summary and Q&A. Arcturus has been exposed, and destroyed by Ssorg, reduced to nothing more than a gooey green blob with a disgorged eyeball (it's not as if he consisted of very much to start with!).
The Doctor explains that Arcturus and Hepesh were in cahoots, and that Hepesh's ultimate aim was to unseat King Peladon and seize control of the planet for himself, thereby preserving its ancient customs and ridding his beloved people of the Galactic Federation altogether. This doesn't quite ring true with me because at no stage did Hepesh come across as your typical power-mad conspirator. All he really wants is for progress to go away. He is not a man who embraces change; he prefers tradition and custom. He's the sort of man who catches the same bus to work every day for 40 years and always sits on the same seat, reading the same newspaper, and doing the same crossword.