While in space, Roger is seen wearing a captain's uniform from The Orville.
The "sun madness" premise and the music in the climax reference the 2007 Danny Boyle movie "Sunshine".
A supposed third planet between Earth and the Sun, after Venus and Mercury, turns out to be a pepperoni slice stuck on the spaceship window. This is a nod to the prank that turned into an unintentional hoax, the so-called ChorizoGate, about the outstanding performance of the James Webb Space Telescope posted on Twitter first by cosmologist Peter Coles (30 July 2022)and then physicist Etienne Klein (31 July 2022).
The car hit by the spaceship/restaurant is the Tesla launched in space by SpaceX when testing their heavy lift rocket.
The restaurant turning into a spaceship is a reference to the starship Bistromathics from Life, The Universe, and Everything by Douglas Adams.