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Amy is collecting data for her doctoral thesis. She thinks she doesn't have any time to prepare, but Professor Farnsworth tells her that actually she's been his grad student for twelve years: she was ready six years ago. He probably should have told her. Her doctoral exam is tomorrow, and the Professor advises her to relax tonight and have a good time. The gang goes out... and Amy gets wasted. Meanwhile, Nibbler complains to Leela about being treated like an adorable pet. He wants to be treated with respect, like one of the crew. The next morning Amy oversleeps, and rushes to the lecture hall, where Professor Katz ⎯ a white cat in his lap ⎯ archly informs her that she's late. Her examining committee consists of Professor Wernstrom, Ethan "Bubblegum" Tate, and Professor Fisherprice Shpeaknspell. Amy outlines her theory about using the Earth's rotation and magnetic field to generate virtually unlimited energy by threading a superconductive wire into the Earth's core. She begins to sneeze: she's allergic to cats, but Prof. Katz won't take the cat outside. The panel is unimpressed, and her doctorate is denied. They come home... and the white cat has stowed away on their ship.
Nibbler ⎯ in his first staff meeting ⎯ tries to command respect, but the cat's cuteness distracts everyone... except for Amy and Nibbler, both of whom hate the cat as it takes up everyone's attention. Nibbler knows that nothing acts that cute without some sort of ulterior motive... and then he does a cute act to get Amy to change his diaper. They decide to watch the cat's every move. They find nothing, and Nibbler misses being Leela's shnookums. Before he can apologize and ask for a pitty-pat, they see a hypnotized Leela stroking the cat ⎯ whose collar contains a glowing, pulsing gem ⎯ and saying that Amy and Nibbler are a threat who must be spayed and neutered. The cat summons a flying saucer full of cats from space. They try to warn the crew, but everybody is now in the thrall of an adorable kitty cat. They flee, and then return to spy on the activity at Planet Express. What are they doing in the basement? Nobody can go down there without a cat. They pay a visit to Professor Katz... and find that he's actually one of those dog-operated puppets that's been adapted for use by a cat!
They return to Planet Express, and sneak into the basement. They discover that the crew, commanded by the cats, are actually building the planetary ratchet from Amy's thesis. Amy sneezes, giving them away. Once they are imprisoned, Katz explains that all cats are actually from the world of Thuban, an ideal world for cats... until their world's rotation began to gradually slow, leading to half the planet being flamingly hot, and the other half arctic-ly cold. They searched for a new home, and found Earth, which had the right rotation and magnetic field to siphon to save their own world. They call our planet "Blue-blue Shiny Ball." They landed on Earth in 3500 BC, where the Egyptians worshipped them as gods. They built the Great Pyramid of Gitz as a huge antenna to beam Earth's rotational energy to their own world... but the Egyptians pampered them so much that they grew fat and domesticated, and settled on Earth.
Now, their homeworld is nearing total destruction, but the technology to save their planet had become lost... until Amy's thesis. Now, Earth will suffer the same fate as Thuban. A static charge is needed to start the process... and 50,000 cats rub up against the Planet Express building as the device is fired up, summoned to the building by Prof. Farnsworth broadcasting the sound of an enormous can of tuna being opened. The Earth shakes as its rotation is slowed. Nibbler tries to distract the humans with his own hypnotic cuteness, but the cats retaliate by dancing together. So cute! The Earth's rotation stops completely, throwing islands and landmarks across continents... and the energy is beamed to Thuban, which begins rotating once more.
The crew comes to their senses as the cats leave. Katz tells them to enjoy being broiled alive by the sun... "and also the dead bird we left in your slipper." They try to turn the ratchet the other way to restart the Earth, but it doesn't work. The device can only apply force in one direction. As the city begins to burn, Amy has an idea: keep pushing the ratchet forwards, not backwards. Earth will start turning again... in the wrong direction, but so what? The plan works, and the rotational energy is siphoned back from Thuban to Earth. Amy is awarded her doctorate at last. She's finally done with school! How's the job market? Well... it looks like Amy will still be working at Planet Express for a while. Meanwhile, Nibbler and Leela make up; he's her schnookums once more. "You've got a bright future, Amy," says the Professor, "as sure as the sun sets in the East."