Something, Something, Something Dark Side

As the Griffin family is watching television, the power suddenly goes out, leading Peter to retell the story of The Empire Strikes Back.
After the "opening crawl" an Imperial Star Destroyer deploys a series of probe droids in search of the Rebel Alliance. One of the probe droids (Joe) lands on the ice planet Hoth, where the Rebels have set up a base. Rebel commander Luke Skywalker (Chris) is patrolling when he is attacked by a large wampa (Cookie Monster) and taken back to its lair. At the base, Han Solo (Peter) announces his intention to leave the Rebellion to Princess Leia (Lois) and Carlist Rieekan (Dr. Hartman), with Leia objecting to his decision, however she denies it when confronted, saying she would rather kiss George Takei. When he finds out that Luke has not yet returned, Han sets out on his "Dondon" to find him. Luke escapes the wampa lair and has a vision of his late mentor Obi-Wan Kenobi (Herbert), who tells him to go to the Dagobah system to learn the ways of the Force from Jedi Master Yoda, after offering him a bowl of Zima soup. Han quickly locates Luke, and the two are rescued soon after.
Soon after, the Empire discovers the Rebel base, and Darth Vader (Stewie) orders an attack. The Imperial fleet exits hyperspace too early, giving the Rebels time to evacuate the base while Luke leads his squadron of snowspeeders to hold off the Empire's battalion of Imperial Walkers. Imperial stormtroopers break into the base, forcing Han to escape in the Millennium Falcon with Leia, C-3PO (Quagmire) and Chewbacca (Brian), while Luke escapes in his X-wing with R2-D2 (Cleveland), stopping to see R2's niece's violin recital. The Millennium Falcon enters an asteroid field and Han decides to dock inside a cave to repair the ship. They flee when they discover they have actually landed in the belly of a space slug (Meg). Meanwhile, Luke crash-lands in the swamps of Dagobah and finds Yoda (Carl) amid the foggy landscape. Yoda trains Luke, guiding him through a series of training exercises, including watching "sweet-ass DVD releases", and a training montage that parodies Rocky IV.
Darth Vader is ordered by the Emperor (Carter) to capture Luke and turn him to the dark side of the Force. Vader recruits bounty hunters to track down and capture Luke's friends, intending to use them as bait to trap Luke, including Raggedy Andy, whom he orders to leave. With the Millennium Falcon's hyperdrive broken, Han and company escape by hiding amongst a field of disposed trash, but are tracked by Boba Fett (Ernie the Giant Chicken), after hitting a "space bum" collecting some of the garbage. Luke has a premonition that his friends are in danger and leaves Dagobah to save them, although he has not finished his Jedi training. Yoda initially doesn't want him to go, but encourages it after Luke suggests Yoda fight Vader himself.
Han and the others go to Cloud City on the planet Bespin to obtain help from Han's friend Lando Calrissian (Mort), "the only black guy in the galaxy", only to be turned over to Darth Vader. Han willingly reveals the location of Luke and the Rebel base but is tortured by being forced to listen to Paula Cole's "Where Have All the Cowboys Gone?", as punishment for clogging a toilet on the 16th floor of Cloud City, which forced Vader to use the "little pig people's" bathroom. Han is used to test a carbon freezing chamber Vader intends to use on Luke to take him to the Emperor. Leia professes her love to Han, but Han tells her to fuck off and is then frozen in carbonite for posterity. Lando later double-crosses the Empire, freeing Leia, Chewbacca and C-3PO, motivating the guards with a pizza party. Despite R2-D2 having sex with the combination lock, and subsequently being discovered by her husband, to get the door open, they are too late to stop Boba Fett from flying off with Han. Luke arrives at Cloud City and, after being briefly interrupted by Ryan Seacrest on American Idol, engages Vader in a lightsaber duel. Vader cuts off Luke's right hand. With Luke cornered and defenseless, Vader goads Luke to join the dark side, revealing that he is his father. Luke casts himself into an air shaft and, after discovering that a worker has shoved his severed hand down his pants, ends up hanging on an antenna beneath the city, calling out to Ben, Leia, and Tom Selleck. Leia senses Luke's call from within the Millennium Falcon and has him rescued. On board a Nebulon-B frigate, Luke is fitted with an artificial hand, but told to practice masturbating with a hot dog first, while Lando, dressed in Han's clothes, sets off with Chewbacca on the Millennium Falcon to rescue Han. Before the story ends, Luke is angry because of the way the story ends. Then he receives a letter from Doc Brown, a reference to the ending of Back to the Future Part II.
In the Griffins' home, the power returns as Peter finishes his story, only to get into another argument with Chris over Robot Chicken. Chris vows to not let Peter get his goat this time, but eventually storms off when Peter brings up Without a Paddle.

Question: Which hand of Luke's does Vader cut off?
Answer: right