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Battle against Raditz
Main article: Saiyan Saga
Raditz was sent to Earth on Frieza's orders and to uncover why his brother Kakarot had not destroyed all lifeforms on the planet. When arriving on the 12th of October, 761, he found his brother who was now known as Goku. After revealing Goku's origins, Raditz then attacked and kidnapped Goku's young son, Gohan. Goku and Piccolo proceeded to team up to defeat Raditz, putting their differences aside just for this occasion. After a difficult struggle against the Saiyan brute, Piccolo decided to use the Special Beam Cannon in an attempt to kill Raditz. Goku attempted to stall him but proved no match for his older brother. However, when he then grabbed onto Raditz's tail, the Saiyan was immobilized for a short time. Raditz was able to plead Goku to let him go, a trick that would allow him to escape and resume his carnage. Raditz proceeds to kill Goku, but hearing his fathers cries, Gohan became furious and unleashed his hidden powers, allowing him to smash into Raditz, badly injuring him. Goku then grabbed onto Raditz and put him in an arm hold long enough so that Piccolo could kill him. Both Goku and Raditz were killed by the beam, but before Raditz died he gave the message about the Dragonballs to his cohorts, Vegeta and Nappa who promptly decided to use said Dragon Balls to wish for immortality.
Battle on Arlia (anime only)
On their way to Earth, Nappa and Vegeta landed on a planet inhabited by an insect-like race. The two Saiyan warriors decided to allow themselves to be captured by King Moai's soldiers and imprisoned. King Moai ordered them to fight his soldiers, whom Vegeta and Nappa effortlessly killed. King Moai's pet known as Yetti was unleashed to kill Vegeta and Nappa, but the monster was also annihilated with ease. They then proceeded to kill the King himself, much to the praise of the prisoners, one of which regarded them as heroes. As they leave the planet, Vegeta decides to destroy it.
Arrival on Earth
Roughly a year later on the 3rd of November, 762, the two Saiyans arrived on Earth. Upon arrival, Nappa blew up the East City, much to the dismay of Vegeta who remarked that he could destroy the Dragon Balls by doing such foolish things. They then use their scouters to identify two warriors on the planet: Piccolo and Gohan.
Battle against the Saibaimen
After arriving on the battlefield, the Saiyans stood off against Piccolo, Krillin, and Gohan. In a strange turn of events, Nappa planted some seeds and put a strange green liquid on them. Six little green men known as Saibamen then appeared and attacked the three warriors. Yamcha, Tien Shinhan, and Chiaotzu then appeared and each fighter took a turn to combat the Saibamen. Tien Shinhan fought first and defeated a Saibaman, which was then killed by Vegeta for it's failure. Yamcha then fought the next one, but after believing he had won the fight, was killed when it grabbed him and self destructed. Krillin then became enraged and killed the rest, apart from one Piccolo killed after it attacked Gohan.
Nappa then fought the five warriors apart from Gohan, whom was shaken with fear. In an attempt to stop the Saiyan brute's onslaught, Chiaotzu then self destructed with the same intentions as the Saibaman that killed Yamcha, but failed to take the Saiyan down. Tien attacked Nappa in an outrage, only to have his hand smashed off. He then focused all his energy into one spectacular Spirit Tri-Beam, but only managed to damage Nappa's armor. Because of the sheer amount of energy used from the attack and literaly puting his life in the attack, Tien promptly dies. With only three fighters left, Nappa and Vegeta agreed to wait for Goku to arrive. Eventually, the Saiyans grew tired of waiting and the battle continued. Nappa nearly killed Gohan, but Piccolo blocked the attack with his entire body, sacrificing his life to save Goku's son. Gohan then used all of his sheer rage in a Masenko attack, however, it failed to successfully damage Nappa. Before Nappa could kill the young warrior, Goku arrived and fought the Saiyan. Nappa was quickly beaten by Goku's Kaioken attacks. Because of his failure, Vegeta kills Nappa, and proceeds to take on Goku, in a cataclysmic battle that would shape the entire future.
Goku vs. Vegeta
Goku and Vegeta then fought each other in an epic struggle. Vegeta, however, quickly gained the upper hand, but Goku gained more power with the Kaioken attack and then surpassed Vegeta with the 3x Kaioken attack. Vegeta then attempted to destroy the Earth using the Galick Gun attack, which Goku countered with a x3 Kaioken Kamehameha and won the struggle by increasing to Kaioken x4. After being injured, Vegeta created an artificial moon, transforming himself into a Great Ape. He then attacked Goku and nearly brought him to the brink of death before Gohan distracted him so Krillin could cut his tail off with the Destructo Disk. This failed after Vegeta dodges it, but Yajirobe then cut the tail with his sword, bringing Vegeta back to his normal form. Vegeta then proceeded to thrash Yajirobe and then tried to kill Gohan, however, Krillin used Goku's Spirit Bomb and threw it at Vegeta, badly injuring him. However, the might of the Saiyan Prince Vegeta continued to hold up, and he attacked them again, only to have Gohan transform into his Great Ape form after looking up at the artificial moon. Vegeta then cut his tail off, but Gohan as a Great ape fell on top of him, nearly killing him. Krillin then tried to kill Vegeta, but Goku told him to give him mercy, as he hoped Vegeta would turn to good as Piccolo did.
Gohan, Krillin and Bulma then went to Planet Namek to use the Namekian Dragon Balls to bring their friends back to life. Vegeta had the same plan in becoming immortal but so did his master Frieza. This set in motion the events of the Battle on Planet Namek.