Grandpa Gohan is Son Goku's adoptive grandfather. He is a master of material arts, and teaches Goku karate, as well as the Janken fighting pose. He is killed by Goku after transforming at the full moon, though he does not find out about this until later in the Saiyan saga.
When Goku first landed on Earth, his mission was to, in time, destroy the entire human race and sell the planet to another race. Being a Saiyan, who are known to be very aggressive and short-tempered, Goku was very violent and unnaturally strong. Eventually his attitude completely changes after surviving a near-fatal plunge down a deep ravine.
Grandpa Gohan makes his second appearance during the Fortuneteller Baba saga, as the fifth fighter. He makes his final appearance at the end of dragonball where Goku and Chi-Chi are trying to repair the magical furnace that set the Ox-King's castle ablaze.
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Goku's son Gohan is named after his Grandpa Gohan only because the baby went without a name for a while, until the name "Gohan" came into conversation, and the baby laughed because he liked the name, so they Chi-Chi, Goku, and the Ox-King decided to name him that.