Why is Telemachus sent to Sparta?

Telemachus needs to find out what happened to his father, Odysseus. The wise Nestor tells him that, in the wake of the Achaeans' victory at Troy, the king of Sparta, Menelaus, had a huge falling-out with his brother. Menelaus set sail for home while Agamemnon delayed his departure from Troy to continue sacrificing to the gods. Nestor went with Menelaus while Odysseus stayed behind with Agamemnon—that was the last that Nestor saw of Telemachus's father. If Telemachus wants to find out what happened to his father, then perhaps Menelaus might be able to shed some light on the subject.
So Telemachus sets sail for Sparta with Nestor's son Pisistratus in tow. When they arrive at Menelaus's court, the king regales the two young men with tales of Odysseus's daring and courage during the Trojan War. He also tells Telemachus that Proteus, the shape-shifting man of the sea, told him that Odysseus was still alive and was the captive of the sea nymph Calypso on the island of Ogygia. Heartened and encouraged by this good news, Telemachus and Pisistratus return to Pylos. From there, will make their way back to Ithaca.