Is it farther or further?
Old English ham "dwelling, house, estate, village," from Proto-Germanic *haimaz (cf. Old Frisian hem "home, village," Old Norse heimr "residence, world," heima "home," Danish hjem, Middle Dutch heem, German heim "home," Gothic haims "village"), from PIE root *tkei- "to settle, dwell, be home" (cf. Sanskrit kseti "abides, dwells," Armenian shen "inhabited," Greek kome, Lithuanian kaimas "village;" Old Church Slavonic semija "domestic servants").
'Home' in the full range and feeling of [Modern English] home is a conception that belongs distinctively to the word home and some of its Gmc. cognates and is not covered by any single word in most of the IE languages. [Buck]Home stretch (1841) is originally a reference from horse racing. Home base in baseball attested by 1859 (home plate by 1867; home as the goal in a sport or game is from 1778). Home economics first attested 1899. Slang phrase make (oneself) at home "become comfortable in a place one does not live" dates from 1892. To keep the home fires burning is from a song title from 1914. To be nothing to write home about "unremarkable" is from 1907. Home movie is from 1919; home computer is from 1967.
To approach purposefully; go straight toward: I saw these two guys homing in on her at the bar
[1950s+; fr the movement of an airplane, ship, missile, etc, that follows a radio beam or other signal to approach a destination or target; home is found by 1920; perhaps reinforced by the behavior of a homing pigeon]