解：最遠(yuǎn)點(diǎn)在?$F$?到圓?$O$?的切線的切點(diǎn)，即點(diǎn)?$Q$?
∵?$FQ$?與圓?$O$?相切，?$∠FQO=90°$?
?$PF=350\ \mathrm {km}，$??$PO=OQ=6400\ \mathrm {km}，$??$FO=6400+350=6750\ \mathrm {km}$?
∴?$cosα=\frac {OQ}{OF}=\frac {6400}{6750}$?
∴?$α≈18.53° \frac {α}2≈9.27°$?
∴?$PQ=2×6400×sin {\frac {α}2}≈2061.0\ \mathrm {km}$?
