  We study small points for the Arakelov height on the projective line. First,
we identify the smallest positive value taken by the Arakelov height, and we
characterize all cases of equality. Next we solve several archimedean energy
minimization problems with respect to the chordal metric on the projective
line, and as an application, we obtain lower bounds on the Arakelov height in
fields of totally real and totally p-adic numbers.
