1. Since angular momentum L = mvr and is the same throughout the star's orbit, if the r is 1/2 then the v must be twice as high at periastron than when the star is at apastron.
2. If the white dwarf has the same angular momentum as the Sun does today,
and its radius decreases by a factor of 100, then the velocity of a point on
the "surface" must increase by a factor of 100. Currently a point at the solar
equator moves through
circumference =
2
r = 2
x 7 x 105 km
in 25 days or at a velocity of 2.2 km/sec.
As a white dwarf this would increase to 220 km/sec.