(a) Assuming (incorrectly) that the high-velocity stars known to Oort in 1927 are near the escape speed from the Galaxy, estimate the mass of the Milky Way. For simplicity, take the directions of the velocity vectors to be radially away from the Galactic center and assume that all of the mass is spherically distributed and is interior to R0. (This calculation is meant only to be an order-of-magnitude estimate.) Compare your answer with the mass estimate given in Example 24.3.1.
(b) Repeat your calculation using the extremely high-velocity stars discussed on page 908. What could account for the extra mass compared to your answer in part (a)?
(c) Comment on the difficulty of determining the true mass of the Galaxy on the basis of observations of stars in the solar neighborhood.