Imagine a space rock that starts at rest at the Lagrange point between the sun and our nearest stellar neighbor, Alpha Centauri. That would put it at about 2 light years away from the sun.
Now, it gets nudged slightly toward the sun. How fast will it be going when it nears the sun?
I used the formula for instantaneous velocity of a falling object that has traveled distance over a large fall distance, found on this Wikipedia page:
Using the following values:
G = 6.674 × 10^−11 N·m^2/kg^2
M = 1.989 × 10^30 kg
r = 695,700,000 m
d = 2 light years = 9.4607 × 10^15 m
I calculate that by the time the space rock reaches the sun, it is traveling at 617,752 m/s. I would think that this would be the minimum speed of any interstellar object that reaches us because, presumably, it would already have some nonzero speed when it enters the sun's gravitational influence.
However, news reports say that ʻOumuamua is only traveling at 26,330 m/s. Why am I off by a factor of 23?