In 2286, Admiral Kirk and his crew were forced to use the sling

Question

shot effect in a stolen Klingon Bird-of-Prey to travel back in time
to the late 20th century to retrieve two humpback whales. The
stolen Klingon Bird-of-Prey traveled towards the sun at a velocity
of v, while the sun was moving towards them at a velocity of u,
then traveled around the sun (using the sun's gravitational field)
such that the stolen Klingon Bird-of-Prey was now moving in the
opposite direction from whence it started, with a new velocity,
v
new
. Find v
new
in terms of u and v, assuming the mass of the sun is
much larger than the mass of the spaceship.