# Your ship is essentially unpowered through te space. An asteroid almost dead ahead has a mass…

Your ship is essentially unpowered through te space. An asteroid

almost dead ahead has a mass about 1000 times the ship’s mass m.

You are moving with speed v0 in +x direction while asteroid is

moving in -x direction at v0/1000. With directional thrusters, you

can make the ship pass close enough to the asteroid so that

asteroid’s gravitational field will deflect the ship’s direction of

motion by some angle θ that depends exactly on how close the ship

passes. ( The figure shows “after” situtation. ) Encounter with

asteroid can be considered “elastic” collision as you are far from

asteroid both initially and finally, so gravitational potential

energy between ship and asteroid is essentially zero both initially

and finally.

a) You want to know whether this encounter might boost the

ship’s speed, helping ship escape. Can it?

b) If so, what is angle θ that yields highest final speed?

FINAL y asteroid ship d