How can a rocket change direction when it is far out inspace and essentially in a vacuum?

A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ? = 2.67 × 106 g/m3 and volume V =1.71 × 1012 m3. Recall that the universal gravitational constant is G = 6.67 × 10-11 (Nm2)/(kg2).

On Oct 31 2015, massive asteroid TB145 nicknamed "Spooky" passed near the Earth vicinity. The measured diameter of the asteroid: 600meters, and its speed relative to the Sun: 30.5 km/s. (NOTE you are not given the parameters of collision, so they become important part of the "worst case -best case scenario.") Treat the asteroid as spherical object with the density of between 3g/cm³ to 4g/cm³. Treat an Earth's orbit around the Sun as a perfect circle of radius =150 x 106 km. Take one year to be 365.24days. Find the worst case scenario for the collision of such object with the Earth and find the Maximum energy released in the completely inelastic collision of this object with Earth. State your answers to the nearest mega-ton of TNT. (1 megaton of TNT= 4.184 X1015J). Your Answer: Answer