NASA question (spacecraft physics) 10 pts if u give me a quick site or answer?

A rocket from Earth to Mars follows two paths that are piecewise continuous. The first path is a hyperbola relative to Earth. The second path is an ellipse relative to the sun. The rocket follows the first path until the sun's gravity dominates Earth's gravity. Then the rocket does a course correction - i.e., changes its velocity vector - so that it enters a heliofocal elliptical transfer orbit from that position to Mars. If this is done correctly, it can shut down its rockets until the time comes to "put on the brakes" (i.e., change velocity again) to enter a parking orbit around Mars.