You are the captain of a spaceship that is circling through a binary star system. Due to the gravitational forces and the rocket engines, the orbit of your spaceship looks like that:

The position of your spaceship (in AU) at the time t (in days) is given by:
x= 5sin(t) y= sin(2t) z= 0
a) How long does it take your spaceship to circle the orbit once?
b) Find an equation that calculates the velocity v(t) of your spaceship at a given time t.
c) The two stars are positioned at the points (4,0,0) and (-4,0,0): what is the distance of your spaceship to the stars at the time t = π/2 ?