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 ?
1
Expert's answer
2019-05-14T10:15:37-0400
a)
Period of time to circle orbit at once equal to
2π≈6.282π≈6.282π≈6.28days
b)
v(t)=vx(t)2+vy(t)2(1)
where
vx(t)=dtdx=5cos(t)
vy(t)=dtdy=2cos(2t)
We got:
v(t)=25cos(t)2+4cos2(2t)
c)
x=5, y=0, z=0
distance to the star at the point (4,0,0) is equal to 1 a.u., distance to the star at the point (-4,0,0) is equal to 9 a.u.
Comments