Question

You are the captain of a spaceship that is circling through a binary star system. Due to the gravi-tational 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 = 5 sin(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 yourspaceship to the stars at the time t =π2?​

Answer 1

Answer:

                                ( a ) Highest time period  

T = 2π = 6.28 seconds

                                  ( b )  Velocity

v = √ (5cost)^2+(2cos2t)^ 2

                                  ( c )  Position of two stars

r = (5,0,0) AU

The distance from the first star is

(x - x0) = 5 - 4 = 1 AU

x−x1 = 5 − (- 4 ) = 9 AU