Question

You are a navigator on board the Orville, in charge of deciding the ship's path as you explore a distant star system. Visible in the system are an 15 solar mass blue star and a 0.5 solar mass red star. A previous mission's log notes there is also a 4 solar mass black hole in the system, but its coordinates weren't entered by their navigator, so you don't know exactly where it is.
Define a reference frame with fixed to your ship (with you at the origin), the x-axis pointing toward the blue star and the x-y plane containing both stars. The blue star is 700 Gm away along the x-axis, while the red star is 765 Gm away in a direction 14 degrees below the x-axis (i.e., in the fourth quadrant).
a) Draw a picture of the situation, and find both stars' positions in component form.
_{blue star} = [  ,  ] Gm
_{red star} = [  ,  ] Gm

b) Assume the system's members' orbits are all circular, moving the same direction, and going about the center of mass of the system. The blue star is moving directly in the +y direction, and the red star is moving 45 degrees between +x and +y. Assuming you're at rest relative to the center of mass, find the location of the center of mass relative to you at the origin.
_CM = [  ,  ] Gm

c) Given your results above, what is the black hole's position, and in approximately what direction is it moving in?
_{black hole} = [  ,  ] Gm
--- -y -x +x +y

Are you safe at your present location?

Answer 1