In: Physics
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) c) Given your results above, what is the black hole's
position, and in approximately what direction is it moving
in?
black hole = [ , ] Gm
Are you safe at your present location?