Answer:
<em>The mass of the object is 745000 units of the sun</em>
Explanation:
We know that the centripetal force with which the stars orbit the object is represented as
=
and this centripetal force is also proportional to
=
where
m is the mass of the stars
M is the mass of the object
v is the velocity of the stars = 10^6 m/s
r is the distance between the stars and the object = 10^14 m
k is the gravitational constant = 6.67 × 10^-11 m^3 kg^-1 s^-2
We can equate the two centripetal force equations to give
=
which reduces to
=
and then finally
M =
substituting values, we have
M = = 1.49 x 10^36 kg
If the mass of the sun is 2 x 10^30 kg
then, the mass of the the object in units of the mass of the sun is
==> (1.49 x 10^36)/(2 x 10^30) = <em>745000 units of sun</em>