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
= ![\frac{mv^{2} }{r}](https://tex.z-dn.net/?f=%5Cfrac%7Bmv%5E%7B2%7D%20%7D%7Br%7D)
and this centripetal force is also proportional to
= ![\frac{kMm}{r^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7BkMm%7D%7Br%5E%7B2%7D%20%7D)
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
= ![\frac{kMm}{r^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7BkMm%7D%7Br%5E%7B2%7D%20%7D)
which reduces to
= ![\frac{kM}{r}](https://tex.z-dn.net/?f=%5Cfrac%7BkM%7D%7Br%7D)
and then finally
M = ![\frac{rv^{2} }{k}](https://tex.z-dn.net/?f=%5Cfrac%7Brv%5E%7B2%7D%20%7D%7Bk%7D)
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>