Determining the mass of the black hole at the centre of the Milky Way

[moonkey]

Homework Statement

(2) A star orbits the centre of our Galaxy in a plane perpendicular to our line of sight.
If the angular speed of this star in the sky is 40 mas (milli-arc-seconds) per year,
calculate its velocity. Assume that the distance of the Galactic centre is 8 kpc.
(3) If the angular displacement of the star in (2) above from the Galactic centre is 0.1 arc
second, calculate the mass of the black hole in the Galactic centre.

Some numbers you might need:
Distance to Vega = 8.1 pc
Speed of light (c) = 3×108 m s−1
Planck constant (h) = 6.63 × 10−34 J s
Solar mass (M⊙) = 2 × 1030 kg
Solar Luminosity = 3.85 × 1026 W
1 pc = 3.086 × 1016 m

Homework Equations

The Attempt at a Solution

I calculated the speed of the star in question 2 to be 761159.4525m/s (or 761.16km/s) by converting the arcseconds/year into rads/s for ω and used v=ωr (r being 0.5*8kpc)

I just don't understand question 3. Can anyone indicate to me how I should go about this or even what it actually means? I don't think these questions are phrased very well.

 

[Mr.A.Gibson]

You can use the velocity you calculated, along with equation for circular motion to find the acceleration of the star. Then use the law of universal gravitation to find the mass of the black hole

a = v^2/r
F = ma
F = mv^2/r = GMm/r^2

v^2 = GM/r

M = rv^2/G