Question

Our solar system is about 8.3 kpc from the centre of our galaxy. Using Newtons universal gravitation law and kepler's third law, calculate the approximate mass of our milky way if we know that the orbital velocity of the sun around the centre of the galaxy is 225 km/s

Answer 1

We can find the approximate mass of our milky way as follows:

$$F_{Net}=F_g,$$ $$\dfrac{M_{Sun}v^2}{R}=\dfrac{GM_{Sun}M_{Milky\ Way}}{R^2},$$ $$v^2=\dfrac{GM_{Milky\ Way}}{R},$$ $$M_{Milky\ Way}=\dfrac{v^2R}{G},$$ $$M_{Milky\ Way}=\dfrac{(225\ \dfrac{km}{s}\cdot\dfrac{1000\ m}{1\ km})^2\cdot8.3\ kpc\cdot\dfrac{3.086\cdot10^{19}\ m}{1\ kpc}}{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}},$$ $$M_{Milky\ Way}=1.94\cdot10^{41}\ kg.$$