Calculate the rotation velocity of stars 4.0 kpc from the centre of the galaxy. The average density of the galaxy is 5.0 × 10^–21 kg m^–3.

Explain why the rotation curves are evidence for the existence of dark matter.

v = «\(\sqrt {\frac{{4\pi G\rho }}{3}} r\)» \( = \sqrt {\frac{4}{3} \times \pi  \times 6.67 \times {{10}^{ - 11}} \times 5.0 \times {{10}^{ - 21}}}  \times \left( {4000 \times 3.1 \times {{10}^{16}}} \right)\)

v is about 146000 «m s^–1» or 146 «km s^–1»
Accept answer in the range of 140000 to 160000 «m s^–1».

rotation curves/velocity of stars were expected to decrease outside core of galaxy

flat curve suggests existence of matter/mass that cannot be seen – now called dark matter