Outline what is meant by a black hole.

An observer views a distant spacecraft that is 23.0 km from the centre of a black hole. The spacecraft contains a clock that ticks once every second and the ticks can be detected by the distant observer. In 2.00 minutes the observer counts 112 ticks of the clock.

Determine the mass of the black hole.

region of space with extreme/very large curvature of spacetime
such that light cannot escape the region OR escape speed within region is > c
Do not allow “large” or omission of degree of curvature.

time for 1 second spacecraft tick in observer frame =1.07s

\(1.07 = \frac{{1.00}}{{\sqrt {1 - \frac{{{R_{\rm{S}}}}}{{2.3 \times {{10}^4}}}} }}\) OR R_S=2.96×10³m

\(M =  \ll \frac{{{c^2} \times 2.96 \times {{10}^3}}}{{2 \times 6.67 \times {{10}^{ - 11}}}} =  \gg 2.0 \times {10^{30}}\)kg