For an object to be a black hole, the escape velocity ($v_e$) at its surface must be equal to the speed of light ($c$). The formula for escape velocity is $v_e = \sqrt{\frac{2GM}{R}}$ . To find the radius $R$ (Schwarzschild radius) where light cannot escape, we set $v_e = c$: $c = \sqrt{\frac{2GM}{R}} \Rightarrow c^2 = \frac{2GM}{R} \Rightarrow R = \frac{2GM}{c^2}$. Given: $M = 5.98 \times 10^{24}$ kg $G \approx 6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ $c \approx 3 \times 10^8 \text{ m/s}$ Substituting these values: $R = \frac{2 \times (6.67 \times 10^{-11}) \times (5.98 \times 10^{24})}{(3 \times 10^8)^2}$ $R = \frac{79.77 \times 10^{13}}{9 \times 10^{16}} \approx 8.86 \times 10^{-3} \text{ m}$. This value ($8.86 \text{ mm}$) is approximately $10^{-2} \text{ m}$ ($10 \text{ mm}$).