Using G = 6.67 × 10⁻¹¹ N m²/kg², M = 6 × 10²⁴ kg and R = 6.4 × 10⁶ m, what is the escape velocity for the earth?

1. Escape velocity is $v_{esc} = \sqrt{\dfrac{2GM}{R}}$. 2. Numerator: $2GM = 2 \times (6.67\times10^{-11}) \times (6\times10^{24}) = 80.04\times10^{13}$. 3. Divide by $R$: $\dfrac{80.04\times10^{13}}{6.4\times10^{6}} = 1.2506\times10^{8}$. 4. Square root: $v_{esc} = \sqrt{1.2506\times10^{8}} \approx 11.18\times10^{3}\text{ m/s}$. 5. So $v_{esc} \approx 11.2\text{ km/s}$. (3.08 km/s is GEO orbital velocity — rule out.) 6. Hence the earth's escape velocity is about 11.2 km/s. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 10 "Space Missions", p.150_