Question

the asteroid has a mass 7.395x10^20 kg and a radius of 539.7km. what is g on the surface? the value of the universal gravitational constant is 6.67259x10^-11 N*m^2/kg^2
answer in units of m/s^2

Answer 1

The asteroid has a mass $7.395 \times 10^{20} \, \mathrm{kg}$ and a radius of $539.7 \, \mathrm{km}$. What is $g$ on the surface? The value of the universal gravitational constant is $6.67259 \times 10^{-11} \, \mathrm{N}^{2} \, \mathrm{m}^{2} \, \mathrm{kg}^{-2}$.

Answer in units of $\mathrm{m/s^2}$.

Solution:

$$\begin{array}{l} F = G \frac{M * m}{R^{2}} \\ F = m * g \\ m * g = G \frac{M * m}{R^{2}} \\ g = G \frac{M}{R^{2}} \\ g = 6.67259 \times 10^{-11} \, \mathrm{N} * \frac{m^{2}}{kg^{2}} * \frac{7.395 \times 10^{20} \, \mathrm{kg}}{(539700 \, m)^{2}} = 0.1694 \, \mathrm{m/s^2} \end{array}$$