Question

 The mass of Earth is approximately 6.0 x 10²⁴ kg. What would the acceleration due to gravity be on the surface of planet Q which has a mass of 5.0 x 10²⁴ kg and a radius equal to the radius of Earth?  

  

Answer 1

Acceleration due to gravity is $G \frac{M}{r^2}$.

For Earth, $g = G \frac{M_E}{r_E^2}$, and for planet Q it is: $g' = G \frac{M_Q}{r_E^2} = g \cdot \frac{M_Q}{M_E} = 9.81 \frac{m}{s^2} \cdot \frac{5 \cdot 10^{24} kg}{6 \cdot 10^{24} kg} = 9.81 \cdot {5}{6} \approx 8.18 \frac{m}{s^2}$.