Question

Calculate the mass of earth, given g=9.8 m s^-2,r=6.4$\times$10⁶ m, and G=6.6 $\times$10^-11 N m ² Kg^-2.

Answer 1

Step 1: Given

The radius of earth =6.4$\times$10⁶ m

Acceleration due to gravity on earth g=9.8 ms^-2

Gravitational constant =6.6 $\times$10^-11 N m ² Kg^-2.

Step 2: We know that g=$\frac{GM}{r^2}$or

M=$\frac{g{r}^2}{G}$

Putting the values we get,

M=9.8$\times$(6.4$\times$10⁶)²/6.6 $\times$10^-11 kg

M$\approx$6 $\times$10²⁴ Kg.