Question

(a) calculate earth's mass given the acceleration due to gravity at the north pole is 9.830 m/s2 and the radius of the earth is 6371 km from center to pole. (b) compare this with the accepted value of 5.979×1024 kg .

Answer 1

(a) The value of the gravitational acceleration is given by:

$g=\frac{GM}{r^2}$

where

$G=6.67 \cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant

M is the Earth's mass

$r=6371 km=6.371 \cdot 10^6 m$ is the Earth's radius at the pole

If we use the value for g given by the problem, $g=9.830 m/s^2$, and we rearrange the equation above, we find the value of the Earth's mass:

$M=\frac{gr^2}{G}=\frac{(9.830 m/s^2)(6.371 \cdot 10^6 m)^2}{6.67 \cdot 10^{-11} m^3 kg^{-1}s^{-2}}=5.982 \cdot 10^{24} kg$

(b) The value we found for the Earth's mass is $5.982 \cdot 10^{24} kg$, and we see that this value is slightly larger than the accepted value of $5.979 \cdot 10^{24} kg$.