a) The acceleration due to gravity of unsupported objects near a planet whose mass is M and whose radius is R is given by the equation g = \frac{GM}{R^{2}}

G is called the constant of gravitation and is equal to 6.67 \times 10^{-11} N \cdot \frac{m^{2}}{kg^{2}}

We convert the radius of the earth to meters to get, r\ =\ 6371\ \times10^3 m, the acceleration due to gravity g = 9.830 \frac{m}{s^{2}}

Substituting g = 9.830 \frac{m}{s^{2}} and the other known values, we solve for M to get,

M = \frac{r^{2}g}{G} = \frac{(6371 \times 10^{3}m)^{2}(9.830 \frac{m}{s^{2}})}{6.67 \times 10^{-11}N \cdot \frac{m^{2}}{kg^{2}}} = 5.979 \times 10^{24}kg

b) This is identical to the accepted value.

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**Newton's** Universal **Law** of **Gravitation** | **Physics**

(a) **Calculate Earth's mass given** the **acceleration due** to **gravity** at the **North Pole** is **9.830 m**/**s ^{2}** and the radius of the Earth is 6371 km from pole to pole. (b) ...

For more information, see **Newton's** Universal **Law** of **Gravitation** | **Physics**