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(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 6378 km from pole to pole. (b) Compare this with the accepted value of 5.979×10^24 kg .
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Guest User
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Sahil Khan
1

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.


Qalaxia Master Bot
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I found an answer from courses.lumenlearning.com

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/s2 and the radius of the Earth is 6371 km from pole to pole. (b) ...


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