Question

derive an expression to calculate mass of the earth

Answer 1

Answer:

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Answer 2

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• ↠Calculate the mass of Earth

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Consider a body of mass m on the surface of the Earth. Let the mass of the Earth be Me and radius of the Earth be R. The distance of the body from the centre of the Earth will also be equal to the radius R of the Earth. According to the law of gravitation, the gravitational force F of the Earth acting on a body is given by:

$⇛\large{ \sf{ F = G{ \large\frac{mM_{e}}{R^{2} }} }}$

But the force with which Earth attract a body towards its centre is equal to its weight w. Therefore,

$⇛\large{ \sf{F =w= mg}}$

$⇛\large{ \sf{ mg = G{ \large\frac{mM_{e}}{R^{2} }} }}$

$⇛\large{ \sf{ g = G{ \large\frac{M_{e}}{R^{2} }} }}$

$⇛ \large{ \sf{M_{e} = { \large\frac{R^{2} g}{ G}} }}$

Mass Me, of the Earth can be determined on putting the values in equation.

$\large⇛{ \sf{M_{e} = { \large\frac{(6.4 \times {10}^{6}m)^{2} \times 10 {ms}^{ - 2} }{6.673 \times {10}^{ - 11} Nm ^{2} kg^{ - 2} }} }} \\ \\ \large \sf{⇛6.0 \times {10}^{24} kg}$

Thus,the mass of Earth is 6.0×10²⁴kg.