Question

the mass of sun is 2*10^30kg and the mass of earth is 6*10^24kg.if the average distance between the sun and the earth be 1.5*10^8km ,calculate the force of gravitation between them

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Answer 1

• Let the force of gravitation be f.

• Gravitational constant, G = 6.673 × 10^-11 Nm²/kg²

• The mass of the sun , M = 2 × 10³⁰ kg

• Mass of the earth, m = 6 × 10²⁴ kg

• Average distance between the sun and the earth , R = 1.5 × 10⁸ km.

Si unit of length is m.

$1 \: km \: = {10}^{3} \: m \\ \\ 1.5 \times {10}^{8} \: km = 1.5 \times {10}^{8} \times {10}^{3} \: m \\ \\ R = 1.5 \times {10}^{11} \: m$

Gravitational force ,

$f = \dfrac{GMm}{ {R}^{2} } \\ \\ = \dfrac{6.673 \times {10}^{ - 11} \times 2 \times {10}^{30} \times 6 \times {10}^{24} }{ {(1.5 \times {10}^{11}) }^{ 2} } \\ \\ = \dfrac{6.673 \times 2 \times 6 \times {10}^{43} }{1.5 \times 1.5 \times {10}^{22} } \\ \\ f= 35.589 \times {10}^{21} \: N$

The force of gravitation is 35.589× 10²¹ N