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Calculate the force of gravitation between the earth and the S... - Science
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 \times 10^{24} kg and of the Sun = 2 \times 10^{30} kg. The average distance between the two is 1.5 \times 10^{11} m.
Given:
Mass of the Sun (M) = 2 \times 10^{30} \text{ kg}
Mass of the Earth (m) = 6 \times 10^{24} \text{ kg}
Distance (d) = 1.5 \times 10^{11} \text{ m}
Gravitational constant (G) = 6.67 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}
Calculation:
F = G \frac{M \times m}{d^2}
F = \frac{(6.67 \times 10^{-11}) \times (2 \times 10^{30}) \times (6 \times 10^{24})}{(1.5 \times 10^{11})^2}
F = \frac{6.67 \times 2 \times 6 \times 10^{(-11 + 30 + 24)}}{2.25 \times 10^{22}}
F = \frac{80.04 \times 10^{43}}{2.25 \times 10^{22}}
F = 35.57 \times 10^{21} \text{ N}
F \approx 3.56 \times 10^{22} \text{ N}