Question

The moon is 3.9 × 105 km from Earth's center and 1.5 × 108 km from the Sun's center. The masses of earth and the sun are 6.0 × 1024 kg and 2.0 × 1030 kg, respectively. Find the ratio of the gravitational fields due to Earth and the Sun at the center of the Moon.

Answer 1

The gravitational force due to moon by Earth is

$F=\frac{G(M_{Earth}M_{Moon})}{d^2}$

$F=\frac{6.67×10^{-11}(6×10^{24}×7.3×10^{22})}{(3.9×10^5)^2}=1.92×10^{26} N$

The gravitational force due to Moon by Sun is

$F=\frac{G(M_{Sun}M_{Moon})}{d^2}$

$F=\frac{6.67×10^{-11}(2×10^{30}×7.3×10^{22})}{(1.5×10^8)^2}=3.24×10^{34}N$

The ratio of gravitation force due to earth and sun on the centre of moon is

$\frac{3.24×10^{34}}{1.92×10^{26}}=1.69×10^4$