C. When the center of Earth is 2 * 108 kilometers from the center of Mars, the force of gravity between the two planets is about 64.32 * 1022 newtons. The mass of Earth is about 6 * 1024 kilograms, and the mass of Mars is about 6.4 * 1023 kilograms. Using these values, estimate the gravitational constant.

Question

Kadyn Heath

Mathematics

12 September, 19:33

C. When the center of Earth is 2 * 108 kilometers from the center of Mars, the force of gravity between the two planets is about 64.32 * 1022 newtons. The mass of Earth is about 6 * 1024 kilograms, and the mass of Mars is about 6.4 * 1023 kilograms. Using these values, estimate the gravitational constant.

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Nash Stevenson · Answer 1

The equation for gravitational attractive force is: F = G (m1) (m2) / r^2. For this case, we have F = 64.32 x 10^22 N, m1 = 6 x 10^24 kg, m2 = 6.4 x 10^23 kg, and r = 2 x 10^8 km = 2 x 10^11 m.

Substituting:

64.32 x 10^22 N = (G) (6 x 10^24 kg) (6.4 x 10^23 kg) / (2 x 10^11 m) ^2

G = 6.7 x 10^-3 m^3/kg-s^2

This value is far from the expected 6.67 x 10^-11 m^3/kg-s^2, though it may be because the value for the force of gravity is quite far from the usual values in literature nowadays.