How great is the force F of mutual attraction of two spaceships with a mass of m = 10 tons

How great is the force F of mutual attraction of two spaceships with a mass of m = 10 tons each, if they approach each other to a distance of r = 100 m?

The force of mutual gravitational attraction F of two spaceships of mass m located at a distance r is determined using the law of universal gravitation: F = G ∙ m₁ ∙ m₂ / r ^ 2, where the coefficient G = 6.67 ∙ 10 ^ (- 11) N ∙ m ^ 2 / kg ^ 2 – gravitational constant. Since m₁ = m₂ = m, then:

F = G ∙ m ^ 2 / r ^ 2.

From the condition of the problem it is known that two spacecraft are attracted with masses m₁ = m₂ = m = 10 t = 10000 kg each, approaching to a distance of r = 100 m.Let us substitute the values ​​of the quantities in the calculation formula:

F = 6.67 ∙ 10 ^ (- 11) N ∙ m ^ 2 / kg ^ 2 ∙ (10000 kg) ^ 2 / (100 m) ^ 2;

F = 6.67 ∙ 10 ^ (- 5) H = 66.7 μN.

Answer: the force of mutual attraction of two spaceships is 66.7 μN.