Question

What is the gravitational force between two identical 5000 kg asteroids whose centers of mass are seperated by 100 m?

Answer 1

For this question we use the Newtonian relationship F = GMm/r^2.

We often use this relationship when describing one small object orbiting a much more massive one, such as the moon orbiting the Earth. In that case it is obvious that the Earth's mass is M, and the moon's mass is m. In reality it isn't extremely important anyway, but in the case of two identical masses we would ignore the convention.

So, where G is the universal gravitational constant, M = m = 5000kg, and r is the distance between the centres of mass of the two asteroids (100m):

F = GMm/r^2 = (6.67*10^-11)(5000)(5000)/(100^2) = 1.67*10^-7 N.

This answer is to three significant figures. I hope this helps you :)

Answer 2

The gravitational force between two identical 5000 kg asteroids whose centers of mass are separated by 100 m would be 1.667×10⁻⁷ N

What is gravitational force?

The gravitational force is an unobservable force that draws things together. You remain on the ground thanks to Earth's gravity, a gravitational force is force that also causes objects to fall. Gravity applies to everything that has mass. Gravity is stronger for objects with more mass.

The mathematical expression for the gravitational force is given by

F = G× m₁* m₂ / r ²

where F is the gravitational force

m₁ and the m₂ are the masses of the bodies

G is the gravitational constant which has a value of 6.67 ×10⁻¹¹

As given in the problem two identical 5000 kg asteroids whose centers of mass are separated by 100 m

F= 6.67×10⁻¹¹(5000×5000)/100²

F= 1.667×10⁻⁷ N

Thus, The gravitational force between two identical 5000 kg asteroids whose centers of mass are separated by 100 m would be 1.667×10⁻⁷ N

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