Ask AI: Determine the separation distance between two 4,620 kg spheres with a 25.6 N gravitational force between them.

To determine this, you should use the formula for gravitational force: F = G * m1 * m2 / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the two masses, and r is the distance we want to find. Given that each sphere has a mass of 4620 kg (so m1 = m2 = 4620 kg), the gravitational force F is 25.6 N, and the gravitational constant G is 6.674 x 10^-11 N(m/kg)^2, we can plug these values into the equation and solve for r. Rearranging the equation for r gives: r = sqrt((G * m1 * m2) / F). Substituting our values in we get: r = sqrt((6.674 x 10^-11 N(m/kg)^2 * 4620 kg * 4620 kg) / 25.6 N). This simplifies to: r = sqrt((1.425135968 x 10^6 kg^2 m^3 /s^2) / 25.6 N), which equals: r = 7.42 x 10^3 meters or 7.42 km, which is the separation distance between the two spheres.