The separation distance between the two balls, each with a mass of 0.844 kg and exerting a gravitational force of 8.45 × 10^(-11) N on each other, is approximately 2 micrometers.
The gravitational force between two masses is given by Newton's law of gravitation, expressed as F = G * m1 * m2 / r^2, where F is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses, and r is the separation distance between the masses.
In this case, both masses (m1 and m2) are 0.844 kg, and the gravitational force (F) is 8.45 × 10^(-11) N. The value of the universal gravitational constant (G) is 6.673 × 10^(-11) N m^2/kg^2.
Rearranging the formula to solve for the separation distance (r):
r = square root of (G * m1 * m2 / F)
Substituting the given values:
r = square root of ((6.673 × 10^(-11) N m^2/kg^2) * (0.844 kg) * (0.844 kg) / (8.45 × 10^(-11) N))
Calculating this expression gives the separation distance r.
r ≈ square root of (3.99 × 10^(-11) m^2)
r ≈ 2 × 10^(-6) m
Therefore, the two balls are approximately 2 × 10^(-6) meters or 2 micrometers apart.