Two balls, each with a mass of 0.845 kg, exert a gravitational force of 8.43 × 10−11 N on each other. How far apart are the balls? The value...

The Universal Gravitation Law states that the gravitational force between two objects is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.  The proportionality constant is the universal gravitational constant G. The equation for this law is:

`F = G (m_1 m_2)/d^2`

You need to solve for d, the distance between the two objects. Here's the data you've provided:

F = 8.43 x10^(-11) N

m1 = m2 = 0.85 kg

G = 6.673 x 10^(-11) N (m^2)/(kg^2

Now we'll substitute these values into the equation:

`d^2 = G(m_1 m_2)/F = 6.673 x 10^(-11)(N m^2/(kg)^2)(0.85kg)^2/(8.43x10^(-11)N`  

`d=sqrt(0.57m^2) = 0.75 m`

The distance between the objects is 0.75 meters.