Final answer:
The gravitational force between two masses is inversely proportional to the square of the distance between them. When the separation distance is halved, the gravitational force between two objects is quadrupled. Therefore, the new gravitational force is 72.0 units.
Step-by-step explanation:
According to Newton's universal law of gravitation, the gravitational force (Fgravity) between two masses is directly proportional to the product of their masses (M₁ and M₂) and inversely proportional to the square of the distance (R) between them. The gravitational constant (G) is used in the calculation of this force, with the equation being Fgravity = G(M₁M₂/R²).
Halving the distance between the two objects means the new distance is R/2. Thus, the distance squared term in the denominator of the gravitational equation becomes (R/2)² = R²/4. Because the force is inversely proportional to the square of the distance, if you reduce the distance to one-half of its original value, you would increase the force by a factor of 4 (since 1/(1/2)² = 4).
Therefore, if the original gravitational force was 18.0 units, the new gravitational force when the distance is halved would be 18.0 units times 4, resulting in a gravitational force of 72.0 units.