Suppose the force of gravitation between two bodies of equal masses is F. If each mass is doubled keeping the distance of separation between them unchanged, the force would become

According to Newton's Law of Universal Gravitation, the gravitational force (F) between two bodies is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (d) between them. The mathematical formula is F = G(m1*m2)/d^2. In the initial scenario, the force is F. If each mass is doubled, the new masses become 2m1 and 2m2. Keeping the distance (d) unchanged, the new force (F') is calculated as F' = G(2m1*2m2)/d^2, which simplifies to F' = 4 * G(m1*m2)/d^2. Since the term G(m1*m2)/d^2 represents the original force F, the new force becomes 4F. Thus, doubling both masses while maintaining the same separation results in a gravitational force that is four times the original magnitude.