Final answer:
To reduce the gravitational force between the Earth and the Sun to one-fourth its current value, we would need to double the distance between the two bodies.
Step-by-step explanation:
To reduce the force between the Earth and the Sun to one-fourth its current value, one could increase the separation distance between them by a factor of two. According to Newton's law of universal gravitation, the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This relationship is mathematically expressed as F = G (m1 * m2) / r², where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two masses.
Since we want to reduce the gravitational force to one-fourth, we are looking for a situation where (1/2)² = 1/4. So by doubling the separation distance (2r), we achieve the desired reduction in force, as the new force would be F/4.