Final answer:
Doubling the mass of an object doubles its gravitational force towards another object, while doubling the distance between objects results in a gravitational force that is one-fourth as strong due to the inverse square law of gravity.
Step-by-step explanation:
When the mass of one of the objects in a two-object system is doubled, the gravitational force between them is also doubled, assuming the distance between their centers of mass remains constant. This is due to the gravitational formula Fgravity = G × (M1 × M2) / R2, where Fgravity is the gravitational force, G is the gravitational constant, M1 and M2 are the masses of the objects, and R is the distance between the centers of mass of the objects. If the weight of an object is its gravitational force towards Earth, and one of the object's masses were to double, the weight of that object would double as well. However, if the distance from the center of Earth were to double, the weight decreases by a factor of four because the gravitational force is inversely proportional to the square of the distance (R2) between the centers of mass. This is explained by Newton's law of universal gravitation and is a foundational concept in Newtonian Mechanics.
When calculating the gravitational force for an object whose mass has doubled, simply substitute the doubled mass into the M1 or M2 portion of the gravitational formula and solve for Fgravity.