Doubles
Explanation
The magnitude of the gravitational force between two objects is governed by Newton's Law of Universal Gravitation. This law states that the force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers.
Mathematical Analysis:
The formula for gravitational force (F) is given by:
F = G (m1 m2) / r2
Where:
- G is the gravitational constant.
- m1 and m2 are the masses of the two objects.
- r is the distance between them.
If the mass of one object is doubled (e.g., m1 becomes 2m1), the new force (F') becomes:
F' = G (2m1 m2) / r2
F' = 2 × [G (m1 m2) / r2]
F' = 2F
Thus, the gravitational force doubles.
Key Takeaway:
Gravitational force has a linear relationship with the mass of the interacting bodies; increasing the mass of either body by a factor directly increases the force by the same factor.