The change in gravitational attraction between two objects is not linear; it is actually inversely proportional to the square of the distance between them. This means that the force of gravitational attraction decreases exponentially as the distance between the objects increases.
The reason behind this inverse square law can be understood through the principles of gravitational field and geometry. According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Mathematically, the gravitational force (F) between two objects with masses (m1 and m2) separated by a distance (r) can be expressed as:
F = G * (m1 * m2) / r^2
Where G is the gravitational constant, a fundamental constant in physics.
As you can see from this equation, the force is divided by the square of the distance. This means that as the distance between the objects increases, the force of gravitational attraction decreases rapidly. If the distance between the objects doubles, the force of attraction decreases by a factor of four. If the distance triples, the force decreases by a factor of nine, and so on.
This inverse square relationship is a consequence of the way gravitational fields propagate through space. The gravitational field lines spread out as they move away from the objects, leading to a dilution of the field's strength. This is similar to how the intensity of light diminishes as you move further away from a source.
So, in summary, the change in gravitational attraction between two objects follows an inverse square law, not a linear or exponential relationship.