What is the relationship between acceleration and gravitational force?

Acceleration is directly proportional to the gravitational force and inversely proportional to the mass of the object.

In more detail, the relationship between acceleration and gravitational force is governed by Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F=ma). In the context of gravity, the gravitational force acting on an object is the product of the object's mass and the acceleration due to gravity (F=mg).

The acceleration due to gravity is a constant at a given location on Earth, approximately 9.8 m/s². This means that all objects, regardless of their mass, will accelerate towards the Earth at this rate in the absence of other forces (such as air resistance). However, the gravitational force experienced by an object will increase with its mass. For example, a heavier object will experience a greater gravitational force than a lighter one, but both will accelerate towards the Earth at the same rate.

This relationship can also be seen in the equation for gravitational force, F = G(m1m2/r²), where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centres. Here, the gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. This means that the gravitational force (and thus the acceleration of an object due to this force) will increase if the mass of either object increases or if the distance between them decreases.

In summary, the acceleration an object experiences due to gravity is directly related to the gravitational force acting on it, which in turn depends on the object's mass and its distance from the source of the gravitational force.