Newton's law of universal gravitation doesn't directly state a law about acceleration. Instead, it describes the force of attraction between two objects with mass. However, we can derive the acceleration due to gravity from Newton's law of gravitation and Newton's second law of motion.

Here's how:

1. Newton's Law of Universal Gravitation:

This law states that the force of attraction between two objects with masses *m1* and *m2* separated by a distance *r* is given by:

*F = G(m1*m2)/r²*

where G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N⋅m²/kg²).

2. Newton's Second Law of Motion:

This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:

*F = ma*

3. Deriving Acceleration due to Gravity (g):

Let's consider a small object of mass *m* near the surface of the Earth (mass *M* and radius *R*). The force of gravity acting on this object is:

*F = G(Mm)/R²*

Applying Newton's second law, we can relate this force to the object's acceleration:

*F = ma = G(Mm)/R²*

Solving for *a*, we get:

*a = G(M)/R²*

This acceleration is usually denoted as *g* and is called the acceleration due to gravity. It's the acceleration experienced by any object near the Earth's surface due to gravity.

Therefore, the acceleration due to gravity is not a separate law but a consequence of Newton's law of universal gravitation and his second law of motion.

Important Points:

* The acceleration due to gravity is a constant value near the Earth's surface, approximately 9.8 m/s².

* The value of *g* varies slightly depending on altitude and latitude.

* The acceleration due to gravity is independent of the mass of the object experiencing it.