The mathematical form of the universal law of gravitation is defined by Sir Isaac Newton and is given by the equation:

F = G * ((m1 * m2) / r^2)

Where:
- F represents the force of gravitational attraction between two objects.
- G is the gravitational constant, which has a value of approximately 6.67430 × 10^-11 N(m/kg)^2.
- m1 and m2 are the masses of the two objects involved in the gravitational interaction.
- r is the distance between the centers of mass of the two objects.

The equation can be further explained in the following manner:

1. Gravitational Force:
The equation represents the gravitational force, which is the attractive force that exists between any two objects with mass. This force is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between their centers of mass.

2. Gravitational Constant:
The gravitational constant, denoted by G, is a fundamental constant that represents the strength of the gravitational force in the universe. It is a fixed value and does not change. The value of G was determined through experimentation and is necessary to calculate the force of gravity accurately.

3. Masses of Objects:
The masses of the two objects, m1 and m2, are the quantities that determine the strength of the gravitational force. The greater the masses, the stronger the gravitational attraction between them. The masses are measured in kilograms (kg).

4. Distance between Centers of Mass:
The distance between the centers of mass of the two objects, denoted by r, is a crucial factor in the equation. It is the distance between the two objects and is measured in meters (m). The force of gravity decreases as the distance between the objects increases. Moreover, the force is inversely proportional to the square of the distance, meaning that doubling the distance will result in one-fourth of the gravitational force.

In summary, the mathematical form of the universal law of gravitation describes the relationship between the masses and the distance between two objects, and the resulting gravitational force. It quantifies the fundamental force of nature responsible for the attraction between objects with mass.