Why they need to use gravitational constant in the formula? What would be the problem if the formula is like F=m1*m2/d2 ?

The use of the gravitational constant in the formula is crucial because it provides a necessary scale factor and establishes the relationship between the mass and the force of attraction between two objects.

Let me explain with an example. Imagine you have two masses, m1 and m2, and you want to calculate the force of attraction between them. If you were to use the formula F = m1 * m2 / d^2 (where d is the distance between the masses), you would find that the force of attraction is directly proportional to the masses and inversely proportional to the square of the distance between them.

However, the problem with this formula is that it does not consider the fundamental nature of gravity as explained by Isaac Newton. According to Newton's law of universal gravitation, the force of attraction between two objects not only depends on their masses and distance but also on a constant factor known as the gravitational constant (G).

The gravitational constant, denoted by G, is a fundamental constant of nature that determines the strength of the gravitational force. It acts as a proportionality factor, ensuring that the units of mass, distance, and force are consistent in the formula.

By incorporating the gravitational constant (F = G * (m1 * m2) / d^2), the resulting force will be measured in Newtons, which is the standard unit of force. Without the gravitational constant, the units of force would not be consistent, and the equation would not accurately describe the relationship between mass, distance, and force.

In summary, the inclusion of the gravitational constant in the formula ensures that the force of attraction between two objects is accurately calculated and is consistent with the principles of gravitational physics.