The Mathematical model of Antigravitational forces

In physics, the Newtonian gravitational force is exclusively attractive [1]. There is no fundamental force of the same nature that acts as a universal repulsive "opposite." However, the concept of a "mathematical opposite" force that causes repulsion, and actual physical forces that counteract gravity in specific contexts, can be described.

 Mathematical "Opposite" (Repulsion) Newton's Law of Universal Gravitation describes an attractive force: F=G\m1,m2/r2

To represent a repulsive force using the exact same mathematical form, one would conceptually need a negative gravitational constant \(G\), 

negative mass, or a repulsive "gravitational charge." [1] The mathematical form for such a hypothetical repulsive force would have a positive sign, indicating the force pushes objects apart: 

F repulsive=+G\m1,m2/r2

However, neither negative mass nor a negative \(G\) has been observed in nature. Forces That Provide Resistance to Gravity In practical mechanics, other actual physical forces can act in the direction opposite to the effect of gravity: Normal Force: This is the support force exerted by a surface that prevents an object from falling through it. When an object rests on a horizontal surface, the normal force \(\vec{N}\) is equal in magnitude and opposite in direction to the object's weight \(\vec{W}\) (\(mg\)).Air Resistance/Drag: When an object falls through the atmosphere, air exerts a drag force (\(\vec{F}_{D}\)) in the direction opposite to the object's velocity, resisting the downward pull of gravity.Buoyancy: An upward force exerted by a fluid that opposes gravity, as described by Archimedes' principle. Its magnitude is equal to the weight of the fluid displaced by the object. Cosmological "Opposite" In modern cosmology, dark energy is theorized to be responsible for the accelerating expansion of the universe, acting as a repulsive force on a massive, universal scale [1]. This effect is described within the framework of Einstein's General Relativity (often represented by the cosmological constant, \(\Lambda \)) and not a direct modification of Newton's force law.