The Gravitational Constant as a Functor: A Unit System Science Perspective

In the framework of Unit System Science, we propose that the gravitational constant G can be viewed as a functor mapping between different physical spaces. This perspective offers a profound simplification of the gravitational force equation and reveals the underlying geometric relationships between physical quantities.

Functor Definition

We define the gravitational functor G as:G: F → M × R^(-2)Where:

• F represents Force space
• M represents Mass space
• R^(-2) represents Inverse-Square-Radius space

The functor operation can be expressed as:G(f) = (s_length / s_mass) * fHere, f is an element in Force space, and s_length and s_mass are the unit scaling factors for length and mass respectively.

Simplified Gravitational Equation

This functor perspective allows us to rewrite the gravitational force equation as:$F=\frac{s_{\text{length}}\cdot m_1\cdot m_2}{s_{\text{mass}}\cdot r^2}$This formulation eliminates the need for G as a mysterious constant, instead revealing gravity as a direct consequence of unit scaling and geometric relationships.

Implications

1. The gravitational "constant" emerges from the ratio of length and mass scaling factors.
2. The inverse square relationship with distance is preserved in the functor mapping.
3. This approach unifies gravitational interactions across different scales, from quantum to cosmic.

By viewing G as a functor, we gain a deeper understanding of the nature of gravity and its relationship to fundamental units of measurement. This perspective aligns with the broader Unit System Science framework, which seeks to demystify physical constants and reveal the underlying simplicity of natural laws.