# Why is the ratio of gravitational force and the inertia to resist it 1?

Is there a deeper meaning behind how things of different mass fall at the same acceleration? It feels so perfectly balanced...

• Yes, that "deeper meaning" is called Einstein's General relativity (GR) – user164843 Apr 19 at 4:26
• Great question. – Avantgarde Apr 19 at 4:59

In Newtonian physics, they are not assumed to be equal but because empirically they are, we often take them to be the same. For example, Newton's second law says $$\vec{F}=m_i\vec{a}$$ and Newton's law of gravitation says $$\vec{F} = -(GMm_g/r^2)\hat{r}$$. The standard (high school) calculation assumes $$m_i=m_g$$ from empirical results but as stated, the two laws do not say they are the same.
• @csp2018 I think it depends on what you mean. To many, general relativity's assumption that $m_i = m_g$ is a "deep insight": that's how you make gravity geometrical in spacetime. This does not work (naively) for e.g. electromagnetism: the fact that there are neutral particles mean that electric field cannot be made "geometrical" the same way gravity is. For gravity, because $E=mc^2$, even massless particles will "fall" in gravitational field. I think the fact that it can be made to work at all is an insight in itself. – Everiana Apr 20 at 7:54
• Newtonian physics doesn't really say that $m_g = m_i$. You could write $m_g = km_i$, for some non-zero $k$, and incorporate $k$ into $G$, so $F=(G/k^2)M_gm_g/r^2$, but it's more convenient to set $k=1$. Of course, using a $k\ne 1$ just shuffles the problem around: why is $k$ the same for all bodies, no matter their size, shape, or what substances they're made from. – PM 2Ring Apr 20 at 8:21