That's a really interesting and subtle point, and it touches on some of the deepest aspects of modern physics, particularly General Relativity. It's not quite accurate to say that gravity is completely independent of mass, but your statement gets at a crucial distinction often made in physics.
Here's a breakdown:
* Newtonian Gravity:
* In Newton's Law of Universal Gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. So, F = G \frac{M_1 M_2}{r^2}.
* Here, mass is clearly central to both the source of gravity (the M_1 and M_2 that create the gravitational field) and the response to gravity (the force felt by each mass).
* Acceleration due to Gravity:
* However, when you look at the acceleration due to gravity (g), it is independent of the mass of the falling object. This is a crucial distinction.
* From Newton's second law, F = ma. If the gravitational force is F = G \frac{M_{planet} m_{object}}{r^2}, then equating the two:
m_{object} a = G \frac{M_{planet} m_{object}}{r^2}
a = G \frac{M_{planet}}{r^2}
* In this equation, a is the acceleration due to gravity (which we call g near the Earth's surface), and you can see that the mass of the object (m_{object}) cancels out. This means a feather and a bowling ball (in a vacuum) fall at the same rate. This is what Galileo famously demonstrated.
* General Relativity and Spacetime Curvature:
* This is where your point becomes even more profound. In Einstein's General Theory of Relativity, gravity isn't described as a force in the traditional sense, but as a manifestation of the curvature of spacetime.
* What causes spacetime to curve? Mass and energy (and momentum and stress-energy). Einstein's famous equation E=mc^2 shows the equivalence of mass and energy. In General Relativity, all forms of energy (including the energy contained within mass, but also kinetic energy, electromagnetic energy, pressure, etc.) contribute to the stress-energy tensor, which dictates how spacetime is curved.
* So, a massive object (like a star or a galaxy) warps the spacetime around it. Other objects then simply follow the "straightest possible paths" (geodesics) through this curved spacetime. The "force" of gravity we feel is just us being compelled to follow these curved paths.
* In this framework, the presence of mass (and energy) is what creates the gravitational field (the curvature of spacetime). The response of an object to that field (its acceleration) depends only on the geometry of spacetime, not on its own mass. This is a deeper explanation for why all objects fall with the same acceleration, regardless of their mass – they are all responding to the same spacetime curvature.
In summary:
* Mass is the source of gravity (spacetime curvature) in General Relativity. Without mass (or energy), there is no curvature, and thus no gravity.
* The effect of gravity (acceleration) on an object is independent of the object's mass. All objects follow the same curved paths in a given gravitational field.
So, while the acceleration experienced by an object due to gravity is independent of its own mass, gravity itself (the phenomenon of spacetime curvature) is absolutely dependent on the presence of mass and energy. This is a subtle but critical distinction in understanding gravity from a modern physics perspective.