# I Confusion about gravitational acceleration

1. Jun 7, 2017

### kmm

I understand that gravitational acceleration is independent of mass. However, I've seen a common mathematical description of this that I can't help but find circular. I suspect that there's an error in my thinking that I'm hoping someone can point out for me. It goes like this; $F=mg$ but we know that $F=ma$. If we substitute the first equation into the second, we get $mg=ma$, therefore $g=a$. OK, but what seems wrong to me is that, once you state that the gravitational acceleration is the constant 'g', you're already saying it's independent of mass, BECAUSE it's a constant. And of course 'g' has to equal 'a' here; it is the acceleration. It seems to me that it's merely an experimental fact, so there's no need to justify it mathematically in this way. I feel like there's a subtlety I'm missing here.

2. Jun 7, 2017

### Staff: Mentor

This is correct. It is experimentally observed that the acceleration is independent of the mass. The form of the force law follows from that.

3. Jun 7, 2017

### kmm

Thanks, I wonder why some explain it in this way..

4. Jun 7, 2017

### Staff: Mentor

Well, the properties are encoded into the math so it is easy enough to start with the math and derive the properties

Last edited: Jun 8, 2017
5. Jun 7, 2017

### Staff: Mentor

Try deriving it from f=ma and Newton's law of gravity...

6. Jun 8, 2017

### kmm

Ok, in that case, we have $$ma = G \frac {mM} {R^2}$$ so $$a = G \frac {M} {R^2}$$ which is independent of the mass 'm'. I guess deriving it from Newton's law of gravity, which is more general than the special case of 'f=mg', is actually bit more illuminating. Thanks