Question

Question #b1481

Answer 1

No. Gravity is a constant and not a force. The force due to gravity does increase as your body mass increases though.

`F_g = mg`

Answer 2

Yes, the force due to gravity (`F_g`) that an object experiences depends on its mass .

Explanation:

Newton's universal law of gravitation is:

`F_g = G {M m}/{r^2}`

`G=6.673×10^(−11) N m^2/{kg^2}`

Where `F_g` is the force of gravity between two objects, `G` is a constant, `M` is the mass of your first object, and `m` is the mass of your second object and `r` is the distance between the two objects.

The force of gravity between two objects does depend on mass (more mass, more force), and the distance (bigger distance, less force).

Let's consider the special case where you are on the surface of the earth (or very close to the surface). We can plug in the mass and radius of the earth:

`M = M_{Earth}`
`r= R_{Earth}`

`F_g = G {M_{Earth} m}/{R_{Earth}^2}`

You will notice that `R_{Earth}`, `M_{Earth}`, and `G` are all just constants (they are numbers we know or could look up), so we can combine them:

`g = G {M_{Earth}}/{R_{Earth}^2}`

`F_g = m g`

Which looks a lot like Newton's second law: `F= ma`, where g is an acceleration.

This is just a long-winded way of saying `g` (little g) is not gravity, it is the local value of the acceleration due to gravity . It is a constant (on the surface of the Earth).

The force due to gravity is not a constant. `F_g` depends on the mass of your object. It also depends a little bit on how far away you are from the center of the Earth, but most human-scale things are so small compared to the radius of the Earth, this is negligible.