# How does gravitational attraction relate to weight? [duplicate]

I understand that gravitational attraction is the attraction of a particle by another particle or matter, which in this case is the earth. But I don't understand why this (gravitational attraction) is related to weight. I mean gravitational attraction is just attraction and not a force. Please explain.

## marked as duplicate by Aaron Stevens, Kyle Kanos, M. Enns, Buzz, Jon CusterDec 30 '18 at 1:33

Gravitational attraction refers to the force of attraction between you and the earth. Weight is the amount of force you exert on the earth. These two are essentially the same thing.

Gravitational force of attraction is given by $$F=\frac{GMm}{r^2}$$, where $$M$$ is the mass of earth, $$m$$ is that of object, and $$r$$ the distance of the object to earth. Since you are of negligible height as compared to the earth radius, taking $$\frac{GMm}{r^2}=mg$$ is possible, and we get $$g$$, the acceleration of free fall near the earth;s surface to be $$9.813646...ms^{-2}$$.

• sorry but what do you mean by "between you and the earth"? – Taofeek Dec 29 '18 at 12:01
• Attraction is between two objects. in this case you and the earth @Taofeek – QuIcKmAtHs Dec 29 '18 at 12:02
• @QuicKmAtHs You correctly define g as acceleration close to earth’s surface, but why do you also mention the height of the person? Once that g is accepted to be substantially the same even kms away from the surface, it’s out of question that it will not significantly vary (causing tidal effects!) along a person’s body... – Sierra Dec 29 '18 at 17:01
• @Sierra yes, the difference is small, but I thought I should also mention it. – QuIcKmAtHs Dec 30 '18 at 1:05

It is a force in classical mechanics. It's a force of attraction. The mass (not the weight) is the source of this force, that "always pulls and never push" . You can't go deeper than masses attract each other. This is a fact and we have to accept it as an empirical statement. But we may want to know more about this fact that we constantly observe, so we ask the following question:

• how do they attract they each other?

Newton was the first one to answer that question. He stated that the force of attraction between two bodies is proportional to the masses of the bodies and inversely proportional to the square of the distance. In a formula:

$${\bf{F}}_G = -G \frac{m_1 m_2}{|{\bf{r_1}} - {\bf{r_1}}|^2} \hat{\bf{r}}$$

Where $$G$$ is the universal constant of gravitation. At the numerator you have the product of the masses of the two bodies and at the denominator the square of the distance between the bodies, as stated above. The object $$\hat{\bf{r}}$$ tells you the direction of the force, which is along a straight line connecting the two bodies. The minus sign tells you that the force is attractive.