I am currently reading about Newton's Law of Universal Gravitation and I am so confused as to why there is a negative sign in front of the equation Fg = (G* m1m2)/r^2.
Fg = (G* m1m2)/r^2
There is a vector form of the magnitude of the gravitational force F12 = - ((G*m1m2)/r^2 )r12
F12 = force exerted by object 1 on object 2
G = 6.67 x 10^-11 N⋅m^2 /kg^2
m1 = mass of object 1
m2 = mass of object 2
r = distance between the centers of masses of objects 1 and 2
The Attempt at a Solution
The text states that the negative sign indicates that object 1 is attracted toward object 2 and that through Newton's 3rd law, the force exerted by m2 on m1, F21 is equal in magnitude to F12 but opposite in direction. Therefore, these forces form an action-reaction pair⇒F21=-F12.
So if F12= (G*m1m2)/r^2, then F21 = -(G*m1m2)/r^2
I know that force is a vector quantity, but I am not sure when to use the vector form; and why is the vector form negative? I am so confused...Could anyone please help me understand this mathematically and conceptually?