>>12186918holy shit can no one explain basic shit here?
F = Gm1m2/r^2
The force due to gravity exerted on each body by the other (i.e. weight) is equal to the gravitational constant times the two masses divided by the distance between the (center of the) two masses squared. We'll say that m1 is the mass of the Earth here, and m2 is the mass of the falling object.
F = ma
the weight of the falling object is F (i.e. the force acting on the object due to gravity), the mass of the falling object is m and its acceleration due to gravity is a
so to find the acceleration, we rearrange the equation to get:
a = F/m
from here we can substitute in F from our first equation to get:
a = Gm1m2/(m*r^2)
Since m2 = m (they're both the mass of the falling object), we can cancel them to get:
a = Gm1/r^2
this equation tells us that the acceleration of an object due to the gravity of the Earth is proportional to a) the gravitational constant and b) the mass of the Earth, and is inversely proportional to the square of the distance between the center of mass of the falling object and the center of mass of the Earth. You may now notice how the mass of the falling object does not come into this equation.
