Free fall means a body falls down under no influence of external force except gravitational force.

So when a body is under free fall

According to Force ## ‘F’ = (G*m_1*m_2)/d^2 ##.

where ##m_1 =##mass of the earth = ##M##.

##m_2 =##mass of the body = ##m##.

##d =##distance between the bodies =##R+h = R##

since ##h##<<##R## .
##R =##Radius of the Earth.
So the Gravitational Force = ##F = (GMm)/R^2 ## .
When we calculate the value of ##(GM)/R^2##we get ##9.8ms^-2##which is taken as ##g =##gravitational .
Hence the formula is changed as ##F = mg##.
And that wayit is related to gravity.The acceleration of the body is provided by gravitywhich in turn lets the body to fall freely.