Gravity
Newton’s theory regarding gravity surfaces throughout the Principia, though most notably in Book III, and is rooted in the reasoning that first appeared when Newton’s was a child. This reasoning was moulded, reshaped and perfected until it became what the world now recognises as Newton’s Theory of “Universal Gravitation”. This theory states that any two masses are attracted with a force proportional to the product of the two masses that are attracted to each other, and that force is inversely proportional to the square of the distance between them. Newton used this theory to explain the motion of planets, moons and comets, as well as the action of the tides. This law of gravitation, when simplified into a formula, states:
F = G (Mm/R²)
Where,
F = the force with which the two masses are attracted
M = one of the masses
m = the other mass
R = the distance between the two masses
G = a constant (required because this law refers to proportionality) whose value depends on the units used for mass and distance.
Further simplified, the formula can be given as:
W = mg
Where,
W = weight; this is the force attracting the masses
m = mass
g = gravity; this is the acceleration that the mass undergoes as it is attracted to the other mass
As you can see, the above formula W = mg, closes resembles the formula F = ma, which is mentioned in Newton’s 2nd Law of Motion. They are, in fact, the same, as weight equals the force of the attraction and gravity indicates the acceleration as the masses are attracted to each other.
F = G (Mm/R²)
Where,
F = the force with which the two masses are attracted
M = one of the masses
m = the other mass
R = the distance between the two masses
G = a constant (required because this law refers to proportionality) whose value depends on the units used for mass and distance.
Further simplified, the formula can be given as:
W = mg
Where,
W = weight; this is the force attracting the masses
m = mass
g = gravity; this is the acceleration that the mass undergoes as it is attracted to the other mass
As you can see, the above formula W = mg, closes resembles the formula F = ma, which is mentioned in Newton’s 2nd Law of Motion. They are, in fact, the same, as weight equals the force of the attraction and gravity indicates the acceleration as the masses are attracted to each other.
Author: Hannah Davies