Prior to Isaac Newton (1642-1717), the concept of physical motion came from Aristotle. As Newton began his work, his world was dominated by the work of Aristotle. (Though Kepler and Galileo had made some inroads). Aristotle held that there were three types of motion. Natural motion is where objects wanted to go to their natural state. Free fall motion is an example. Voluntary motion, as when a person goes to where they want to go. And, finally, forced motion such as when one object collided with another object.(1)
Newton required two models to make his theory of Gravity work. First, he needed the second law of motion which states Force equals Mass times Acceleration. Second he needed to find a description of gravity in a form which could be solved by the second law.
Newton’s law of gravity is written Force = GmM/(x^2). (At least in terms of magnitude.)
Here G is a constant, m and M are the masses involved and x is the distance between the centers of the two masses. The reader should note that G, m, M are all multiplied together and divided by the distance between their centers squared. Due to restraints of posting on this site, I will generally use the notation x^y to mean x raised to the y power.
To better understand why Newton considered Force to be proportional to Acceleration, one should consider that objects traveling with a constant velocity seem to maintain that motion unless acted on by an external force such as a resistance force. Newton therefore defined Force at an arbitrary time as the instantaneous change in velocity at that time, which is the definition of Acceleration.
To find the precise velocity of a particle Newton needed to find the change in position per the corresponding change in time at an arbitrary point in time. This requires the construct of the limit.
Because the concept of a limit gives a very precise solution to the problem of finding a slope of a curved line, I will give a general definition, and a specific example.
In general we say that the limit as t approaches t[size=85]0[/size] of f(t) is f(t[size=75]0[/size]) if and [size=100]only[/size] if for every e there exists a d such that if |t - t[size=75]0[/size]|<d [size=100]then[/size] |f(t) - f(t[size=75]0[/size])|<e where d and e are [size=100]Real[/size] numbers > 0. The order of this game is absolutely critical and any precise analysis will break down if it is not followed exactly. To find the slope (sometimes called the derivative) of the function f we look at the limit as t approaches t0 of (f(t) -f(t[size=75]0[/size])) [size=100]/[/size] (t- t[size=75]0[/size]) and [size=100]we[/size] denote that limit as df(t)/dt.
Working with these equations Newton was able to predict the motion of the planets as they moved around the Sun. ( the only exception to his predictions, and it was a minor one at that, was Mercury)
This Model of Gravity was so successful (to 15 decimal places) that many people started to believe that the world was completely deterministic. (There were some people who believed that the world was deterministic before this development but they were in the small minority). This belief eventually extended to some prominent representatives of the Church itself!
Not only were everyday average people affected due to the wave of Determinism that followed it, but many of the great physicists that followed wanted their models to have Newton’s physics as a limiting model under “Normal” circumstances.
My goal in presenting a series of models is to look for relationships amoung the models, and therefore critiquing the models is probably unnecessary. However due to the impact of Newtonian Physics I will make an exception.
Critical points to consider:
Newton’s Law of Gravity only considers only two objects. The three object problem, called the Three Body Problem is insolvable(3). (Newton never claimed otherwise, but Determinists seem to over look this point). Newton assumed that space time is continuous. The embedded Galilean Transform x’ = x - vt is assumed.
My personal assessment is that Newton’s achievement was absolutely stunning by any measurement, and even today Newtonian Physics has more impact than any physical model of the Universe ever developed.
(1) Background from: bookrags.com/sciences/physic … s-wop.html
(2) I was able to confirm that the second law came prior to the law of gravitation in the Encyclopedia Britannia 1973-74 version.
(3) chaos.org.uk/~eddy/physics/prial.html