Absolute and Relative Motion
Table of Contents
PROPOSITION 1. Theorem.
- Every body that is carried from one place to another place by relative or absolute motion, passes through all the intermediate positions.
It is not able to suddenly arrive at the final place.
Demonstration for absolute motion
If the body were suddenly able to arrive at the final place from the first place, it would be necessary for the body to be annihilated at the first place and suddenly produced in the final place.
Superphysics Note
This cannot be done according to the laws of nature, except by agreeing to a miracle.
Therefore it proceeds from place to place until finally it arrives at the final place.
Demonstration for relative motion
A body moving in relative space must pass through the individual intermediate places.
Therefore the relative motion will be successive through the intermediate positions. Q. E. D.
Corollary 1.
- It follows that a motion cannot be immediate. Time is needed for the body to arrive at some place from some previous place.
Since it has to pass through the individual intermediate places, this cannot be consistent with instantaneous motion.
Corollary 2.
- Therefore it is necessary for the path to be assigned.
The body moves through this path. The body then passes through all the points on that path from the first to the last through in its progression.
This is usually called the path that the body runs through or traverses.
Scholium.
- This view is readily adapted too for bodies rotating around an axis because the position of the body itself does not change.
This motion is made up of many different motions.
The individual parts with respect to infinite space change their position,
The only parts that are at rest are those on the axis itself.
Similarly, bodies to be considered in every respect, so that not only a whole body, but also the situation of the individual parts of the body, needs to be examined for change.
DEFINITION 4: Uniform Motion
- A body is moving uniformly if it traverses equal intervals of time at equal distances.
A motion is truly not equable that in equal times travels through unequal distances, or in traveling through equal distances are resolved by unequal intervals of time.
Corollary 1.
- Therefore a body with a uniform motion extended by twice the time completes twice the distance, three times as long results in three times as far, and in general the distances traveled through are in proportion to the times, and in turn the times with the distances.
As a ship at sea begins with an uniform motion, if in one hour it travels through two miles, then in two hours the distance completed is four miles, in three hours six miles, and in n hours, 2n miles.
Corollary 2.
- Uniform motion can give an accurate measurement of the time.
For the ratio of the distances measured that the body traverses with a uniform motion, is noted to be the same as of the times in the same intervals.
Scholium
- Neither truly do we have from elsewhere the division of time into years, days, and hours other than from a motion that we consider as being regular.
In the geocentric theory, the ancients believed that the sun was carried around in a regular motion.
The time it took to revolve around the earth they called a day.
They had taken the motion of the fixed stars around the earth to be regular too.
The time it took for the sunrise to return to its original position with respect to the fixed stars they called a year.
Then these times were divided into equal parts, and in this way the hours, minutes, and seconds were arrived at.
But those motions were not really uniform.
This caused errors in the measurement of time too.
Recently, astronomers have detected an irregularity in these motions. They have found that not all days are of the same length.