De motu corporum in gyrum

From Wikipedia, the free encyclopedia

De motu corporum in gyrum (On the motion of bodies in an orbit) is a manuscript by Isaac Newton sent to Edmund Halley in November 1684. It derived the three laws of Kepler assuming an inverse square law of force, and generalized the answer to conic sections. It tried to set out the foundations of modern dynamics and extended its methodology by adding to the derivation of Kepler's laws the solution of a problem on the motion of a body through a resisting medium. Halley reported these results to the Royal Society on 1684-12-10 (Julian calendar). Three versions of the manuscript exist: they differ from each other in some crucial respects. The book Philosophiae Naturalis Principia Mathematica, commonly known as Principia Mathematica, is a correction and an expansion of this note.

Two important definitions in the first version of this work are worth drawing attention to in the light that they throw on the development of Newton's thoughts on dynamics -

that of centripetal force, accepting totally the tutorial on the role of inertia in circular motion given by Robert Hooke in his letter of 1674,
that of force inherent in a body which forces it to move in a straight line, showing that the nature of inertia was still not clear.

This error was further compounded by adding this inherent force to an external force by the parallelogram law.

The first version was reported to the Royal Society, but was not published since Newton wanted to revise it. The second version (possibly dating from December or January) contained minor corrections. The last version of this note attempts a reconstruction of dynamics by stating five laws of dynamics -

Law 1: stated that a body moved uniformly by inherent force alone.
Law 2: asserted that the "change in the state of moving or resting is proportional to" the impressed force and is made in the direction of the line in which the force acts.
Law 3: held that the motion in a given space did not depend on any rectilinear uniform motion of that space.
Law 4: stated that mutual interactions of bodies do not change the motion of their center of mass.
Law 5: contained an empirical statement about the resistance of media.

In addition he added to this last version an explicit hypothesis about an absolute frame of reference, with respect to which the motion of bodies could be determined: this in spite of already undermining this notion by the above Law 3.

Two separate papers of revision followed the last version of De motu. In these he reduced the number of laws of motion to 3. He sharpened the law of inertia without giving up an inherent force, but introduced a distinction between inherent and impressed force, clarifying that the latter only changes the motion of the body, but is not added to the inherent force. The inherent force disappeared in the Principia Mathematica.