To Letters Editor
Physics Today.

Re: Did Newton Need Hooke's Program to Divine Planetary Motions?
Physics Today, Sept. 2003


This year marks the anniversary of the death of Robert Hooke
one of the greatest 
scientist of the 17th century, who is currently being rehabilitated 
from three centuries of oblivion.
It might be expected that by now  his seminal  
influence  on Newton's development of the theory of planetary 
motion would be well understood, if not by physicists 
then at least by historians and philosophers of science, 
who  have argued about this subject during the past century.
But this is not the case as one finds, for example, in reading the  
recent book by Ofer Gal,  subtitled "Hooke, Newton and the 
'Compounding of the Celestiall Motions 
of the Planetts'", which was  reviewed in this journal by
George E. Smith.

In order to appreciate the importance of Hooke's contribution,
to planetary motion, which he communicated to Newton during 
a correspondence in the Fall of  1679, it is necessary to  
understand not only Hooke's  views, described at length 
in Gal's book, but also Newton's 
own understanding of this subject at the time
of this correspondence. 
Smith repeats the usual comment by historians of science that 
" before his correspondence with Hooke, Newton (along
with many others) thought of the planetary orbits as an equilibrium
between 'an endeavor to recede from the center' associated with
circular motion and some other mechanism". But this explanation 
is inadequate and, moreover, it is not 
the one offered by  Gal, who makes the bizarre claim
that before Hooke's intervention, Newton  represented "force-driven 
motion by straight lines or open curves, while reserving
the closed orbits to represent force-free motion" [1].
Newton's  Dec. 13, 1679 letter to Hooke shows 
that this claim is incorrect [2]. Unlike his contemporaries, 
Newton had developed by that time  a sophisticated  mathematical 
theory of orbital motion, as is evident in his  
description of orbital curves under the action of various central forces. 
In this letter, Newton included even   
the special case of a $1/r^3$ force (usually not treated in physics 
textbooks) which leads to an orbit that rotates  towards the center 
" by an infinite number of spiral revolutions" [2], but this
remarkable result has been universally ignored by 
historians of science. 

There is considerable evidence that Newton's theory of orbital motion  
was based on the mathematical description of curvature 
which he, and independently  Huygens, had developed  earlier [3]. 
However, an essential ingredient was missing 
in Newton's approach, which was based on a decomposition of 
motion along the tangent and the normal to the orbital curve.
Newton was not yet aware that for central forces, angular momentum 
is conserved,  justifying  Kepler's second law (area law).  
Newton later admitted that "in the year 1679, in answer to a letter
to Dr. Hook..I found now that whatsoever was the law of the forces
which kept the Planets in their Orbs, the areas described by the Radius
drawn from them to the Sun would be proportional to the times in which
they were described..." [4].  
What Hooke had suggested in 1679 to Newton  
is that orbital motion could be decomposed 
into "a direct [inertial]  motion by the tangent, and 
an attractive motion [radial] towards the central body" 
For a central impulsive force acting 
at periodic intervals, this decomposition of motion
makes the conservation of angular momentum manifest, 
as Newton subsequently  showed in
De Motu, his first draft of the Principia.  
This proof  became a cornerstone of
the Principia, as Proposition 1 in Book 1, because it permitted him 
to completely geometrize orbital dynamics by  replacing the time variable 
by the area swept by the radius drawn to the center of force [5].

Contrary to the  argument  by  Gal, 
that  Hooke "had a scientific style radically different from  Newton's",  
and  Smith's assertion  that  there exists a 
"monumental contrast" between their approaches
to science, in fact both Hooke and Newton  had   
a very similar and quite  modern approach to the  
understanding of  natural phenomena  based on   
observations and experiments. For example, Hooke reached his views of
planetary motion by an analysis of the motion of a conical
pendulum, as he explained in considerable  detail in a 
lecture given at the Royal Society on May 23, 1666 [4][6].
The essential difference is that  Newton
was able to translate  physical concepts into mathematical form 
and solve the resulting equations, while Hooke lacked far behind Newton 
in this ability. The physical basis for planetary motion
was not "divined" (coming from God) by Newton, but should be recognized
as a remarkable joint scientific achievement of Newton and Hooke [7].

References:

[1] O. Gal, "Meanest Foundations and Nobler Superstructures, Hooke, Newton
    and the 'Compounding of the Celestiall Motions of the Planetts'"
    (Kluwer Academic Publishers 2003) p. 184.  Gal also
    makes the unprecedent  claim that the "novelty of {\it De Motu} 
    [Newton's  first draft of the Principia written  5 years 
    after his correspondence with Hooke] thus encapsulated the willingness 
    [of Newton] to represent forced motions by closed curves" p. 188,
     

{2} M. Nauenberg, "Newton's Early Computational Method for Dynamics"
    Archives for History of Exact Sciences, 46, (1994) 221-251

[3] J.B. Brackenridge and M. Nauenberg, "Curvature in Newton's Dynamics" in
    The Cambridge Companion to Newton, edited by I.B. Cohen and G.E. Smith
    (Cambridge Univ. Press 2003) pp. 85-137

[4] M. Nauenberg, "Hooke, orbital motion, and Newton's Principia"
    American Journal of Physics 62, (1994) 331-350

[5] M. Nauenberg, "Kepler's area law in the Principia: Filling in some
                   details in Newton's proof of Proposition 1"
                   Historia Mathematica v. 30 (to be published)

[6] In his review,  Smith states "that the great value of Gal's book
    lies in his analysis of how Hooke arrived at this conception
    through his research in optics". But in his Royal Society lecture
    Hooke explicitly rejected the optical analogy that the "bending"
    of the orbital motion of planets  into a curve 
    is caused by  the "unequal density of the medium".

[7] M. Nauenberg, " Robert Hooke's seminal contribution to orbital dynamics" 
    Invited paper presented at a conference at the Royal Society in London, 
    July 7-8,2003, to mark the tercentenary of the death of Robert Hooke 
    (1635-1703) (to be published)