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Historical Perspectives on Sir Isaac Newton
««« By Andris Krumins
Andris Krumins is a beginning physics teacher who is currently moonlighting as a history instructor at Ryerson University. He
was a recipient of STAO’s pre-service award with this article submission. If you wish to offer him any feedback about this article, please contact him at [email protected]
Curriculum Connection: Physics
Physics teachers often pay lip-service to history,
but the majority of them do not take it too seriously. Oh,
sure, Newton wrote the Principia in the late 17th century,
and here are his three laws. Now, go do some problems.
Sound familiar? If you have been teaching this way, then I
believe you have been turning your back upon a valuable
resource. I like to incorporate historical facts into my
physics lessons on a regular basis, and my students really
seem to enjoy it. The history helps them to appreciate the
human side of physics, and I think that it helps to make
the subject more approachable for them as well.
In the classroom, we spend a great deal of time explaining
Newton’s laws, yet we make little reference to the man’s
actual words. Why is this? Isaac Newton (1643-1727) was
unquestionably the most celebrated and influential of all
of the natural philosophers of the 17th century. He must
have had something good to say! How else could his science have triumphed, especially considering that some of
his views were met with ferocity when they were first
introduced?
The story that the idea of universal gravitation was suggested to Newton by the fall of an apple seems to be accurate. Newton simply asked himself, what if the same force
responsible for the fall of an apple extended to the orbit of
Historical Perspectives on Newton
the Moon? If you browse through Volume II of Sir Isaac
Newton’s Mathematical Principles of Natural Philosophy
and His System of the World, translated from the Latin
original, you will find a beautiful figure which I like to
show directly to my students.1
How could we possibly improve upon this diagram? It
clearly shows that as we increase the initial speed of a
projectile more and more, it lands further and further
away from the starting point, even though the projectile is
experiencing the same downward force in each case. If the
projectile has a great enough speed, it will continue to fall
as before (of course!), but it will still manage to stay in
orbit around the Earth. In Newton’s own words (translated
into English),
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“… for a stone that is projected by the pressure of its
own weight forced out of the rectilinear path, which by
the initial projection alone it should have pursued, and
made to describe a curved line in the air; and through
that crooked way is at last brought down to the
ground; and the greater the velocity is with which it is
projected, the farther it goes before it falls to the
earth. We may therefore suppose the velocity to be so
increased… till at last, exceeding the limits of the
earth, it should pass into space without touching it.”2
To put the strength of Newton’s achievement into perspective for your students, recall that Galileo (1564-1642)
never attempted to offer any scheme of forces that would
account for the movements of the planets, or their satellites. In 1543, the year of his death, Copernicus (14731543) had shown in his masterpiece De revolutionibus that
the Sun is at the centre of the orbits of the planets, but his
work contained no insights into celestial mechanics.
Johannes Kepler (1571-1630), on the other hand, made an
attempt to supply a celestial mechanism, but he met with
little success. He believed in a force (he called it an anima
motrix) emanating from the Sun that would cause the
planets to revolve about its centre in circles, which would
then be influenced by magnetic interactions between Sun
and planet such that the orbit would be shifted from circular to elliptical, with the Sun at one of the foci.3 Newton
stands out among these great men as the first to successfully unify the physics of the terrestrial and celestial.
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emanating from the Sun must spread out in all directions,
presumably diminishing in the same way as intensity of
light diminishes with distance. Saying this much, however,
is very different from proving it mathematically, and Hooke
could not prove it.
In August of that year (1684), Halley went to Cambridge to
consult Newton. Halley was astounded that Newton
claimed that he had already shown how a body could be
made to travel in an elliptical orbit by a centripetal force
spreading out from one of the foci, and moreover, he had
done it a full five years earlier! Spurred on by Halley,
Newton developed his earlier work into a series of lectures which quickly led to his masterpiece, the Principia of
1687. Newton’s fame spread like wildfire (he later became
the first English scientist to be knighted), and Hooke was
extremely jealous. He bitterly asked for credit for the
inverse-square law, which Newton correctly believed followed simply enough from an analysis of circular motion.6
Hooke had been unable to either prove the result mathematically, or to fit it into a framework of dynamics, and so
Newton was completely justified in responding,
“Now is not this very fine? Mathematicians that find
out, settle, and do all the business must content themselves with being nothing but dry calculators and
drudges; and another, that does nothing but pretend
and grasp at all things, must carry away all the invention, as well of those that were to follow him as of
those that went before.”7
In the late 17th century, other members of the Royal
Society had also been attempting to discover the relationship between dynamics and Kepler’s laws. The foremost of
Newton’s opponents was Robert Hooke (1635-1703)4. In
1684, there was a famous meeting between Hooke, the
astronomer Edmond Halley (1656-1742), and the architect
Sir Christopher Wren (1632-1723) which centred upon the
question, “Under what laws of force would a planet follow
an elliptical orbit?”5 From Kepler’s laws, it was clear that
the Sun must somehow or other control, or at least affect,
the motion of any planet in its proximity. Hooke suspected
an inverse-square law, since he reasoned that any force
Historical Perspectives on Newton – Page 2
Take that, Robert Hooke! Quotes like this underline for
students that science is a human activity. Many of them
might be at least vaguely familiar with Newton’s famous
saying, “If I have seen further, it is by standing on the
shoulders of giants.” When did Newton become so magnanimous? The answer is: he did not. These words first
appeared in a letter written directly to Hooke, who may
have been a great thinker, but who also happened to be of
remarkably short stature. This explanation, which is completely true, is sure to elicit a response from your class.
As we all know, when students are interested and
Volume 38 • 2 November 2006
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involved, they are much more likely to learn. History has
proven it!
Endnotes
1. The figure is taken from p. 551 of the Cajori translation
of Newton’s Philosphiae naturalis principia mathematica.
References
Cajori, F. (1934, 1966). Sir Isaac Newton’s Mathematical
Principles of Natural Philosophy and his System of the
World. Translated into English by Andrew Motte in 1729.
Translations revised, and supplied with an historical and
explanatory appendix, by Florian Cajori. Berkeley:
University of California Press.
2. Cajori, p. 551.
3. Cohen, p. 149.
4. Hooke may have been given no credit for the inversesquare law of gravitation, but he was, at least, immortalized by his eponymous law for the restoring force of a
spring.
Cohen, I.B. (1960, 1985). Birth of a new physics. New York:
Norton.
MacLachlan, J. (1988). Children of Prometheus. Toronto:
Wall and Emerson.
5. MacLachlan, p. 143.
6. Cohen, p. 218.
7. Cohen, p. 150.
Historical Perspectives on Newton – Page 3
Volume 38 • 2 November 2006