Portrait of Isaac Newton by
Godfrey Kneller (1689)
Painting of Robert Hooke by Rita
Greer (2004)
Newton versus Hooke
Simulating the debate on bodies falling through a rotating Earth.
Synopsis of the Debate
The debate between Newton and Hooke about the fall of a body through a
rotating Earth was carried out through a series of letters between the
two men. On 24 November 1679 Hooke wrote to Newton, inviting Newton
to take part in the scientific discussions of the Royal Society (of
which Hooke had recently been appointed Secretary). The debate was
carried out in subsequent letters, as summarized below (all dates "old
style").
28 Nov 1679: Newton suggests dropping object from tall tower (or down deep
well) to prove rotation of Earth. He suggests that the object will
experience an eastward deflection because it is moving faster than
the point on Earth's surface directly below it. (See Fall To Earth
simulation.) He sketches the path of a body (in the Earth's
rotating frame), showing the body fall through the Earth and
eventually reach the center.
9 Dec 1679: Hooke agrees about the eastward deflection for an
object on the Equator, but suggests that
the object's path would "resemble An Elleipse" if the "gravitation to
the former Center remained as before." (See Hooke's Ellipse
simulation.) If the Earth resists the
object's motion, then the path would be an elliptispiral. (See
Hooke's ElliptiSpiral simulation.)
13 Dec 1679: Newton replies that if the force on the object inside Earth is
constant in magnitude then the path would not be an ellipse but
would precess. (See Newton's Constant Force simulation.)
6 Jan 1680: Hooke replies that by "remain as before" he didn't mean constant
magnitude, he meant that it will be inverse square all the way. But
he doesn't really think this would happen: "on the contrary I rather
conceive that the more the body approaches the center the lesse will
it be urged by the attraction, possibly somewhat like the
gravitation on a pendulum ..."
Note that Hooke is correct if Earth is treated as a uniform
sphere. In that case the magnitude of the force should be
proportional to the distance from the center (so it is a harmonic,
or "Hooke's Law" force). Newton would later prove this in his
Principia. But if we use this model for Earth, and a linear
resistive force when the object is inside Earth, then we get a
result that looks very much like Newton's original diagram from his
28 Nov 1679 letter. (See Newton's Spiral simulation.)
In his 9 Dec 1679 letter Hooke also suggested that an object
dropped from the latitude of London (51.5 degrees North) would be
deflected southward as well as eastward. This is true if "up" is
defined as directly away from the center of Earth. (See Southeast
Deflection simulation.) However, if up is defined with a plumb line
then the effects of Earth's rotation come into play and the object
will actually start off at a more northern latitude than that of the
point "below" it. As a result, the southward deflection is
difficult to detect because it is offset by the direction of the
plumb line. (See Plumb Line Effect simulation.)
Easy Java Simulations, Launcher, and LaunchBuilder are part of the
Open Source Physics collection created by Wolfgang Christian (http://www.compadre.org/osp/).
FallingBodyOnRotatingEarth2D and FallingBodyOnRotatingEarth3D by
Todd Timberlake.