Astronomy Principles and Practice Fourth Edition.pdf

The Principia of Isaac Newton 173
Now
2π
θ =
27·322 × 86 400
taking the sidereal period of revolution of the Moon to be 27·322 mean solar days and the number of
seconds in a day to be 86 400.
The radius BE of the Moon’s orbit is 60 × 3960 × 5280 × 12 inches, taking the Earth’s radius to
be 3960 miles. Hence, it is found that
CD = 0·0533 inch
in satisfactory agreement with the value of 0·0535 inches predicted by the law of gravitation.
In fact, the value obtained by Newton was 0·044 inches. Because of this disappointing
disagreement he abandoned the theory as contradicted by the facts. Six years later, in 1671, Picard’s
measurement of the arc of a meridian in France corrected an error in the previously accepted value of
the size of the Earth. Newton heard of this, repeated the calculation and now found agreement. He
thereupon resumed the subject, carrying out the brilliant series of research projects that culminated in
the publication of the Principia.
13.5 The Principia of Isaac Newton
In this great work, Newton seized all the astronomical and physical phenomena available, organized
them, demonstrated how they followed from his three laws of motion and the law of universal
gravitation, predicted new observational data and laid the foundations of mathematical physics so
firmly that much of the researches of mathematicians, scientists and astronomers in the next two and a
half centuries became efforts to develop logically the consequences of his theory of the World.
Among the contents of the Principia were the following:
He proved that a rotating globe such as the Earth would be flattened slightly at the poles due
to the centrifugal force in its equatorial regions ‘diluting’ the force of gravity in these regions. This
protuberance of matter at the equator would be acted upon by the Moon and Sun, causing the Earth’s
axis of rotation to precess slowly like the axis of a spinning top or gyroscope so that the axis sweeps
out a cone. The precession of the equinoxes, a consequence of this, had been discovered by Hipparchus
about 134 BC but until Newton’s time had remained unexplained.
He proved that under the law of gravitation, a planet would move in an ellipse about the Sun
under Kepler’s laws and that this ellipse would change slightly in size, shape and orientation over the
years because of the attractions of the other planets. In this way he accounted for hitherto unexplained
changes in the orbits of Jupiter and Saturn. He also showed how to measure the mass of any planet that
had one or more satellites.
In the case of the Moon’s orbit—an extremely complicated problem that, as Newton once
remarked to his friend Edmund Halley, ‘made his head ache and kept him awake so often that he
would think of it no more’—he was able to prove that certain irregularities in its movement about the
Earth were due to the Sun’s attraction and he predicted some features that were subsequently found by
observation.
He even demonstrated (see figure 13.5) that if a projectile were fired with sufficient velocity from
a cannon at the top of a terrestrial mountain so high it was outside the Earth’s atmosphere, it would
describe a circle or ellipse about the Earth. It would, barring a collision, go on revolving about the
Earth indefinitely. In other words, three hundred years before Newtonian science had developed far
enough to put the first artificial satellite into orbit, Isaac Newton predicted its possibility.
He also explained the phenomenon of the tides as an additional consequence of the law of
gravitation, laying the foundations of all the modern work on that subject. He showed that the orbits
of comets were also governed by this law and described how their paths could be calculated.