Astronomy Explained Upon Sir Isaac Newton's Principles: And made easy to those who have not studied mathematicsFerguson, James
Science
Astronomy Explained Upon Sir Isaac Newton's Principles: And made easy to those who have not studied mathematics
Ferguson, James
Astronomy -- Early works to 1800
154. As the Planets approach nearer the Sun, and recede farther from
him, in every Revolution; there may be some difficulty in conceiving the
reason why the power of gravity, when it once gets the better of the
projectile force, does not bring the Planets nearer and nearer the Sun
in every Revolution, till they fall upon and unite with him. Or why the
projectile force, when it once gets the better of gravity, does not
carry the Planets farther and farther from the Sun, till it removes them
quite out of the sphere of his attraction, and causes them to go on in
straight lines for ever afterward. But by considering the effects of
these powers as described in the two last Articles, this difficulty will
be removed. Suppose a Planet at _B_ to be carried by the projectile
force as far as from _B_ to _b_, in the time that gravity would have
brought it down from _B_ to 1: by these two forces it will describe the
curve _BC_. When the Planet comes down to _K_, it will be but half as
far from the Sun _S_ as it was at _B_; and therefore, by gravitating
four times as strongly towards him, it would fall from _K_ to _V_ in the
same length of time that it would have fallen from _B_ to 1 in the
higher part of it’s Orbit, that is, through four times as much space;
but it’s projectile force is then so much increased at _K_, as would
carry it from _K_ to _k_ in the same time; being double of what it was
at _B_, and is therefore too strong for the tendency of the gravitating
power, either to draw the Planet to the Sun, or cause it to go round him
in the circle _Klmn_, &c. which would require it’s falling from _K_ to
_w_, through a greater space than gravity can draw it whilst the
projectile force is such as would carry it from _K_ to _k_: and
therefore the Planet ascends in it’s Orbit _KLMN_, decreasing in it’s
velocity for the cause already assigned in § 152.
[Sidenote: The Planetary Orbits elliptical.
Their Excentricities.]
155. The Orbits of all the Planets are Ellipses, very little different
from Circles: but the Orbits of the Comets are very long Ellipses; the
lower focus of them all being in the Sun. If we suppose the mean
distance (or middle between the greatest and least) of every Planet and
Comet from the Sun to be divided into 1000 equal parts, the
Excentricities of their Orbits, both in such parts and in _English_
miles, will be as follows. Mercury’s, 210 parts, or 6,720,000 miles;
Venus’s, 7 parts, or 413,000 miles; the Earth’s, 17 parts, or 1,377,000
miles; Mars’s, 93 parts, or 11,439,000 miles; Jupiter’s, 48 parts, or
20,352,000 miles; Saturn’s, 55 parts, or 42,735,000 miles. Of the
nearest of the three forementioned Comets, 1,458,000 miles; of the
middlemost, 2,025,000,000 miles; and of the outermost, 6,600,000,000.
[Sidenote: The above laws sufficient for motions both in circular and
elliptic Orbits.]
Public-domain text, read in full here on John Shaqi.
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