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
156. By the above-mentioned laws § 150 _& seq._ bodies will move in all
kinds of Ellipses, whether long or short, if the spaces they move in be
void of resistance. Only, those which move in the longer Ellipses, have
so much the less projectile force impressed upon them in the higher
parts of their Orbits; and their velocities, in coming down towards the
Sun, are so prodigiously increased by his attraction, that their
centrifugal forces in the lower parts of their Orbits are so great as to
overcome the Sun’s attraction there, and cause them to ascend again
towards the higher parts of their Orbits; during which time, the Sun’s
attraction acting so contrary to the motions of those bodies, causes
them to move slower and slower, until their projectile forces are
diminished almost to nothing; and then they are brought back again by
the Sun’s attraction, as before.
[Sidenote: In what times the Planets would fall to the Sun by the power
of gravity.]
157. If the projectile forces of all the Planets and Comets were
destroyed at their mean distances from the Sun, their gravities would
bring them down so, as that Mercury would fall to the Sun in 15 days 13
hours; Venus in 39 days 17 hours; the Earth or Moon in 64 days 10 hours;
Mars in 121 days; Jupiter in 290; and Saturn in 767. The nearest Comet
in 13 thousand days; the middlemost in 23 thousand days; and the
outermost in 66 thousand days. The Moon would fall to the Earth in 4
days 20 hours; Jupiter’s first Moon would fall to him in 7 hours, his
second in 15, his third in 30, and his fourth in 71 hours. Saturn’s
first Moon would fall to him in 8 hours; his second in 12, his third in
19, his fourth in 68 hours, and the fifth in 336. A stone would fall to
the Earth’s center, if there were an hollow passage, in 21 minutes 9
seconds. Mr. WHISTON gives the following Rule for such Computations.
“[31]It is demonstrable, that half the Period of any Planet, when it is
diminished in the sesquialteral proportion of the number 1 to the number
2, or nearly in the proportion of 1000 to 2828, is the time that it
would fall to the Center of it’s Orbit.” This proportion is, when a
quantity or number contains another once and a half as much more.
[Sidenote: The prodigious attraction of the Sun and Planets.]
Public-domain text, read in full here on John Shaqi.
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