# Gravity and Mass

September 20, 2022

## Newton and the Shape of the Planets as Oblate Spheroids

Before the theory of gravity, people thought that the Earth was perfectly globular.

But Sir Isaac Newton shows that the Poles must be somewhat elevated at the first, and flattened at the second because of the agitation from her daily revolution at the Equator.

• This is proven by the oscillations of pendulums being slower at the Equator than at the Poles.
• This means that gravity was stronger at the Poles and weaker at the Equator.

This proved that the Equator was further from the centre than the Poles.

All the measures, however, which had hitherto been made of the Earth, seemed to show the contrary, that it was drawn out towards the Poles, and flattened towards the Equator.

Newton, however, preferred his mechanical computations to the former measures of Geographers and Astronomers.

This was confirmed by the observations of Astronomers on the shape of Jupiter.

• Its diameter at the Pole relative to its Equator is 12= 13.
• It is a much greater inequality than could be supposed to take place between the correspondent diameters of the Earth.
• But it is exactly proportioneal to Jupiter’s=
• superior size
• superior rapidity in rotation

The observations of Astronomers at Lapland and Peru have fully confirmed Sir Isaac’s and have not only demonstrated, that the figure of the Earth is, in general, system, such as he supposed it; but that the proportion of its axis to the diameter of its Equator is almost precisely such as he had computed it.

## Newton and The Earth’s Axis

All the proofs that have ever been adduced of the daily revolution of the Earth, this perhaps is the most solid and satisfactory.

Hipparchus compared his own observations with those of some former Astronomers. He found that the equinoxial points were not always opposite to the same part of the Heavens. Instead, they advanced gradually eastward so slowly as to be sensible only in 100 years. It would require 36,000 to make a complete revolution of the Equinoxes and to carry them successively through all the different points of the Ecliptic.

More accurate observations of the Equinoxes was not so slow as Hipparchus had discovered that this precession imagined it, and that it required somewhat less than 26,000 years to give them a complete revolution.

During the geocentric era, this appearance was accounted for by supposing that the Firmament, besides its rapid daily revolution round the poles of the Equator, also had a slow periodical one round those of the Ecliptic.

When Hipparchus’ system was united by the schoolmen with the solid Spheres of Aristotle, they placed a new christaline Sphere above the Firmament to join this motion to the rest.

In the Copernican system, this appearance had hitherto been connected with the other parts of that hypothesis, by supposing a small revolution in the Earth’s axis from east to west.

Sir Isaac Newton connected this motion through gravity which united all the others. It showed that, by the Sun’s gravity, the elevation at the Earth’s equator produces the same retrograde motion of the Nodes of the Ecliptic which it produced of the Nodes of the Moon.

He computed the quantity of motion which could arise from this action of the Sun, and his calculations here too entirely corresponded with the observations of Astronomers.

## Newton and Comets

Before Newton, comets were the least attended to by Astronomers because of their rarity and inconstant appearance.

Aristotle, Hipparchus, Ptolemy, and Purbach had all degraded them below the Moon, and ranked them among the meteors.

Tycho Brahe’s observations demonstrated that they ascended into the celestial regions, and were often higher than Venus or the Sun.

Descartes supposed them to be always higher than even the orbit of Saturn. By the superior elevation, he thus bestowed on them, to have been willing to compensate that unjust degradation which they had suffered for so many ages before.

Later observations also demonstrated that they also revolved around the Sun and were therefore parts of the Solar System.

Newton applied his mechanical principle of gravity to explain the motions of comets. He said that they traveled in equal areas in equal times. This was later discovered by the later Astronomers.

Newton tried to show how from this principle, and those observations, the nature and position of their several orbits might be ascertained, and their revolution-times determined.

His followers used his principles to predict the returns of several comets, particularly the one for 1758.

• We must wait for that time before we can determine, whether his philosophy corresponds as happily to this part of the system as to all the others.

In the meantime, however, the ductility of this principle, which applied itself so happily to these, the most irregular of all the celestial appearances, and which has introduced such complete coherence into the motions of all the Heavenly Bodies, has served not a little to recommend it to the imaginations of mankind.

But of all the attempts of Newtonian Philosophy that appeared the most above the reach of human reason and experience is the attempt to compute the weights and densities of the Sun and the Planets.

## Gravity depends on mass

According to to Newton, the gravitational power in each body is proportional to the quantity of matter in that body.

But the revolution-time of small body around a bigger body that attracts it, is shorter as this attractive power is greater. Consequently, there is more matter in the attracting body.

If the densities of Jupiter and Saturn were the same with that of the Earth, then the revolutions of their moons would be shorter than actual. This is because the quantity of matter, and consequently their gravity would be as the cubes of their diameters*.

*Superphysics note= This from Kepler

By comparing the visual size of those Planets and the revolutions of their moons, they found that=

• Jupiter’s density is greater than that of Saturn
• Earth’s density is greater than that of Jupiter

This seems to establish in the Newtonian system that the nearer the Planets are to the Sun, the density of their matter is the greater.

## Newton’s Inverse Square Law

Newton’s system is more strictly connected together than those of any other philosophical hypothesis.

The universality of gravity states that gravity decreases as the squares of the distance increase*. Everything then follows this rule.

*Superphysics note= This was implied by Kepler’s kinships

This rule is precise and is observed everywhere, different from the loose principles of most other systems.

• It accurately predicts the time, place, quantity, and duration of each phenomenon.

Of all the qualities of matter, gravity is the most familiar to us after its inertness.

• We never act on it without having occasion to observe this property.

The inverse square law reduces as it leaves the center.

• It applies to all qualities that are propagated in rays from a centre, in light and in everything else of the same kind.

This is why we find it in all such qualities, and we expect to find it.

France and other foreign nations opposed the Newtonian system because the Cartesian system prevailed so generally prior.