Adam Smith's History of Astronomy

Sir Isaac Netwon

September 9, 2015

Keplers’ laws were cemented by the observations of Cassini. But there were still constant irregularities in the motions of heavenly bodies.

Sir Isaac Newton first attempted to give a physical account of the motions of the Planets to solve such irregularities.

The physical connection, by which

Descartes tried to bind the movements of the Planets through the laws of impulse. These flow from the inertness of matter and are the easiest for the mind to undertand.

Aside from this, we do not have any other natural concept such as that of gravity. This is because we never gravitate matter. Instead, we just observe how gravity affects matter.

Sir Isaac Newton had the superior genius and sagacity to discover that he could join the movements of the Planets by a familiar principle of connection.

He demonstrated that=

  • the Planets gravitated towards the Sun and to one another, amd
  • had a projecting force originally impressed on them.

The primary ones might all described ellipses in one of the foci of the sun.

The secondary ones might describe figures of the same kind round their respective primaries, without being disturbed by the continual motion of the centers of their revolutions.

If the force which kept the planets in their orbits was like that of gravity and directed towards the Sun they individually would describe equal areas in equal times.

This attractive power of the Sun*=

  • is diffused in rays from a center and
  • is diminished in the same proportion as the squares of the distances increased

*Superphysics note= This is Kepler’s inverse square law

The motions of the planets would be swiftest when nearest the Sun, and slowest when farthest in the same proportion.

This gradual reduction of their respective gravities, their periodic times would bear the same proportion to their distances, which Kepler and Cassini had established between them.

He then proved that gravity was the connecting principle which joined the movements of the Planets by showing that the gravity on Earth is stronger* near the surface of the Earth.

*Superphysics note= Descartes also proves this

Gravity can make a body fall by around 15 Parisian feet in the first 1 second of its descent.

The Moon’s Irregular Orbit

The Moon is around 60 radii of the Earth distant from its surface.

Gravity diminished as the squares of the distance increase. Therefore, an object on the Moon would fall towards the Earth in 60 seconds.

But the arch which the Moon describes in 60 seconds falls, by observation, around 15 Parisian feet below the tangent drawn at the beginning of it.

Thus, the Moon is constantly falling towards the Earth.

The system of Sir Isaac Newton explained the many other irregularities which Astronomers had observed in the Heavens.

  • It explained that the centers of the planets’ revolutions were not precisely in the Sun’s center because the planets were also attracting* each other.

*Superphysics note= Kepler proved this earlier as Kepler’s Third Law

This explained the irregularities with Jupiter and Saturn, whenever they are nearly in conjunction with one another.

But the Moon’s irregularities had perplexed Astronomers the most. It was solved by Newton’s system.

The Moon=

  • appears furthest from the Earth when the Moon is nearest to the Sun. At this point, the Moon is more attracted to the sun and more separated from the Earth
  • appears nearest to the Earth when the Moon is in her quarters. At these points, both the Earth and the Moon are at equal distance from the Sun. The Earth and Moon are not attracted to the sun in parallel lines, but in lines which meet in his center.

Sir Isaac Newton computed the difference of the forces, with which the Moon and the Earth should, in all those different situations, according to his theory, to be impelled towards one another.

He found, that the different degrees of their approaches, as they had been observed by Astronomers, corresponded exactly to his computations.

The attraction of the Sun, in the conjunctions and oppositions, reduces the gravity of the Moon towards the Earth. This makes her extend her orbit and require a longer time to revolve around the Earth.

But, when the Moon and the Earth are in that part of the orbit which is nearest the Sun, this attraction of the Sun will be the greatest. Consequently, the gravity of the Moon towards the Earth, will there be most diminished. The moon’s orbit becomes most extended. This cases her orbit time to be the longest.

The Moon’s orbit is not precisely in the same plane with that of the Earth, but is at an angle.

  • The intersection of those two planes are called the Nodes of the Moon.
  • These Nodes of the Moon are in continual motion. In 18 or 19 years, these revolve backwards from east to west, through all the different points of the Ecliptic.

For the Moon, after having finished her revolution, generally intersects the orbit of the Earth somewhat behind the point where she had intersected it before.

Generally, the motion of the Nodes is retrograde. But not always. It is sometimes direct, and sometimes even stationary.

The Moon generally intersects the Plane of the Earth’s orbit, behind the point where she had intersected it in her former revolution. But she sometimes intersects it before that point, and sometimes in the very same point.

It is the situation of those Nodes which determines the times of Eclipses. Their motions had always been attended to by Astronomers who were perplexed by their inconsistencies because they assumed that the Moon’s orbin was perfectly regular and equable.

Astronomy, therefore, has been focused the most on theories for connecting the Moon’s motions than for all the other heavenly bodies taken together.

The theory of gravity connected most accurately all those irregular motions by the different actions of the Sun and the Earth.

The time, quantity, and duration of those direct and retrograde motions of the Nodes, as well as of their stationary appearances, could then be predicted by calculation.

The attraction of the Sun thus accounts for=

  • the motions of the Nodes.
  • the perpetual variation in the inclination of her orbit to that of the Earth.

The Moon revolves in an ellipse, which has the centre of the Earth in one of its foci.

  • The longer axis of its orbit is called the Line of its Apsides
    • This line is not to be always directed towards the same points of outer space. Instead, it revolves forwards, from west to east, so as to pass through all the points of the Ecliptic, and to complete its period in about 9 years.

*Superphysics Note= Lateral precession?

This wasanother irregularity that very much perplexed Astronomers. This was also solved by the theory of gravity.

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.

It had accustomed mankind=

  • to conceive motion as never beginning, but in consequence of external impulse, and
  • to connect the fall of heavy bodies, near the surface of the Earth, and the other Planets, by this more general bond of union

His system, however, now prevails and has advanced to be the most universal kind of philosophy.

  • It is so solid that even us philosophers use his terminologies to explain the connection of dijointed ideas and discordant phenomena of nature, as if gravity were real chains which Nature uses to bind together her several operations.

This is why Newton’s system gained the general and complete approbation of mankind and is the greatest discovery that ever was made by man. It discovered an immense chain of the most important and sublime truths, all closely connected together, by one capital fact called gravity which we experience daily.