Gravity

The ancients believed that:

• the fixed stars stood immoveable in the highest parts of the universe
• under the fixed stars the planets were carried about the sun
• the earth, as one of the planets, described an annual course about the sun,
• by a diurnal motion it was in the mean time revolved about its own axis
• the sun, as the common fire which served to warm the whole, was fixed in the centre of the universe.

This was the philosophy taught by:

• Philolans
• Aristarchus of Samos
• Plato in his riper years
• the Pythagoreans

This was also the judgment of:

• Anaximander who was the most ancient of them all,
• Numa Pompilins, the wise king of the Romans
  • He built a temple in honour of Vesta and ordained perpetual fire to be kept in the middle of it, as a symbol of the world with the sun in the centre

The Egyptians were early observers of the heavens. This heliocentric philosophy came from them and was spread abroad, especially among the Greeks who were addicted to the study of philology than of nature.

Anaxa&oras, Democritus, etc, did began the idea that:

• the earth was the centre of the world, and
• the stars revolved towards the west around the earth

Both sides agreed that the motions of the celestial bodies were performed in spaces free of resistance.

The whimsical solid orbs were later added by Eudoxus, Calippus, and Aristotle when the ancient philosophy began to decline.

Comets are totally inconsistent with solid orbs.

The Chaldeans were the most learned astronomers of their time. They thought of comets as planets with very eccentric orbits which showed themselves once in a revolution, when they descended into the lower parts of their orbits.

This caused comets to be placed under the moon, until recent observations caused them to be put higher out and solid orbs to be discarded forever.

The planets were thought to be put in their orbits by:

• vortices, as proposed by Kepler and Descartes.
• impulse or attraction, as proposed by Borelli, Honke, etc.

My goal is just to:

• trace the quantity and properties of this force from the phenomena (p. 218)
• apply what we discover in some simple cases as principles
  • In a mathematical way, we can estimate the effects thereof in more involved cases. It would be impossible to bring every phenomena to direct observation.

By using mathematics, we can avoid all questions about the nature of this force. This lets us call it generally as a centripetal force when it is directed towards some centre. We call it circumsolar, circum-terrestrial, circum-jovial, etc in reference to the center of the sun, earth, and Jupiter respectively.

These centripetal forces helps us understand the motions of projectiles.

Let:

• AFB be the earth’s surface
• C its centre
• VD, VE, VF, the curve lines which a body traces if projected horizontally from the top of a mountain successively with more and more velocity

Assuming there is no air around the earth:

• the body projected with a less velocity traces the lesser arc VD
• the body projected with a greater velocity traces the greater arc VE and goes farther and farther to F and G
  • If the velocity was still more increased, it would reach beyond the earth’s circumference and return where it was projected

This radius of this motion relative to the Earth’s centre (Prop. 1, Book 1, Principia Mathematica) is proportional to the times in which they are drawn. Thus, its velocity when it returns to its starting point, will be the same as its initial velocity. It will repeat the same curve over and over.

But if the body was projected from greater heights of 5, 10, 100, 1000, or more, those bodies will be affected by different strength of gravity will trace arcs either concentric with the earth, or eccentric. They will go on revolving through the heavens in those trajectories in their orbits just as the planets do.

Gravity must press downwards. All bodies around the earth either:

• falls directly to the earth, if they are let fall from rest, or
• at from straight lines towards the earth, if they arc so from gravity directed to least perpetually deviate projected obliquely

These motions are caused by forces as shown in the first Books of our Principles of Philosophy.

If the earth stood still, and the stars revolved around it in 24 hours, then those forces which retain the stars in their orbs are not directed to the earth, but to the centers of those orbs, creating parallel circles.

This difficulty (Cor. 1, Prop. 2) arises from the twofold motion observed in the stars:

• one diurnal around the axis of the earth
• the other exceedingly slow round the axis of the ecliptic.

This requires forces so perplexed and variable that it cannot be reconciled with any physical theory.