How does the law of inertia redefine the “problem of the planets”? In what way does it figure in Newton’s general conception of force and his overall strategy for providing a demonstration of the Copernican system?
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“If I have seen further it is only by standing on the shoulders of giants.”
–Newton in a letter to Hooke
Modern astronomy and modern science emerging between the deaths of Copernicus and Galileo breathe new life into learning in all fields. People accepted a different understanding of their place in the universe and also approved a different model of the universe. The period after the death of Copernicus saw a transition from Aristotle’s and Ptolemy’s ancient astronomy to Newton’s new breakthroughs in gravitation and the understanding of motion. The modern science of this period helped in understanding the universe.
The Copernican Revolution answered the question of our place in the universe, but Kepler’s law only partially answered the question of planetary movements. Though Galileo put forth several theories on inertia, free-fall and projectile motion, he was not able to reconcile terrestrial motions with the motions of the heavens. That step fell to Isaac Newton. The work of Newton brought about the concept of a mechanical universe.
Issac Newton was a calm boy from a farming family. He was born on Christmas day 1642 in the English village of Woolsthorpe. He studied mathematics and physics at Trinity College. It was during this period that he made most of his discoveries in optics, physics, and mathematics. Among other things, he studied optics, developed three laws of motion, prophesied the nature of gravity, and invented differential calculus. His work got published in his book Principia in 1687. The book placed science on a firm analytical base. 1
Newton’s concepts of motion and gravitation changed the direction of development of thought in astronomy. Using the work of Galileo, Kepler, and others, Newton developed three laws of motion that reconciled the force acting on a body and the body’s subsequent motion. Thus, using these laws and given an external force acting on a body, one could accurately predict the movement of the body. Applying these laws to the heavens, Newton claimed that, there must be some force attracting the moon to the Earth or else the moon would move away from Earth. The Earth must be emitting an attractive force on the moon. He soon realized that the same force that makes apples fall from trees, maintains the moon in orbit around the Earth — gravity.
The Cosmology Of Newton
Aristotle, Ptolemy, and others considered the universe to be bounded by the sphere of the fixed stars. Galileo believed in the notion of an infinite universe but did not provide any strong justifications to back his claim. Newton strongly believed that space was not bounded, his laws required it, and put forth his idea of a limitless universe, correcting Aristotelian models of the cosmos. He sided with Copernicus’s heliocentric theory of the cosmos and changed the size of it to infinity. Thus, Newton improved/strengthened the Copernican model of the cosmos.
Kepler tried to attribute the workings of the universe to a singular force but failed. Newton accomplished this aim of Kepler. Though Newton achieved this objective only after Copernicus, Kepler and Galileo had laid a sufficient foundation. Galileo’s and Kepler’s work with motions of the heavens and Copernicus’s theories of attractive and repulsive magnetic forces directly shaped Newton’s theories of a cosmos been guided by a singular force.
A Mechanical View Of Nature
A mechanized view of nature had been conceptualized, long ago, from the likes Descartes and the Greeks. Descartes’s geometry, vortices and philosophical principals influenced Newton’s mathematics and mechanistic view of nature. Newton’s mechanistic view was, and still is, the superior model in science. Newton proposed that the cosmos was made up ‘matter, motion and space,’ conforming with Copernicus 2. Newton modeled the universe according to his law of inertia: a body continues to be in the state it is in – rest or motion – until an external force acts upon it; hence one could imagine the universe as a ‘vast billiard table’ – something moves only if another thing causes it to move 3. According to this model, since a body cannot come to rest from motion or move from rest by itself in the absence of an external force, Newton, being a devout Christian, was inclined to say that a deity created and set the universe in motion. 4
Newton’s Three Laws of Motion 5:
a. A body continues to be in the state it is in – rest or motion – until an external force acts upon it. This law improves upon Galileo’s notion of inertia. According to this law, uniform motion is a natural state of all bodies.
b. The change of motion – acceleration ‘a’ – of a body of mass ‘m’ is directly proportional to the force ‘f’ acting upon it. Motion is in the direction of the force.
c. Every force has an equal and opposite reaction.
The Law of Gravitation And The Problem Of The Planets
Newton, from his principles of motion and force, developed the law of gravitation. The law became Newton’s biggest contribution in support of Copernicus. Using this law he attacked the problem of the planets. Newton was faced with two problems, (a) what is the direction in which the gravity acts? and (b) what is the quantity of that force? The first problem deals with recognizing the general nature of force and the second problem deals with the physical properties of force. Newton solved these two problems with the help of the law of gravitation which he deduced from combining his laws of motion with Kepler’s planetary laws. 6
Newton provided theories, in detail, of the age-old question of how the planets moved. His predictions of the motions of planets were far more innovative and accurate than any of his former influences. At last, the Copernican model got the physical support, by the hands of Newton, it needed to bolster a heliocentric system in which the sun holds the planets in orbit.
Newton proved that a basic force, acting towards the center of motion, is responsible for the elliptical orbits of Kepler’s first law. He also showed that Kepler’s second law still holds when applying this basic force to planets. He derived a new force law from the geometric properties of ellipses and then re-derived Kepler’s third law from his new force law. 7 Hence, Newton made certain that his work conformed to the concepts/theories and laws in his time.
Newton’s vision led to a new understanding of planetary motion and orbits, resulting in the claim that the sun emits an attractive force on the planets maintaining them in orbit. Newton arrived at this conclusion with the help of Kepler’s work and re-deriving Kepler’s third law by introducing two new constants – gravity and the individual masses of the attracting bodies. Newton’s re-derived third law became instrumental in determining the masses of heavenly bodies. 8
Principia gained popularity because it provided an answer to a challenge – the problem of the planets – that puzzled ancient observers. The stars appeared fixed relative to one another, but the planets move against the background of the stars. Their appearances, apparent wandering and retro-gradation has always been a problem for observers for centuries. Plato asked observers to deduce an order to the motions of the planets in the form of uniform circular motions that would “save the phenomena” of the wandering planets. Ptolemy and Copernicus both worked, in this tradition, to try and “save the phenomena,” though Copernicus put forth the claim of a heliocentric cosmos. Circular motion remained a critical element for Kepler in his findings of the “archetypal cause central to God’s plan of the universe.” 9 His findings were strengthened by his primary concern for a physical cause. Besides Kepler, Aristotle held that the distinct eternal motion of the celestial sphere was circular motion. The stars moved in two ways around the earth. (1) A daily circular motion and (2) an annual circular motion.10 But the planets and the sun seemed to wander around a lot. Some observers claimed that the apparent motions of the planets can be resolved by complex epicycles. Copernicus proposed combinations of epicycles to predict the uniform circularity of the planets. However, Newton employed the use of circular motions in his dynamics in a radically different way than his predecessors.
Being influenced by Descartes, Newton’s astronomy was constructed partly by Cartesian images;11 but shortly after solving the problem of the planets in 1679 he separated himself from the Cartesian tradition. 12 Newton shifted his focus to the analysis of forces from the knowledge of observable physical phenomena and then to find more physical phenomena from these revealed forces. His primary concern, of course, was the problem of the planets. The problem of the planets, for Newton, wasn’t the question of resolving the motions of the heavens into uniform circular motions. It wasn’t the question of seeking mechanical explanations either. The problem of the planets, for Newton, was the difficult task of finding the mathematical explanations – not physical – of the force responsible for Kepler’s elliptical planetary orbits. Proposing a solution in Principia, his concept, in the beginning, was not well received. This was due to the fact that, everyone at that time was interested in the physical causes of gravity. 13
Newton’s solution to the problem of the planets, in short, is: assuming the elliptical orbit of the planet with the sun as its center – the sun is at the focus of the ellipse – emitting an attractive force on the planet – this assumption is derived from Kepler’s work – the centripetal force must be inversely proportional to the square of the distance. 14 Then, he applied this force to other physical phenomena given the functional form of the law of universal gravitation. 15 Though there were some astronomers who expected this solution, Newton’s demonstration was the first of it’s kind. All that remained, for Newton, was a mathematical description of the force.
Using his law of gravitation, Newton sought to solve the objections of the Copernican model. (a) Due to the earth’s rotation, objects should fly away if they are not tied to the ground. Newton claimed that gravity was the force responsible for holding things down and not flying off. (b) Objects dropped from some distance above the earth’s surface should not land at their initial positions, but be left behind by the rotation of the earth. Newton explained that all bodies have the property of inertia which is preserved while falling.
Orbital Motion 16
Newton’s proposed dynamics and law of gravitation revealed a new understanding of the orbital motion of the planets – he described the orbital motions as a “form of falling”.17
a. When a body orbits the earth, it is actually falling towards the center of the Earth but misses Earth due to it’s motion. The body needs circular velocity in order to maintain a circular orbit.
This explains how some type of satellites remain at a fixed position above the Earth.
b. When 2 bodies orbit each other, they are revolving around their center of mass.
c. Finally, Newton made a distinction between closed orbits and open orbits. To escape orbit, one must have enough escape velocity.
The significance of gravity is greater than one can imagine. This force, as Newton explains, besides making apples fall from trees affects tides “which intern can pull gasses away from stars, rip galaxies apart, and melt the interiors of small moons orbiting near massive planets.” 18
The Newtonian Universe
Newton’s ideas provided us with a new way of looking at the universe. His dynamics and laws of gravitation provided us with the ability to predict the motions of bodies when acted on by outside forces. Some other laws, such as Kepler’s third law, could be derived based on these concepts of Newton. His insight, made it possible for astronomers to measure the, present and future, motions and positions of planetary bodies and gravitational forces and interaction with the highest caliber of accuracy and precision. Hence, in the Newtonian universe, celestial and terrestrial motions are undivided.
Even today astronomers are building on the foundation laid by the findings of Newton, similar to how Newton improved and worked on the findings of his predecessors. It is inherent in the nature of science to build on the discoveries of others. Hence he says, modestly, “If I have seen farther than other men, it is because I stood upon the shoulders of giants.” 19
Our Special Place In The Universe
When Copernicus placed Earth as part of the celestial sphere it sparked a discussion on the distinction between terrestrial and celestial spheres. This new notion heralded the scientific revolution. Prior to Copernicus, Earth was always thought to be a different/special than the heavens; but Copernicus made Earth one of the planets. This concept had far reaching conclusions. Earth, and by extension us, became part of the cosmos. Then Kepler explained the motions of the planets based on laws devoid of any deity. Newton discovered these laws to be gravity – the same force that causes the fall of an apple. We are no longer special nor are we the center of the universe, but part of an intricate cosmos and its many phenomenas (which can now be understood by some fundamental laws) not ruled or caused by the Gods; hence making the cosmos a subject of scientific study. We are only special because of the ability of our minds to comprehend and understand the intricacies of us and everything around us.
Conclusion
The overwhelming success of Newton’s achievements has been astonishing. His laws proved to be right and it helped measure, with great accuracy, the positions and motions of heavenly bodies. Different laws for free-falling bodies, motions of stars and planets were no longer needed. A singular force explains all these phenomena – gravity.
One could say that he saw “further” than other scientists; though his discoveries could not have been possible without the findings of scientists, such as Galileo, Ptolemy, Tycho, Copernicus, Kepler, and others. The Copernicus revolution reached it’s peak under Newton. He furthered our understanding in optics, dynamics and other fields. Scientists, today, “are trying to make new discoveries by standing on the shoulder of the greatest giant of all, Sir Isaac Newton.” 20
Refrences
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6 Astronomy: the evolving universe By Michael Zeilik
7 http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion
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9 The key to Newton’s dynamics: the Kepler problem and the Principia … By J. Bruce Brackenridge, Sir Isaac Newton
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