(Galileo’s principle of inertia / Newton’s force / Sun might be the angel)
In this section, the three interesting points are Galileo’s principle of inertia, Newton’s force, and the Sun might be the angel.
1. Galileo’s principle of inertia:
“Galileo discovered a very remarkable fact about motion, which was essential for understanding these laws. That is the principle of inertia (Feynman et al., 1963, section 7.3 Development of dynamics).”
It is controversial to say that Galileo discovered a principle of inertia in which a body may keep on coasting forever in a straight line. First, Galileo did not explicitly state a theorem or a general principle of inertia. Next, Galileo suggested a concept of circular inertia: “a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping and placed at rest it would perpetually remain at rest, if in the first case all extrinsic impediments could be removed, and in the second case no external cause of motion were added (Galilei, 1613, pp. 113–114.)” In other words, a body may continue in its state of circular motion unless it is compelled to change that state by an external force.
In Principia, Newton (1687) states the First Law of motion (Motte's translation) as “Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon (p. 19).” In explaining his First Law, Newton writes that “A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time.” In general, Newton suggested two kinds of uniform motion: progressive motion in a right line and circular motion (Westfall, 1971).
2. Newton’s force:
“Newton modified this idea, saying that the only way to change the motion of a body is to use force (Feynman et al., 1963, section 7.3 Development of dynamics).”
According to Feynman, Newton’s second law of motion means that the acceleration produced by a force is inversely proportional to a mass, or the force is proportional to the mass times the acceleration. Simply put, a force is needed to change the speed or the direction of motion of a body. In Principia, Newton (1687) states the Second Law as “[t]he alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed (p. 19).” The term motion means momentum and thus, Newton has specified a relationship between a motive force (F) and a change of momentum (Δmv). The equation F = ma is not stated in Newton’s second law.
Currently, physicists define force as an interaction between two objects rather than an innate property of an object (Brookes & Etkina, 2009). In Principia, Newton (1687) writes that “vis insita, or innate force of matter is a power of resisting, by which everybody, as much as in it lies, endeavors to preserve in its present state, whether it be of rest, or of moving uniformly forward in a right line (p. 9).” In short, Newton views inertia as an innate force of a body that is different from the motive (external) force. One may debate whether Newton’s innate force has a connotation of momentum or energy. It is not surprising that the law of conservation of force was developed subsequently (Nicolson, 1871).
3. Sun might be the angel:
“If there is a force toward the sun, the sun might be the angel, of course! (Feynman et al., 1963, section 7.3 Development of dynamics).”
Feynman explains that the brilliant idea in planetary (circular) motions is that no tangential force is needed to keep a planet coasting in its orbit. On the contrary, a presence of tangential force would increase the speed of the planet in a circular orbit. (The speed of a planet in an elliptical orbit can be changed by a central force because the path of the planet is not perpendicular to this force.) More important, the force needed to control the planetary motion is not a force around the sun but toward the sun. This force causes the actual motion of a body to deviate from the line of which the body would have gone. Interestingly, Feynman adds that if there is a force toward the sun, the sun might be the angel.
Kepler is sometimes cited for asserting planetary motion was driven by angels about the sun. Historically speaking, Kepler proposes the existence of a magnetic force between the planets and the Sun. Thus, it is not true that Kepler hypothesizes angels pushing the planets around the sun. In The Divine Comedy (c. 1308 to c. 1320), Dante writes “To those celestial lights, that towards us came, leaving the circuit of their joyous ring, conducted by the lofty seraphim… moves the third heaven… (Alighieri, 1909, p. 317).” Note that a seraphim is an angel that has six wings. Medieval scholars debated whether the angels were external or internal movers and whether the angels’ powers were independent of God (Tubbs, 2009).
Questions for discussion:
1. Should the principle of inertia be applicable to circular motions?
2. How is Newton’s original concept of force different from current physicists’ formulation of force?
3. Why did Feynman explain that the force needed to control the motion of a planet around the sun is a force toward the sun because of the principle of inertia?
The moral of the lesson: the force needed to control the motion of a planet around the sun is not a force around the sun but toward the sun.
References:
1. Alighieri, D. (1909/2009). The Divine Comedy (translated by Henry F. Cary). New York: Cosimo.
2. Brookes, D. & Etkina, E. (2009). Force, ontology, and language. Physical Review, Special Topics, Physics Education Research, 5, 010110.
3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
4. Galilei, G. (1913). Letters on Sunspots (translated by S. Drake). In G. Galilei (1957). Discoveries and Opinions of Galileo. New York: Doubleday.
5. Newton, I. (1687/1995). The Principia (translated by A. Motte). New York: Prometheus.
6. Nicolson, J. (1871). The Conservation of Force. Nature, 4, 47-48.
7. Tubbs, R. (2009). What Is a Number? : Mathematical Concepts and Their Origins. Baltimore: Johns Hopkins University Press.
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