### Which Of These Men Formulated The Law Of Universal Gravitation?

- Marvin Harvey
- 0
- 4

Sir Isaac Newton developed the three basic laws of motion and the theory of universal gravity, which together laid the foundation for our current understanding of physics and the Universe.

#### Which of these men formulated the law of universal gravitation quizlet?

Johannes Kepler. Which of these men formulated the Law of Universal Gravitation? Sir Isaac Newton.

## Who of the following developed the law of gravitation quizlet?

Terms in this set (9) Isaac Newton is credited with the law of universal gravitation.

#### Who was the first modern astronomer to propose a sun centered universe?

Nicolaus Copernicus was a Polish astronomer and mathematician known as the father of modern astronomy. He was the first European scientist to propose that Earth and other planets revolve around the sun, the heliocentric theory of the solar system. Prior to the publication of his major astronomical work, “On the Revolutions of the Heavenly Spheres,” in 1543, European astronomers argued that Earth lay at the center of the universe, the view also held by most ancient philosophers.

## Which scientist determine the nature of the forces that kept the planets in their orbits?

Evolution of an Idea – “We revolve around the Sun like any other planet.” —Nicolaus Copernicus “Of all discoveries and opinions, none may have exerted a greater effect on the human spirit than the doctrine of Copernicus. The world has scarcely become known as round and complete in itself when it was asked to waive the tremendous privilege of being the center of the universe.” —Johann Wolfgang von Goethe The ancient Greek philosophers, whose ideas shaped the worldview of Western Civilization leading up to the Scientific Revolution in the sixteenth century, had conflicting theories about why the planets moved across the sky.

One camp thought that the planets orbited around the Sun, but Aristotle, whose ideas prevailed, believed that the planets and the Sun orbited Earth. He saw no sign that the Earth was in motion: no perpetual wind blew over the surface of the Earth, and a ball thrown straight up into the air doesn’t land behind the thrower, as Aristotle assumed it would if the Earth were moving.

### Newton’s Law of Universal Gravitation

For Aristotle, this meant that the Earth had to be stationary, and the planets, the Sun, and the fixed dome of stars rotated around Earth. A long-exposure photograph reveals the apparent rotation of the stars around the Earth. (Photograph ©1992 Philip Greenspun.) For nearly 1,000 years, Aristotle’s view of a stationary Earth at the center of a revolving universe dominated natural philosophy, the name that scholars of the time used for studies of the physical world.

A geocentric worldview became engrained in Christian theology, making it a doctrine of religion as much as natural philosophy. Despite that, it was a priest who brought back the idea that the Earth moves around the Sun. In 1515, a Polish priest named Nicolaus Copernicus proposed that the Earth was a planet like Venus or Saturn, and that all planets circled the Sun.

Afraid of criticism (some scholars think Copernicus was more concerned about scientific shortcomings of his theories than he was about the Church’s disapproval), he did not publish his theory until 1543, shortly before his death. The theory gathered few followers, and for a time, some of those who did give credence to the idea faced charges of heresy. In 1543, Nicolaus Copernicus detailed his radical theory of the Universe in which the Earth, along with the other planets, rotated around the Sun. His theory took more than a century to become widely accepted. But the evidence for a heliocentric solar system gradually mounted.

When Galileo pointed his telescope into the night sky in 1610, he saw for the first time in human history that moons orbited Jupiter. If Aristotle were right about all things orbiting Earth, then these moons could not exist. Galileo also observed the phases of Venus, which proved that the planet orbits the Sun.

While Galileo did not share Bruno’s fate, he was tried for heresy under the Roman Inquisition and placed under house arrest for life. Galileo discovered evidence to support Copernicus’ heliocentric theory when he observed four moons in orbit around Jupiter. Beginning on January 7, 1610, he mapped nightly the position of the 4 “Medicean stars” (later renamed the Galilean moons). Over time Galileo deduced that the “stars” were in fact moons in orbit around Jupiter.

At about the same time, German mathematician Johannes Kepler was publishing a series of laws that describe the orbits of the planets around the Sun. Still in use today, the mathematical equations provided accurate predictions of the planets’ movement under Copernican theory. In 1687, Isaac Newton put the final nail in the coffin for the Aristotelian, geocentric view of the Universe.

Building on Kepler’s laws, Newton explained why the planets moved as they did around the Sun and he gave the force that kept them in check a name: gravity.

#### Who first developed a universal law of how gravity works?

Isaac Newton: Who He Was, Why Apples Are Falling

- Legend has it that Isaac Newton formulated gravitational theory in 1665 or 1666 after watching an apple fall and asking why the apple fell straight down, rather than sideways or even upward.
- “He showed that the force that makes the apple fall and that holds us on the ground is the same as the force that keeps the moon and planets in their orbits,” said Martin Rees, a former president of Britain’s Royal Society, the United Kingdom’s national academy of science, which was once headed by Newton himself.
- Isaac Newton, Underachiever?

“His theory of gravity wouldn’t have got us global positioning satellites,” said Jeremy Gray, a mathematical historian at the Milton Keynes, U.K.-based Open University. “But it was enough to develop space travel.”Born two to three months prematurely on January 4, 1643, in a hamlet in Lincolnshire, England, Isaac Newton was a tiny baby who, according to his mother, could have fit inside a quart mug.

- A practical child, he enjoyed constructing models, including a tiny mill that actually ground flour—powered by a mouse running in a wheel.Admitted to the University of Cambridge on 1661, Newton at first failed to shine as a student.
- In 1665 the school temporarily closed because of a bubonic plague epidemic and Newton returned home to Lincolnshire for two years.

It was then that the apple-falling brainstorm occurred, and he described his years on hiatus as “the prime of my age for invention.” Despite his apparent affinity for private study, Newton returned to Cambridge in 1667 and served as a mathematics professor and in other capacities until 1696.

- Isaac Newton: More than Master of Gravity Decoding gravity was only part of Newton’s contribution to mathematics and science.
- His other major mathematical preoccupation was calculus, and along with German mathematician Gottfried Leibniz, Newton developed differentiation and integration —techniques that remain fundamental to mathematicians and scientists.

Meanwhile, his interest in optics led him to propose, correctly, that white light is actually the combination of light of all the colors of the rainbow. This, in turn, made plain the cause of chromatic aberration—inaccurate color reproduction—in the telescopes of the day.To solve the problem, Newton designed a telescope that used mirrors rather than just glass lenses, which allowed the new apparatus to focus all the colors on a single point—resulting in a crisper, more accurate image.

- Newton’s Law of Inertia : Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it.
- Newton’s Law of Acceleration : Force is equal to the change in momentum (mV) per change in time. For a constant mass, force equals mass times acceleration,
- Newton’s Law of Action and Reaction: For every action, there is an equal and opposite reaction.

- Newton published his findings in 1687 in a book called Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia,
- “Newton’s Principia made him famous—few people read it, and even fewer understood it, but everyone knew that it was a great work, rather like Einstein’s Theory of Relativity over two hundred years later,” writes mathematician Robert Wilson of the Open University in an,
- Isaac Newton’s “Unattractive Personality”

Despite his wealth of discoveries, Isaac Newton wasn’t well liked, particularly in old age, when he served as the head of Britain’s Royal Mint, served in Parliament, and wrote on religion, among other things.”As a personality, Newton was unattractive—solitary and reclusive when young, vain and vindictive in his later years, when he tyrannized the Royal Society and vigorously sabotaged his rivals,” the Royal Society’s Rees said.Sir David Wallace, director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, U.K., added, “He was a complex character, who also pursued alchemy”—the search for a method to turn base metals into gold—”and, as Master of the Mint, showed no clemency towards coiners sentenced to death.”In 1727, at 84, Sir Isaac Newton died in his sleep and was buried with pomp and ceremony in Westminster Abbey in London.

### Who formulated the three laws of motion and universal gravitation?

What are Newton’s Laws of Motion? –

- An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.
- The acceleration of an object depends on the mass of the object and the amount of force applied.
- Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.

Sir Isaac Newton worked in many areas of mathematics and physics. He developed the theories of gravitation in 1666 when he was only 23 years old. In 1686, he presented his three laws of motion in the “Principia Mathematica Philosophiae Naturalis.” By developing his three laws of motion, Newton revolutionized science.

#### Who developed the gravity model?

Abstract – The gravity equation is a current workhorse of empirical trade theory. It is generally acknowledged that this theory, which relates the extent of trade between countries to their respective sizes, distances, and relative trade barriers, was first developed by Jan Tinbergen in 1962.

- Acceptance of the gravity model as part of the discipline’s core was limited by its scant theoretical foundation for the first 40 years of its existence.
- This paper finds that a theory of trade gravity was first developed by Adam Smith in The Wealth of Nations,
- Moreover, it is shown that Smith’s statement of a proportional relation between economic size and distance came about as an application of his general theory of differential capital productivity in different economic sectors, and his elaboration of a theory of the gains from trade originated by David Hume.

It is further shown that Smith had an explanation of the size of border affects in trade volumes, and a gravity theory of trade restrictions.

### Who was the first famous astronomer?

The first stellar catalogue – In the second century BCE, the famed Greek astronomer Hipparchus of Nicaea compiled the first stellar catalogue. A record of his work was handed down by Ptolemy, an astronomer writing three hundred years later at Alexandria – by then part of the Roman Empire.

To measure angles in the sky, Hipparchus employed the ancient Babylonian practice, still in use today, of dividing a circle into 360 degrees, and each degree into 60 arc minutes. Hipparchus’s catalogue, one of the earliest successful attempts to chart the heavens, lists the positions of 850 stars across the sky with a precision of about one degree (about twice the angular size of the full Moon).

He was able to attain this precision exclusively with naked-eye observations and the few instruments available at the time – gnomons, astrolabes, and armillary spheres. Hipparchus also created the magnitude system for describing the brightness of stars, which is still in use today, and studied the relative distance of the Sun and the Moon from Earth.

### Who is the first father of modern astronomy?

NICHOLAS COPERNICUS : THE FATHER OF MODERN ASTRONOMY 1543-1943.

#### Who was the first person to prove that the Earth moves around the Sun in India?

“The Earth revolves around the sun not the sun revolves around the earth”. This conclusion was made by _.A. CopernicusB. EinsteinC. NewtonD. Galileo Answer Verified Hint: The view that earth and other planets revolve around the sun is the Heliocentric astronomical model.

- Aristarchus, Nicolaus Copernicus, William Herschel, Freidrich Bessel, Galileo Galilei and other astronomers and scientists worked on the revolution of planets around the sun.
- Complete answer: Through the model of Heliocentrism it was concluded that the Earth and other planets revolve around the sun at the center of the Universe.

This model was earlier opposed to geocentrism, which placed the Earth at the center. In the 16th century the mathematical model of the heliocentric system was presented by the astronomer, Catholic cleric and Mathematician Nicolaus Copernicus which was known as the Copernican Revolution.

He concluded that earth revolves around the sun not the sun revolves around the earth. Looking at the options given: Option A. Copernicus was the one who in the 16th century concluded that earth revolves around the sun. This is the correct answer.Option B. Einstein is famous for his theory of relativity.

It is an incorrect option.Option C. Newton discovered the laws of gravity and motion. It is an incorrect option. Option D. Galileo Galilei was an astronomer who invented the first telescope in 1609. It is an incorrect option.

So, the correct answer is option A. Note: Copernicus also argued that earth turned daily on its axis and that gradual shifts of this axis accounted for the changing seasons.

: “The Earth revolves around the sun not the sun revolves around the earth”. This conclusion was made by _.A. CopernicusB. EinsteinC. NewtonD. Galileo

### Who discovered the force that pulls objects towards Earth is the same force that keeps the planets orbiting the Sun?

GALILEO AND GRAVITY Galileo was a famous scientist in the 16th and 17th Century. His most famous observation was that two objects of the same size but different weights hit the ground at the same time if they are dropped from the same height. This happens because the force of gravity acting on both objects is the same.

### Which Indian scientist said Earth revolves around the Sun?

Āryabhaṭa | |
---|---|

Statue of Aryabhata at the IUCAA, Pune (although there is no historical record of his appearance). | |

Born | 476 CE (Unclear) Kusumapura, Pataliputra (present day Patna, Bihar ). or, Asmaka (Modern-day Maharashtra – Telangana ) |

Died | 550 CE Pataliputra, Gupta Empire (modern-day Patna, India ) |

Academic background | |

Influences | Surya Siddhanta |

Academic work | |

Era | Gupta era |

Main interests | Mathematics, astronomy |

Notable works | Āryabhaṭīya, Arya- siddhanta |

Notable ideas | Explanation of lunar eclipse and solar eclipse, rotation of Earth on its axis, reflection of light by moon, sinusoidal functions, solution of single variable quadratic equation, value of π correct to 4 decimal places, diameter of Earth, calculation of the length of sidereal year |

Influenced | Lalla, Bhaskara I, Brahmagupta, Varahamihira, Kerala school of astronomy and mathematics, Islamic Astronomy and Mathematics |

Aryabhata Photo on Wall of Patna Junction Aryabhata ( ISO : Āryabhaṭa ) or Aryabhata I (476–550 CE ) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy, He flourished in the Gupta Era and produced works such as the Aryabhatiya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old) and the Arya-siddhanta.

- Aryabhata created a system of phonemic number notation in which numbers were represented by consonant-vowel monosyllables.
- Later commentators such as Brahmagupta divide his work into Ganita (“Mathematics”), Kalakriya (“Calculations on Time”) and Golapada (“Spherical Astronomy”),
- His pure mathematics discusses topics such as determination of square and cube roots, geometrical figures with their properties and mensuration, arithmetric progression problems on the shadow of the gnomon, quadratic equations, linear and indeterminate equations,

Aryabhata calculated the value of pi ( π) to the fourth decimal digit and was likely aware that pi ( π) is an irrational number, around 1300 years before Lambert proved the same. Aryabhata’s sine table and his work on trignometry were extremely influential on the Islamic Golden Age ; his works were translated into Arabic and influenced Al-Khwarizmi and Al-Zarqali,

## Did Galileo or Newton discover gravity?

Who really discovered the law of gravity? Everyone knows that Isaac Newton came up with the law of gravity after seeing an apple fall from a tree in his mother’s garden. Newton himself told the story to several contemporaries, who recorded it for posterity.

Ever since, Newton has been credited with discovering the law, describing how “All celestial bodies whatsoever have an attraction or gravitating power towards their own centres”. But these words are not Newton’s. They were penned by his scientific rival Robert Hooke in 1670, decades before Newton started telling people the apple story.

This has led some historians to suspect Newton deliberately made up the story of the apple to back his claim to priority. While Hooke is best known today for a dull law about springs, he was one of the most brilliant scientists of his time, and made a host of discoveries.

He even showed Newton to be wrong on an esoteric point concerning falling bodies. This did not go down well with the pathologically prickly Newton, who seems to have set about showing he had worked on gravity years before Hooke, leading to his claim about being inspired by the apple back in 1666. No one doubts that Newton made the biggest contribution to understanding gravity, but sadly for Hooke, Newton wanted to have the credit for everything.

Subscribe to for fascinating new Q&As every month and follow on Twitter for your daily dose of fun facts. : Who really discovered the law of gravity?

#### Which is Newton’s law of gravitation?

Newton’s Law of Universal Gravitation states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them. The universal gravitation equation thus takes the form. F ∝ m 1 m 2 r 2.

#### Did Galileo discover laws of gravity?

Innovations of the law of fall. – In the period before Galileo, scientists thought that force causes speed, as claimed by Aristotle, Galileo showed that force causes acceleration. On the basis of the law of parabolic fall, Galileo reached the conclusion that bodies fall on the surface of the earth at a constant acceleration, and that the force of gravity which causes all bodies to move downward is a constant force.

In other words, a constant force does not lead to constant speed but to constant acceleration. Galileo’s claim that force causes acceleration is inseparable from his claim that bodies do not require a cause to continue their movement. This latter claim states that a body in motion will continue its motion so long as no factor disturbs that motion.

This principle is called the principle of inertia,

The law of parabolic fall was an innovation in that it claimed that the speed of a body will continue to increase endlessly. Contrary to the claims of the natural philosophers of his period, Galileo claimed that a body will not attain a certain speed which will remain constant but will continue accelerating until it comes into contact with the ground. This claim is of course true so long as one ignores air resistance, which can be very significant for certain bodies and at high speeds. |

it is important to remember that Galileo’s law of fall claims that bodies fall at a constant acceleration, i.e., that their speed increases by equal increments within equal time periods, and that the distance traveled by them in equal time periods is not equal. If during the first second, the ball traveled a distance of 10 cm, it will travel a distance of 30 cm during the second second, of 50 cm during the third second, 70 cm during the fourth second, and so on. Mathematically:

## Who made the universal laws of physics?

The Development of Dynamics – Isaac Newton began with a problem that was simple enough to solve, yet complex enough to yield crucial new insights. He began by analyzing the form of motion that the Greeks had regarded as perfect: uniform circular motion.

In one sense, it was perfect—it was perfectly suited to expose the errors of Newton’s predecessors and illuminate the principles of a new dynamics. Galileo had never grasped that bodies move with constant speed in a straight line in the absence of all external forces. Lacking the concept “gravity,” he suggested that horizontal motion at constant speed ultimately meant motion in a circle around Earth, which he thought could occur in the absence of an external force.

Kepler, on the other hand, had never grasped that any motion could occur in the absence of a force; he assumed that every motion is the result of an external push in the direction of the motion. In his analysis of circular motion, Newton identified and rejected both of these errors.

- Prior to Newton, the case of the moon circling Earth was regarded as entirely different from the case of a hawk circling its prey.
- Newton, however, ascended to a level of abstraction that treated these two phenomena as the same; his goal was to analyze circular motion as such, and apply what he found to any and all instances of it.

His policy here is expressed in the dictum he would later identify as a “rule of reasoning”: “o the same natural effects we must, as far as possible, assign the same causes.” 2 A major part of Newton’s motivation for studying circular motion was the planetary orbits, which are nearly circular.

- But he did not begin his analysis by considering the planets; he began with cases in which the cause of the motion is much easier to identify.
- He considered a weight attached to the end of a rope and swung around in a circle, and a ball rolling around in a circle inside a bowl.
- In these cases, what is the cause of the circular motion? For the weight, it is the tension in the rope; the man holding the rope must pull inward.

If he lets go, the weight will no longer move in a circle, but will fly off horizontally in a straight line (until the force of gravity pulls it to Earth). For the ball in the bowl, the circular motion is caused by the inward push exerted by the surface of the bowl.

- If the ball escapes the bowl, then it too will initially fly off in a straight line.
- In both cases, the uniform circular motion of the body is sustained by a constant force directed toward the center of the circle.
- In a notebook, Newton wrote an early version of what later became his first law of motion: “A quantity will always move on in the same straight line (not changing the determination or celerity of its motion) unless some external cause divert it.” 3 The external cause is a force, some push or pull.

Newton recognized that it was crucial to distinguish between the type of motion that results from a force and the type that can occur in the absence of force. The concepts of motion used by Galileo were inadequate for this purpose. Galileo’s definition of “constant acceleration” applied only to the case of motion in a constant direction; in other words, acceleration was a scalar quantity that referred only to change of speed.

In the case of uniform circular motion, the speed of the body is constant and therefore its “Galilean acceleration” is zero. However, something is essentially the same about the cases of acceleration studied by Galileo and the case of uniform circular motion: In both, a change in the motion results from an applied force on the body.

An expanded concept of “acceleration” was needed to integrate these instances. In order to study and understand the effects of forces, motion had to be characterized in terms of both its magnitude and direction. Thus the concept “velocity” was formed, and “acceleration” was then defined as the rate of change of velocity.

Both velocity and acceleration are vector quantities—integrations of magnitude and direction. The formation of these concepts was a revolutionary step that made possible the science of dynamics. Armed with these concepts, Newton could ask: What is the acceleration of a body that moves with constant speed in a circle? From symmetry, he knew that the acceleration is constant and always directed toward the center of the circle.

But what is its magnitude? Newton considered a short time interval in which the body moves through a small arc on the circle. During this time, the body has deviated from a straight path by a small distance. For cases of constant acceleration, Galileo had given the mathematical law relating this distance to the acceleration and the time interval.

Using Galileo’s law and classical geometry, Newton was able to derive an equation that expressed the acceleration as a function of the “arc chord” (the line segment connecting the endpoints of the arc), the time interval, and the radius of the circle. In his next step, Newton made use of a new concept—”limit”—that lies at the foundation of calculus, the branch of mathematics he had discovered.

As the above time interval is made progressively shorter, the chord of the arc becomes ever more nearly equal to the arc itself. In the “limit,” as the time interval approaches zero, the ratio of the chord length to the arc length approaches one. Therefore, in this limit, the chord can be replaced with the arc.

- Newton made this substitution and arrived at his law of uniform circular motion: The magnitude of the acceleration at any point on the circle is equal to the speed of the body squared divided by the radius of the circle.
- Newton assumed nothing about the specific nature of the force causing this acceleration.

His analysis relied only upon the fact that a force causes a body to deviate from motion in a straight line at constant speed, and hence for the purpose of studying forces we must define acceleration as indicated earlier. Therefore, his law does not specify the physical causes operating in any particular case; it is applicable to any body moving uniformly in a circle.

- It was at this stage that Newton turned his attention to the planets.
- If the orbits are approximated as circular and if we express the speed as a function of radius and period, then Newton’s law implies that a planet’s acceleration is proportional to its orbital radius divided by its period squared.
- He then recalled that, according to Kepler’s third law, the period squared is proportional to the radius cubed.

By combining these two relationships, he derived an extraordinary result: The sun exerts an attractive force on each of the planets, causing accelerations that are inversely proportional to the square of the planet’s distance from the sun. Next he considered the moon and its approximately circular orbit around Earth.

- Such motion, he knew, implies that Earth exerts an attractive force on the moon.
- Since he was always seeking to connect disparate but related facts, Newton thought to ask: Is Earth’s attractive force of the same nature as the solar force; does it cause accelerations that also vary as the inverse square of the distance? If Earth had multiple moons at different distances, then the question could be answered by comparing the different accelerations.

But we have only the one moon—so how could Newton determine the variation of acceleration with distance? The answer lies in the concept of acceleration itself. The concept identifies an essential similarity between uniform circular motion and free fall: A body in circular motion is continuously falling away from a straight path and accelerating toward the center of the circle.

- Thus the moon accelerates toward Earth at a constant rate, as does a body dropped near the surface of Earth.
- Galileo had studied terrestrial free fall, and it was this acceleration that Newton could compare to that of the moon.
- This legendary comparison between the moon and the falling apple was demanded by the (inductively reached) vector concept of acceleration.

The quantities needed to make the comparison were known. The distance of the apple from the center of Earth is one Earth radius and the distance to the moon is sixty Earth radii. If the acceleration varies as the inverse square of the distance, then the apple’s acceleration will be greater than the moon’s acceleration by the factor (60) 2.

Using rough data about free fall and the size of Earth, Newton calculated the ratio of accelerations and found approximate agreement with the inverse square law. Thus terrestrial gravity seemed to be the same force that holds the moon in its orbit and that the sun exerts on the planets. Kepler’s dream of one integrated science encompassing physics and astronomy was no longer merely a dream; with this calculation, it became a real possibility.

This was the birth of the idea of universal gravitation, but it was far from being the proof of it. At this early stage, Newton had many more questions than answers. For example, what about the fact that the actual orbits are ellipses, not circles? And what is the justification for using one Earth radius as the distance between the apple and Earth? Much of Earth is closer to the apple, and much is farther away; why would Earth attract from its center? Furthermore, if gravity is truly universal and each bit of matter attracts all other matter, the implications and complexities are daunting.

For example, what is the effect of the moon’s attraction of Earth, or of the sun’s attraction of the moon, or of a planet’s attraction of other planets? What about strange bodies like comets, which move so differently? The main difficulty that Newton confronted was not that such questions were as yet unanswered.

The difficulty was that they were not yet answerable—not without a much deeper understanding of the relation between force and motion. It is one thing to say that a push or pull is necessary to change a body’s velocity; it is quite another feat to identify the exact mathematical law relating the external force to the body’s acceleration, and it is still another feat to identify a law that tells us what happens to the body exerting the force.

- Newton was just beginning to develop the cognitive tools he would need to prove universal gravitation.
- We have seen how Newton grasped that a body’s velocity remains constant in the absence of an external force, which is his first law of motion.
- Now let us follow the main steps of reasoning that led to his second and third laws of motion.

The concept of “force” originates from sensations of pressure that we experience directly when we hold a weight or when we push or pull a body. Force has magnitude and direction, and men learned to measure the magnitude using balances, steelyards, and spring scales.

- The concept of “acceleration,” on the other hand, is a more advanced development.
- It was Galileo who first explained how linear acceleration could be calculated from measured times and distances, and we have now seen the concept expanded from a scalar to a vector quantity.
- At this stage, when Newton inquires into the mathematical relation of force and acceleration, both quantities are clearly defined and independently measurable.

Furthermore, a key fact had already been discovered. Force is directly proportional to acceleration, which had been proven by experiments in which the force was varied in a known way and the resulting acceleration was measured. Galileo’s investigations of a ball rolling down an inclined plane provided the first such experiments.

Galileo described a procedure for directly measuring the force on the ball.4 First, he said, attach the ball to a known weight by means of a string and attach a pulley to the top of the inclined plane. Place the ball on the inclined plane with the string over the pulley and the weight hanging vertically over the back of the plane.

Then adjust the weight until it exactly balances the ball; this weight is the force on the ball in the direction of its constrained motion down the plane. The result of this measurement is what one might expect: The force on the ball is simply the component of its weight in the direction of the incline; in other words, it is the weight of the ball multiplied by the height to length ratio of the plane.

- Therefore we can quadruple the force on the ball simply by quadrupling the height of the plane (while keeping the length the same).
- If we do so, we find that the time of descent is half what it was before, which implies that the acceleration has quadrupled—that it has increased by the same factor as the force.

Alternatively, we can demonstrate by experiment that the initial height is proportional to the square of the final speed. With a little algebra, it can be shown that this relationship also implies that force is directly proportional to acceleration. The pendulum provides another experiment that leads to the same conclusion.

- The period of a pendulum swinging along the arc of a cycloid (a curve traced by a point on the rim of a rolling wheel) is independent of amplitude, and it can be demonstrated mathematically that this fact also implies a direct proportionality between force and acceleration.
- Because the inclined plane and pendulum experiments were so well known, Newton took this proportionality for granted and never bothered to present its inductive proof in any detail.

Of course, he did not yet have a law of motion in the form of an equation. A concept was still missing, and one can sense Newton’s frustration in some of his early notes. At one point, he wrote: “As the body A is to the body B so must the power or efficacy, vigor, strength, or virtue of the cause which begets the same quantity of velocity.

” 5 As he was writing, Newton must have been asking himself: As precisely what about the body A is to precisely what about the body B? Nobody had yet formed a clear concept of “mass.” The Greeks had proposed that all matter is endowed with either “heaviness” or “lightness.” The elements earth and water were claimed to be intrinsically heavy, whereas air and fire are intrinsically light.

These properties were regarded as the cause of natural, vertical motion. The invalid Greek concept of “lightness” was an obstacle that prevented anyone from discovering that all matter has the property “mass.” In 1643, Evangelista Torricelli performed a crucial experiment that removed this obstacle from the path of modern physics.

- Torricelli sought to explain a fact that was well known to mining engineers: A pump cannot lift water more than thirty-four feet above its natural level.
- The first question Torricelli asked himself was: Why does a pump work at all? In other words, when one end of a tube is inserted into water and the air is pumped out of the tube, why does the water rise into the tube? The commonly accepted answer was that “nature abhors a vacuum,” but this answer implies that the absence of matter in the tube is the cause of the water’s movement, that “nothingness” is literally pulling the water up the tube.

It was obvious to Torricelli that those who tried to explain the effect by reference to nothingness had in fact explained nothing. Instead, Torricelli identified something that did explain the effect: the weight of the air pressing down on the water surface.

- When air is removed from the tube, the atmosphere outside pressing on the water surface pushes water up the tube.
- It is similar to the action of a lever; the weight of the air (per surface area) will raise that same weight of water.
- Hence the weight of the entire atmosphere above a particular surface must be equal to the weight of thirty-four feet of water over that surface.

Torricelli’s idea implied that air pressure would lift the same weight of any fluid. For example, 2.5 feet of mercury weighs the same as thirty-four feet of water; therefore, when an evacuated tube is placed in a pool of mercury, the mercury should rise 2.5 feet up the tube.

- Torricelli did the experiment and observed precisely this result.
- Note that he used the method of agreement here: The same cause (i.e., the same weight of air) leads to the same effect (i.e., raises the same weight of fluid).
- Later experiments by Blaise Pascal and Robert Boyle demonstrated this relationship by showing that a change in the cause leads to a change in the effect (the method of difference).

These experiments showed that decreasing the amount of air above the fluid surface results in less fluid rising in the tube; in other words, as we remove the cause the effect disappears.6 Thus it was proven that even air is heavy. Contrary to the Greeks, there is no such property as absolute “lightness.” When something rises in air, it does so because it is less heavy than the air it displaces.

- In other words, such “natural” rising is explained by Archimedes’ principle of buoyancy, a principle that applies to air as well as to water.
- After the work of Torricelli, scientists accepted the fact that all matter is heavy.
- The next step was to clarify the meaning of “heaviness.” The Greeks had regarded heaviness as an intrinsic property of a body.

However, to weigh a body is to measure the magnitude of its “downward push,” and this depends on something other than the body itself. As we have seen, Newton realized that heaviness is a measure of Earth’s gravitational attraction, and that this force varies with the position of the body relative to Earth.

Additional evidence for this conclusion was discovered in the 1670s. Two astronomers, Edmund Halley and Jean Richer, independently discovered that pendulum clocks swing more slowly near the equator than at higher latitudes, and they correctly inferred that pendulum bobs weigh less near the equator. Therefore, “heaviness” arises from three factors: the nature of the body, the nature of Earth, and the spatial relationship between the body and Earth.

But what is the property of the body that contributes to its heaviness? Newton identified it as the body’s “quantity of matter,” or “mass.” His reasoning made use of both the method of difference and the method of agreement. First, he considered two solid bodies of the same material, weighed at the same location.

- Their weights are found to be precisely proportional to their volumes, and the constant of proportionality is an invariant characteristic of each pure, incompressible material.
- Therefore the weight of a body is proportional to its “quantity of matter”; by doubling the volume we have doubled the amount of matter, and the weight has doubled (method of difference).

Second, Newton considered a compressible material such as snow. We can weigh a sample of snow, then compress it to a smaller volume, and then weigh it again. The quantity of matter has remained the same, and we find that the weight is the same (method of agreement).

- Newton then asked how a body’s mass affects its motion when a force is applied.
- It is obvious that the mass does affect the motion; in order to cause a particular acceleration, a greater force is required for a greater quantity of matter (e.g., pushing a car requires more effort than pushing a bicycle).

But what is the exact relationship? In order to answer the question, he needed an experiment in which the acceleration is held constant while the mass of the body and the applied force are varied. Newton did not have to look far to find such experiments; Galileo had done them when he investigated free fall.

- From the top of a tower, Galileo had dropped two lead balls that differed greatly in size and weight.
- Let us assume that the larger ball had a volume ten times that of the smaller ball; therefore, its quantity of matter, or mass, was ten times greater.
- The force on each ball is simply its weight; by using a balance or a steelyard, we can determine that the weight of the larger ball is ten times the weight of the smaller ball.

So, considering the larger ball relative to the smaller ball, we have increased both the force and the mass by a factor of ten. Yet Galileo demonstrated that the acceleration of free fall remains the same. We know that acceleration is exactly proportional to force, so it must be exactly inversely proportional to mass (so that the factors of ten cancel).

- This result accords with our common experience; it implies that for a body of greater mass a proportionally greater force is required to achieve a particular acceleration.
- Newton thus arrived at his second law of motion: The applied force is equal to the product of the body’s mass and its acceleration, or F = mA.

The scope of this generalization is breathtaking. It may seem astonishing that Newton could arrive at such an all-encompassing, fundamental law from the observations and experiments that have been described. But once one has the idea of grouping together all pushes and pulls under the concept “force,” and of grouping together all changes of velocity under the concept “acceleration,” and of ascribing to all bodies a property called “mass,” and of searching for a mathematical relationship among these measured quantities—then a few well-designed experiments can give rise to a law.

- At this stage, however, the validation of this universal law is not yet complete.
- It depends not only on the foregoing, but on all the evidence presented in this section and the next; the law is part of a theory that must be evaluated as a whole.
- We have seen how this law rests on Galileo’s principle that all bodies fall with equal acceleration.

Because this principle was so crucial to his theory of motion, Newton demanded that it be established by experiments more accurate than those of Galileo. He wished to prove beyond any doubt that a body’s inertial mass—the property by which it resists acceleration—is exactly proportional to its weight.

- Newton realized that the pendulum provided the means for such an experimental proof.
- He deduced from F = mA that the inertial mass of a pendulum bob is proportional to its weight multiplied by the period squared (assuming the length of the pendulum is held constant).
- Thus if the period is always the same for any and all pendulum bobs, then inertial mass must be exactly proportional to weight.

By using a small container as a pendulum bob, Newton varied both the mass and material of the bobs; he filled the container with gold, silver, glass, sand, salt, wood, water, and even wheat. All the bobs swung back and forth with the same period, and he performed the experiment with such care that he could easily have detected a difference of one part in a thousand.

- The creator of modern physics had a passion for accurate measurement.) So far, Newton had focused on the movement of one body subject to an applied force.
- At this stage, he turned his attention to the force itself and its origin: It is exerted by another body.
- What happens to this other body? In order to answer the question, Newton needed to study the interaction of two bodies under conditions where the forces are known and the subsequent motion of both can be accurately measured.

He devised the perfect experiment using a double pendulum with colliding bobs. He used pendulums with a length of ten feet, and he carefully measured and compensated for the small effects of air resistance. He varied the mass of the bobs and their initial amplitudes, then measured their final amplitudes after the collision.

- Galileo had proven that a bob’s speed at the bottom of the swing is proportional to the chord of the arc through which it has swung.
- At the moment of collision, therefore, Newton knows the relative speed of both bobs.
- Furthermore, from his measurements of the final amplitudes, he could compute the relative speed of both bobs immediately after the collision.

The results of the experiment showed that the mass of the first bob multiplied by the change of its speed is equal to the mass of the second bob multiplied by the change of its speed. Since the force exerted on each bob is equal to the product of its mass and its change of speed, Newton had proven that the bobs exert forces on each other that are equal in magnitude and oppositely directed.

Newton performed this experiment with pendulum bobs made of steel, glass, cork, and even tightly wound wool. In his choice of materials, he deliberately varied the hardness of the bobs and thereby proved that his law applied to both elastic and inelastic collisions. Since all collisions fall into one of these two categories, his generalization followed: Whenever two bodies exert forces on each other by means of direct contact, the forces are equal in magnitude and oppositely directed.

Newton then investigated the case of non-contact forces—forces that act over distances by imperceptible means. He attached a magnet and some iron to a piece of wood and floated the wood in calm water. The magnet and the iron were separated by a short distance, and each exerted a strong attractive force on the other.

Yet the vessel did not move—implying that the two forces were equal in magnitude and oppositely directed, thus giving rise to zero net force. Does the law also apply to bodies that attract each other gravitationally? Newton answered that it does and gave a convincing argument. Since Earth attracts all materials on its surface, it is reasonable to suppose (and it was later proven) that every part of Earth attracts all other parts.

So consider the mutual attraction, say, of Asia and South America. If these two forces were not equal and opposite, there would be a net force on Earth as a whole—and hence Earth would cause itself to accelerate. This self-acceleration would continue indefinitely and lead to disturbances in Earth’s orbit.

- But no such disturbances are observed; on the contrary, Earth’s acceleration is determined by its position relative to the sun.
- Therefore the mutual attractive forces exerted by any two parts of Earth must be equal and opposite.
- Newton also could have pointed out that unbalanced forces would lead to other effects that are not observed, e.g., asymmetries in Earth’s shape and in ocean tides.) At this point, Newton had shown that his law applies to gravitational forces, magnetic forces, elastic collisions, and inelastic collisions—he gathered evidence over the range of known forces and found no exceptions.

He had thus arrived at his third law of motion: All forces are two-body interactions, and the bodies always exert forces on each other that are equal in magnitude and oppositely directed. When considering only one body, the concept “velocity” identified that which remained the same in the absence of an external force (this is the first law).

- In the case of two interacting bodies, Newton now identified a total “quantity of motion” that remains the same before and after the interaction.
- This quantity, which we now call “momentum,” is the product of a body’s mass and its velocity.
- Newton’s third law implies that the total momentum of two interacting bodies always remains the same, provided there is no external force.

Furthermore, this “conservation of momentum” principle applies even to a complex system of many interacting bodies; since it is true for each individual interaction, it is also true of the sum. After forming the concept of “momentum,” Newton could give a more general formulation of his second law.

- In its final form, which is applicable to a body or system of bodies, the law states that the net external force is equal to the rate of change of the total momentum.
- This form of the law can be applied in a straightforward way to more complex cases (e.g., imagine two bodies that collide and explode into many bodies).

Newton recognized that his three laws of motion are intimately related. We have seen that the third law prohibits the self-acceleration of Earth—but notice that such a phenomenon is also prohibited by the first and second laws, which identify the cause of acceleration as an external force.

- Given the fact that forces are two-body interactions, consistency with the second law demands that these interactions conform to the third law.
- The laws name related aspects of one integrated theory of motion; indeed, when the second law is given its general formulation, both the first and third laws can be viewed as its corollaries.

Hence the laws mutually reinforce one another: The experimental evidence for the third law also counts as evidence for the second law. I have outlined the main steps by which Newton induced his laws of motion. In their final statement, the laws appear deceptively simple.

But we can now appreciate that they are very far from self-evident. In order to reach them, Newton needed complex, high-level concepts that did not exist prior to the 17th century, concepts such as “acceleration,” “limit,” “gravity,” “mass,” and “momentum.” He needed a variety of experiments that studied free fall, inclined plane motion, pendulums, projectiles, air pressure, double pendulums, and floating magnets.

He relied upon the observations that had led to the heliocentric theory of the solar system, upon the experience of pulling inward in order to swing a body in a circle, upon the observations that determined the distance to the moon, upon the instruments invented for measuring force, and even upon chemical knowledge of how to purify materials (as this played a role in forming the concept “mass”).

- His laws apply to everything that we observe in motion, and he induced them from knowledge ranging across that enormous database.
- For the past century, however, many philosophers, physicists, and historians of science have claimed that the laws of motion are not really laws at all; rather, they are merely definitions accepted by convention.

This view derives from empiricist philosophy and was famously advocated by Ernst Mach.7 The empiricists regard the second law as a convenient definition of the concept “force,” which allegedly has no meaning except as a name for the product of mass and acceleration; similarly, they argue that the third law amounts to a convenient definition of “mass.” Those advocating such views have left themselves the inconvenient task of answering some obvious questions.

Why is a particular definition “convenient,” whereas any alternative definition would be cognitively disastrous? What about static forces that exist and can be measured in the absence of acceleration? How is it possible that the concept “force” was formed millennia before the concepts “mass” and “acceleration”? No answers have been forthcoming from Mach’s disciples.

Newton did not anticipate the skepticism that became rampant in the post-Kantian era. He regarded as obvious the fact that the laws of motion are general truths reached by induction, and therefore he did not go out of his way to emphasize the point. Indeed, he regarded the laws of motion as uncontroversial, which is why his discussion of them in the Principia is so concise.

## Which of the following was developed by William Gosset quizlet?

Gosset devised the t-test as a way to cheaply monitor the quality of beer.

#### Who discovered gravitation in the 17th century?

Sir Isaac Newton – The Discoverer of Gravity! –

Sir Isaac Newton was an English mathematician and mathematician and physicist who lived from 1642-1727. The legend is that Newton discovered Gravity when he saw a falling apple while thinking about the forces of nature. Whatever really happened, Newton realized that some force must be acting on falling objects like apples because otherwise they would not start moving from rest. Newton also realized that the moon would fly off away from Earth in a straight line tangent to its orbit if some force was not causing it to fall toward the Earth. The moon is only a projectile circling around the Earth under the attraction of Gravity. Newton called this force “gravity” and determined that gravitational forces exist between all objects. Using the idea of Gravity, Newton was able to explain the astronomical observations of Kepler. The work of Galileo, Brahe, Kepler, and Newton proved once and for all that the Earth wasn’t the center of the solar system. The Earth, along with all other planets,orbits around the sun. Two astronomers, J.C. Adams and U.J.J. LeVerrier, later used the concept of Gravity to predict that the planet Neptune would be discovered. They realized that there must be another planet exerting a gravitational force on Uranus because Uranus had odd perturbations in its orbit. (Perturbations are deviations in orbits.)