Magnetic forces seem to be an attribute of a few odd materials—iron, the mineral magnetite, several other solids, but not very many. And these incorporate the north and the south magnetic poles, something that’s intrinsic to those materials. All magnets have these two poles. Magnets are always physical objects. They have seemingly permanent properties.

Electrical forces, on the other hand, appear all around us, whenever an object accumulates a surplus or a deficiency of electrons—a positive or a negative charge, if you will. Electrically charged objects will typically be either positive or negative depending on that surplus or deficiency of electrons. These electric charges seem quite transient. You can charge up an object, the object can lose its charge, and we see these phenomena all around us.

Learn more about electricity.

But of course, there are also some very important similarities between these two forces. These forces set electricity and magnetism apart from, for example, gravity. In each case the force can be either attractive or repulsive; that’s very different from gravity, which is always only attractive. In each case, like poles or like charges repel each other, whereas opposite poles or opposite charges attract each other.

Well, in any event, whatever the nature of electricity and magnetism, Newton’s clear definition of a force allows—this phenomenon that allows a mass to accelerate—both electricity and magnetism to be studied by scientists who wanted to understand the nature of the everyday phenomenon in our world. So, electricity and magnetism, of course, were intensely studied in the 17th, 18th, and into the 19th century.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on Wondrium.

The technological importance of the early discoveries in electromagnetism, was huge. Michael Faraday’s discovery of electromagnetic induction provided an easy way to achieve a previously difficult conversion. Gravitational potential energy, for example, or heat, can be converted into electrical energy by this process. You have to just put an electrical generator in the way, and that takes the one kind of energy and converts it to a different kind of energy.

Before this, people had to build their industries next to sources of energy. But electrical energy can be transferred from many, many miles just over a system of wires. In the 19th century, each household had to manage its own fuel supply. Usually, you had wood coal. Rural electrification in America transformed society. For the first time families all over America were linked physically by an energy source.

In 1871, physicist James Clerk Maxwell was appointed to be the first professor of experimental physics at Cambridge, and he also started the Cavendish Laboratory.

Maxwell set down an elegant mathematical formulation of electricity and magnetism in the 1860s. These were the four equations, Maxwell’s equations, of electromagnetism. These equations are very complex mathematically, but we can describe these four equations in everyday words.

The first equation is just a restatement of Coulomb’s law, that a force exists between any two electrical charged objects. The force is proportional to the charges, and it is inversely proportional to the square of the distance between the charges. The second equation describes the magnetic phenomenon and says that every magnet always has two poles, a north pole and a south pole.

The third equation says that changing an electric field produces magnetic effects. And the symmetrical fourth equation says that changing magnetic fields produces electricity.

Learn more about electromagnetism.

One of the great wonders of mathematics, one of the things that makes mathematics so powerful in science, is that it can lead to unexpected insights. Sets of equations can be manipulated through algebra and other sorts of mathematical processes and you can certainly learn new things about the natural world that you never suspected.

This is what happened to Maxwell. He manipulated his four equations and found that one possible mathematical solution to the way electricity and magnetism works is a wave. And because constants are built into this equation, he found that this wave had some very special properties. Indeed, the most distinctive property is that the wave had to travel at 186,000 miles per second, the speed of light.

As a result, from very esoteric sort of mathematical reasoning in describing these phenomena of electricity and magnetism, Maxwell discovered the nature of light. Light is an electromagnetic property. This was an astonishing discovery that transformed the future of science.

Magnetism is limited to a few physical materials. They have seemingly permanent properties. On the other hand, electricity appears all around us is many forms, but appears to be transient, in that electrical charge can be removed or changed from positive to negative.

In both electricity and magnetism, the force can be either attractive or repulsive, unlike say gravity, which is always only attractive. In each case, like poles or like charges repel each other, whereas opposite poles or opposite charges attract each other.

James Maxwell manipulated his four equations and found that one possible mathematical solution to the way electricity and magnetism works is a wave. The most distinctive property of this wave was that it traveled at 186,000 miles per second, the speed of light. This meant that light was an electromagnetic wave.

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Michael Faraday came to science in a strange roundabout way. He was born in 1791 in South London, the third of four children of a blacksmith. The family’s finances were in terrible shape, so to help make ends meet, the young Michael was apprenticed at the age of 13 to a London bookseller, who taught Michael the art of bookbinding.

Faraday learned to bind books quite beautifully. And he began to read avidly, everything he could get his hands on. He was especially fascinated by the Encyclopedia Britannica, especially the articles on science, which he loved. Especially influential was the article on electricity in that early edition which he was binding at the time.

Faraday became enamored with science. He then began attending public lectures, notably by Humphry Davy at the Royal Institution of Great Britain in London. Faraday transcribed the lecture notes from Davy.

He then bound the notes quite beautifully and presented them to Davy as a calling card. Davy was impressed. Unfortunately, at that time there was no position at the Royal Institution, and Faraday was resigned to spending the rest of his life as a tradesman binding books.

Learn more about magnetism and static electricity.

But, as luck would have it, one of the young assistants in Davy’s laboratory was fired for brawling, and Faraday was hired in 1813 as Davy’s lab assistant. And that really changed the history of science. Faraday served as Humphry Davy’s lab assistant, and he flowered into a distinguished scientist in his own right.

By the 1830s, he had made major contributions in chemistry and physics. He eventually rose to take his mentor’s place as a researcher and as the public lecturer for the Royal Institution.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on Wondrium.

Faraday’s background may have pointed him in the direction of these scientific investigations. He was raised a Sandemanian. This is a Protestant sect that emphasizes the unity of the universe. It’s been suggested that Faraday’s religious background prepared him to look for unity in the different physical phenomena of the natural world.

It was Faraday who demonstrated that the various forms of electricity—that is animal electricity, lightning, the electricity from a battery—are all the same. It’s this kind of unification that Faraday loved, and he looked at electricity and magnetism and wanted to unify those phenomena as well.

Faraday’s most famous experiment took place in 1831, and he incorporated this assumed symmetry of electromagnetism. He attached one coil of wire to a battery, thus creating a magnetic field. Next to this coil, he placed a second coil of wire in a circuit, but there was no battery. Even though the second coil of wire wasn’t attached to any source, an electric current flowed through that second coil of wire just being brought near the first one.

Faraday concluded that the magnetic field produced by the first circuit, the electromagnet, induced a current in the second circuit. This is the phenomenon of electromagnetic induction. The exact same effect occurs when a magnet, when just a normal magnet, is waved or wiggled in the vicinity of a coil of wire.

We use devices called transformers in our lives on a daily basis. In a transformer, you put electrical current from the wall outlet through one coil of wire, so electricity flows into this coil of wire, and that produces an electromagnetic field. You then always will see a second coil of wire nearby, and what happens is that as the current flows through the one magnet it induces a current in the second one.

But, in general, that current will be at a different voltage. And so this is a way in household appliances of transferring voltage of one type, for example, 115 volts from your wall circuit, to another kind of voltage. That’s a transformer, a very important electrical device—something that Michael Faraday invented almost 200 years ago.

Learn more about electricity.

The demonstration that moving magnets can produce electricity in a coil wire immediately suggested a new procedure for generating electricity in our everyday lives. You place a coil of wire between two magnets. Then you spin that coil of wire, and electricity will be produced. This device is what we call an electric generator, or dynamo.

It’s the centerpiece of every electric power plant. The energy to spin those coils to provide that rotary motion can be provided by water. In a hydroelectric plant, water flowing through a dam turns a water wheel device—that’s where the spinning motion can come from.

It can come from steam in a coal burning power plant, or in a nuclear power plant. It can come from gasoline, in a gasoline engine that turns the coils of wire and, therefore, generates electrical power. But all you have to do is rotate coils of wire against another magnet, and you produce electric charge.

At the age of 13, Michael Faraday was apprenticed to a bookseller, who taught him the art of bookbinding.

Faraday demonstrated that the various forms of electricity—that is animal electricity, lightning, the electricity from a battery—are all the same.

Faraday attached one coil of wire to a battery, thus creating a magnetic field. Next to this coil he placed a second coil of wire in a circuit, but there was no battery. Even though the second coil of wire wasn’t attached to any source, an electric current flowed through that second coil. Faraday concluded that the magnetic field produced by the first circuit, the electromagnet, induced a current in the second circuit. This is the phenomenon of electromagnetic induction.

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Hans Christian Oersted was born in 1777. He was the elder son of a Danish pharmacist, and from an early age, he had planned to follow his father’s profession of pharmacy. But he became captivated by electrical studies in 1800, shortly after Volta’s announcement of the battery.

The young Hans Oersted excelled as a student in languages, mathematics, and science. He was home-schooled, but he passed the entrance examinations and enrolled in the University of Copenhagen in 1794 at the young age of 17. He received degrees in both pharmacology and in Kantian philosophy, of all things. And he was, for a short time thereafter, a manager of a pharmacy. But eventually he turned his attention full time to science; that was his real love.

Learn more about the invention of the battery.

While still in his 20s, Oersted secured visits to many of the famous laboratories in Europe, and he was able to learn the types of research that was going on there. He also was able to gain entrance to these laboratories and gain respect because he himself invented an improved compact battery, a battery that was quite powerful, but small and portable.

He returned to Denmark in 1804, and turned to public lecturing, where he did scientific demonstrations for the public on electrical phenomena. He was so successful and popular that he was given a professorship almost by demand at the University of Copenhagen in 1806 because he was so good at bringing science to the public.

Oersted believed that the various forces in nature, including magnetism and electricity, must somehow stem from the same original power. He saw a unity in the universe and its forces. He was, therefore, predisposed to observe links between electricity and magnetism that other people might not have seen.

So, it was in the winter of 1820 that Oersted made his most famous discovery. He was performing demonstrations in electricity and magnetism in front of his classroom. He hooked up a coil of wire to a battery and passed a current through that coil of wire, and he observed that a compass needle next to the coil twitched whenever he did this.

After several weeks of experimentation, Oersted announced that electricity passing through a curved path produces a magnetic field. By July of 1820, he had submitted a manuscript describing this link between electricity and magnetism, and this was the great discovery of the fact that electricity produces magnetic fields.

Prior to Oersted, electricity and magnetism were viewed as two completely separate phenomena. They involved very different kinds of physical situations and conditions, but here Oersted unified this work by showing that one phenomenon was infinitely linked to the other.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on Wondrium.

With the battery, of course, you could convert electrical potential energy into chemical potential energy. That’s the decomposition of water and heat and light. Oersted showed that you could also convert that into magnetic potential energy. So, another kind of energy conversion was brought forth in the scientific world.

Oersted’s discovery led to a number of important inventions quite quickly because it provided a way to convert this electrical potential energy into other forms of energy. Of course, first magnetic energy, but then you also could use magnetic energy to produce kinetic energy.

The first and most obvious of the advances was just the electromagnet. You can use a coil of wire. So this is a continuous long loop of wire that you’ll see in various electromotors. And if you close the circuit, you can then create a magnet just out of a loop of wires—an astonishing effect.

You can go one step further. You can take those coils of wire, and you can wrap them around so they create an electromagnet that attracts a clapper, a piece of metal. And, therefore, you can create a buzzer just by closing the circuit. So that was the principle of the buzzer and various other kinds of sound-making devices.

The same principle, by the way, is used in the telegraph. You have electromagnets that open and close circuits. If you open and close a circuit at your end with long and short pulses, those pulses go through the wire and open and close circuits at the far end, and the same series of long and short pulses is transmitted long distances over a wire.

Learn more about electromagnetism.

And then we come to electric motors. Electric motors are a pervasive use of electromagnets in our society, an incredibly profound ability to convert electrical energy, through magnetic energy, into kinetic energy.

In a motor, you simply have a push-pull effect of one set of magnets against another. In many simple electric motors—for example, the kind you will find in most electric razors—you’ll find permanent magnets, which are fixed into the casing of the motor, and then you’ll have a rotor, which has little coils of wire, which form electromagnets.

As the current flows through these, you get a push-pull effect, and that spins the rotor because magnetic opposites attract, but the same poles repel each other. And by a very careful alternation of opposite and like poles, you can get this push-pull effect causing a rotor to work.

The number of applications of electromagnetism in everyday life is huge. And all this developed from a discovery made when Oersted noticed a compass needle twitch.

Hans Christian Oersted received degrees in both pharmacology and in Kantian philosophy.

Oersted was able to gain entrance to many famous European laboratories because he himself invented an improved compact battery, a battery that is quite powerful, but very small and portable.

While performing demonstrations in electricity and magnetism in front of his classroom, Oersted hooked up a coil of wire to a battery and passed a current through that coil of wire. He observed that a compass needle next to the coil twitched whenever he did this. Further experiments led to the discovery that electricity flowing in a curve creates a magnetic field.

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Scientists at the time were striving for a ‘magic bullet’ that could rid the body of infecting organisms without harming the patient, a concept still striven for today. One such effort occurred in 1888 when German scientists observed that the bacterium *Pseudomonas Aeruginosa* produced a substance in the test tube known as pyocyanase.

Laboratory studies showed that pyocyanase killed dangerous bacteria like staphylococcus. However, when it was tried in patients, it was unsuccessful and even toxic. Nevertheless, pyocyanase was used for nearly 30 more years as a topical skin antibiotic.

In 1910, Paul Ehrlich, a German chemist, took a different approach. He used a chemical compound called salvarsan, an arsenic derivative, to treat syphilis. The drug was toxic, but it represented the first partial success in syphilis treatment.

Dr. Fleming was working in London in the 1920s on a natural chemical from human tears that had antibacterial properties, called lysozyme, which caused bacteria to fall apart. This too never really succeeded as an antibiotic, but it did show that humans could produce a natural antibacterial substance.

This is a transcript from the video series

An Introduction to Infectious Diseases. Watch it now, on Wondrium.

In 1928, a strange twist of fate occurred—after returning from vacation, Fleming noticed a petri dish with staphylococcal bacteria whose growth had been inhibited by a mold growing in the adjacent area.

He eventually demonstrated that the mold was a *Penicillium* fungus. So, an unknown substance, produced by the mold, must have traveled across the agar plate to kill the bacteria. This substance was henceforth named penicillin. The original dried plate still remains today in the archives of St. Mary’s Hospital in London. But it would still be another 10 to 15 years before full advantage could be taken of this discovery, with penicillin’s first human use in 1941.

Although Dr. Fleming warned in 1945 that the misuse of penicillin would lead to mutant-resistant bacteria, by 1946, a study showed that 14 percent of *staph aureus* were already resistant to penicillin, and today it’s greater than 95 percent.

In the 1930s, Gerhard Domagk, a German professor, was examining an assortment of chemical dyes for their possible antibiotic effect. One man-made dye, called prontosil, was active against mice infected with streptococcal bacteria.

Sulfa even saved the life of Winston Churchill in 1943, when he developed pneumonia while traveling in North Africa. Churchill said: “There is no doubt that pneumonia is a very different illness from what it was before this marvelous drug was discovered.”

Learn more about food-borne illness.

In 1939, scientists working at the Rockefeller Institute discovered a bacterium in the soil, *Bacillus Brevis*, which produced a compound that inhibited gram-positive bacteria. This substance contained gramicidin, which has antibacterial properties. But unfortunately, gramicidin was also too toxic when orally consumed.

But similar to Fleming’s pyocyanase, gramicidin was used as a topical skin antibiotic. Elsie, the famous cow of the Borden Company, was one of the first patients to be successfully treated with gramicidin. While attending the 1939 World’s Fair, Elsie developed mastitis, an infection of her udder tissues.

In the 1940s fueled by the new excitement that was generated from sulfonamide and gramicidin, there was renewed interest in pursuing the development of penicillin. Englishman Howard Florey and German-born Ernst Chain learned how to extract penicillin and to produce it in sufficient amounts to test in animals.

Penicillin was subsequently released for human testing for those who were considered near death, often with dramatically favorable results. Florey also managed to convince the United States government to support large-scale production.

The story of antibiotics would not be complete unless it included the discovery of streptomycin in 1943, the first useful drug for tuberculosis, or TB treatment. The bacterium that produces streptomycin was found in a farmer’s field. Not only was streptomycin able to treat TB, but it was useful to cure gram-negative bacterial infections, which penicillin could not.

However, when streptomycin was used alone for TB, not unexpectedly, resistance emerged, and damage by streptomycin to the kidneys prompted further development of an improved antibiotic, neomycin.

Learn more about respiratory and brain infections.

Up to that point, the antibiotics discovered attacked either gram-positive or gram-negative bacteria, but not both. In 1947, a Yale researcher discovered an antibiotic from a soil sample collected in a field in Caracas, Venezuela, and he named it chloramphenicol. This was the first ‘broad-spectrum’ antibiotic to exhibit activity against germs with different cell walls and varied gram staining characteristics.

For someone who was a child in the 1950s, it is likely that they were treated with this antibiotic. However, chloramphenicol isn’t heard about today. It was a first-line drug for typhus and typhoid fever in the mid-1900s. Unfortunately, a rare idiosyncratic side effect of total blood-cell production shutdown occurred in a tiny percentage of treated patients, but this was enough to taint the use of chloramphenicol.

In 1948, another broad-spectrum antibiotic named aureomycin was being studied. This was a prototype drug for the class of drugs known as tetracycline.

In 1964, other beta lactam drugs known as cephalosporins made their debut. They are structurally similar to penicillin and disrupt the bacterial cell wall in a very similar manner. They were discovered from extracts of a mold found in a sewer off the coast of Sardinia by an Italian microbiologist. It took nearly two decades, however, to purify these antibiotics for clinical use.

Cephalexin, an oral antibiotic, made its debut in 1967 and is still one of the major first-line antibiotics in use today. The intravenous form of cefazolin is given to virtually every patient receiving antibiotic prophylaxis for surgical procedures today.

Yes. Even Dr. Fleming himself expected the misuse of Penicillin in 1945, predicting that it would lead to more resistant bacteria.

A broad-spectrum antibiotic can have effects against different types of bacteria. Unlike Penicillin, this type of antibiotic wasn’t used before 1947 until a researcher found one type of it in a soil sample.

There is a natural chemical in human tears that acts as sort of a natural antibiotic. Dr. Fleming was studying this substance before he discovered Penicillin.

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Recognizing the fundamental difference between weight and mass is very significant because these terms are often interchanged. Weight is the gravitational force, and it varies from place to place on the Earth’s surface. It’s different on the Earth than the Moon.

Mass, however, is the amount of stuff or the number of atoms, and it doesn’t vary from one place to another. The mass of an object is constant even though the weight may vary depending on where the object is.

There are two ways to calculate the weight, for example, of a person, on Earth. One, using the second law of motion, force equals mass times acceleration. A 60-kilogram person on Earth equals 588 newtons according to this equation.

The other way is to do the exact same calculation by plugging into the expression for gravity, force equals capital G, the mass of the Earth, times the mass of the object divided by r2. This equation also provides the same answer which is 588 newtons for a 60-kilogram person.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on Wondrium.

Objects weigh less on the Moon because the Moon is a less massive object than the Earth. To determine what is the weight of a 60-kilogram object on the Moon’s surface some variations like the radius and the mass of the Moon are needed.

After plugging the numbers into the same equation for gravity—force equals the mass of the Moon times the mass of the individual divided by the radius of the Moon squared—the answer will be 95 newtons. Of course, 95 newtons is only one-sixth of the weight of an object on the Earth’s surface.

That is why people can skip and jump really high on the Moon, and everything looks like it is taking place in slow motion because the force of gravity is so much less. And because the acceleration on the Moon is one-sixth the acceleration on the Earth, people jump and come down very slowly.

A golf ball could be hit a lot farther on the Moon, largely because of the difference in the gravitational acceleration at the surface of the Moon, also because there is no atmosphere, so there is no wind resistance to that golf ball.

Learn more about Newton’s laws of motion.

Newton’s universal laws of motion and gravity reveal the deep and pervasive order in the natural world. One set of laws applies everywhere in the universe (on the surface of the Earth, Moon, planets, stars, etc.). They provide a framework by which many other phenomena can be more understandable, and they also provide unity to the understanding of the natural world.

There is nothing special about the surface of the Earth in terms of the laws of motion and in terms of the forces involved. Perhaps Newton’s greatest legacy is the view of the universe as a place of deep mathematical order, a clockwork universe. The mechanisms can be deduced through observation and analysis of the natural world.

Learn more about the fact of evolution—the fossil record.

The optimistic view that humans could deduce the order of the natural world had a significant trickle-down effect in other human endeavors. During the enlightenment, which was about a century after Newton, scholars advocated this rationalist approach to all different kinds of human endeavor, like economics, education, political systems, and the law.

It was felt that there must be universal laws that dictated all kinds of activities that humans undertook. Indeed, Newton’s first firm statement of this cause and effect relationship in the natural world seems to have pervaded the legal system today. If something bad happens, there must be a specific cause.

But indeed, cause and effect have become part of people’s thinking about the universe. The drafters of the United States Constitution and the Bill of Rights firmly believed that there was a rational system of government that could be derived, and there were laws and order to the political system as well. The Bill of Rights and the Constitution thus reflect this optimistic view of order—the attempt that humans could find that order, and in fact run their lives according to those laws.

Learn more about Charles Darwin and the theory of natural selection.

Newton’s laws even contributed to theological debates. Some followers of Newton, notably the French mathematician Pierre Simon Laplace, who lived from 1749 to 1827, speculated that since the laws of motion are exact and predict the motions of every possible particle under every kind of force and interaction, hence, the future of every particle in the universe was preordained, and this led to a very interesting theological speculation.

The speculation that, since everything in the universe is preordained, there is no such thing as free will, and people actually act out their lives. Accordingly, every event in people’s lives was something that was preordained just by the way particles were set into motion billions of years ago before anyone had ever heard of Isaac Newton and his laws of motion. But is that possible?

Since clockwork vision was deduced through gravity force laws, the debate speculates that every event in the world is preordained and that all particles were set into motion billions of years ago before gravity was discovered.

Mass is a constant that is not changed according to where it is. However, weight varies from one place to another. These variables help in the comprehension of concepts such as gravity force and its equation.

According to gravity force and Newton’s law, more mass means more force. Since the Moon is less massive than the Earth, its acceleration is only one-sixth of the Earth’s.

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Isaac Newton’s analysis of the force of gravity was rooted in his understanding of the relationship between motion and force. According to that understanding, Newton proposed three laws of motion:

Uniform motion, which is an object moving at a constant velocity in a constant direction, or an object at rest sitting on a table, for example. This law states that nothing happens without force, and an object remains in uniform motion unless it is acted upon by a force.

Acceleration motion, which is any change in either the speed of an object or in the direction of its movement. As an example, circular motion (not uniform motion) at a constant speed is acceleration. This law puts the whole idea in quantitative terms, it says force equals mass times acceleration, and numbers can be plugged into that equation.

The third law presents the idea that forces act in pairs. Equal and opposite forces occur simultaneously. When you push on an object, it pushes back on you with the same force at the same time.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on Wondrium.

During 1665–1666, the bubonic plague struck England, and that’s the period when Newton retreated to his family farm as a consequence of Cambridge University being shut down.

On the farm, he had a year and a half to think and reflect, to ponder the things he’d learned about Kepler’s laws, Galileo’s ideas, and other concepts he had studied as an undergraduate at Cambridge. During those years he burst a remarkable discovery which was deducing a mathematical description of the universal force of gravity.

To Newton’s contemporaries, gravity was a terrestrial force; it was restricted to objects near the Earth’s surface. What Newton discovered in the family apple orchard was that gravity is a universal force. It extends all the way out to the planets, to the Moon, to the stars, and farther. The young scholar looked up to see an apple ripening on the tree, and above it, he saw the Moon in its orbit. Newton’s great advance was realizing that it’s a singular force that is acting on both of these objects.

Learn more about the nature of energy.

The whole discovery was “occasioned by the fall of an apple”. The young Isaac was sitting in the garden thinking about the universe and how it worked and pondering about the difference between the apple and the Moon. The apple falls but the Moon does not. He tried to discover the mystery behind this issue, and finally, he found the answer.

Here’s the gist of Newton’s idea. When the apple breaks loose, it falls to Earth, straight down. But if someone picks up that apple, and throws it sideways with a certain amount of horizontal velocity, as Galileo says, the apple adopts a parabolic path. The harder the apple is thrown, the more horizontal distance it adopts and the farther it goes.

What Newton realized is that if the apple is thrown hard enough, it would go into orbit. It would continuously fall, but as it fell it would move horizontally, and it would keep going around the Earth. That’s what the Moon is doing, it’s going around the Earth, constantly falling, but it has sufficient horizontal velocity to keep it in orbit. The same thing happens with any planet, with any moon, anything that’s orbiting the Sun, anything that’s orbiting the Earth.

Learn more about universal gravitation.

Newton’s concept of qualitative and quantitative gravity is simple. He derived a mathematical equation to explain this force. He described a force in terms of four measurable quantities. The first one is the mass of an object. The second variable is the mass of a second object. The third variable is the distance between these two objects.

And finally, there is the force—the gravitational force that ensues. And this is the equation that Newton came up with. He said: force equals a constant—a capital G for the gravitational constant—times the first mass, times the second mass, divided by the distance squared.

(F = G x [m1 x m ]/d )

Consequently, there exists an attractive force of gravity between any two objects that is proportional to the product of their masses, divided by the distance between them squared.

Learn more about celestial and terrestrial mechanics.

Newton used rather complicated mathematical reasoning and he demonstrated that stable orbits are possible only if there is a 1 over d2 kind of relationship.

If there is an exponent less than 2, it leads to a steadily decaying orbit because the force doesn’t drop off sufficiently with increasing distance. And if there is an exponent greater than 2, 2.1, or 2.2, for example, it allows the orbiting body to escape because the force drops off too quickly and the body just keeps moving outward. Only with 1 over d2 is the exact relationship obtained.

Newton’s powerful equation reveals that an equal gravitational force is experienced by any two objects, for example, the Earth and the Moon. In fact, when an apple falls to the Earth, the Earth also falls a minuscule distance toward the apple, and there’s a kind of lever law here.

To explain more about this, imagine a seesaw between two children that don’t weigh the same, the heavier one has to sit closer to that fulcrum point, and the one who’s farther away experiences a much larger motion on the seesaw.

According to Newton’s laws of motion, force is a phenomenon that induces objects to move either by constant or accelerated speed.

The first law of motion is called uniform motion, and it states that objects move at a constant speed unless they are acted upon by another force.

Newton‘s most remarkable discovery was interpreting a mathematical explanation of gravity.

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The bottom half of Newton’s equation is the 1 over d2 part of it. As the distance of two objects becomes greater, the gravitational force between them drops off. And it doesn’t happen just in proportion to distance, but also in proportion to the square of the distance. That’s called an inverse-square relationship and is actually a very common relationship.

In other words, the difference between the intensity at one distance, and a distance twice as far away would be the ratio of one to one-quarter, or 1 over d2.

To think about gravity in a geometrical way, a gravitational field and an imaginary array of lines that radiates straight out from any object can be imagined. In this suggestion, the gravitational force is the number of those lines that intersect between two masses. As the distance is doubled, the number of intersections of lines lessens.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on Wondrium.

Even after Newton proposed his gravity equation, there was one big gap, and that was the numerical value of the gravitational constant shown with capital G in the equation. This constant is tremendously important, and it helped estimate the magnitude of the gravitational force between any two objects.

Determining G is extremely difficult because the experiment has to be completely independent of the Earth’s huge gravitational force that swamps out most other measurements. The experiment also has to eliminate any other contributions by stray electrical or magnetic fields, and that’s not very easy.

After all, a slight static electric charge on a comb can pick up a piece of paper. Also, a magnet, which is a very tiny device compared to the entire Earth, can pick up objects against the Earth’s entire gravitational force. So to think about gravity, it’s a very weak force compared to some of the other forces that are around all the time.

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The most famous attempt to determine G was undertaken two centuries ago by the English chemist Henry Cavendish. He was born in 1731 in Nice into one of the wealthiest families in all of Britain. He was educated at Cambridge University and spent most of his life, more than 50 years, in London performing scientific experiments. He then died a recluse in a London home in 1810.

One of Henry’s important experiments was devising a very ingenious method for determining the gravitational constant G. In 1798, he suspended a dumbbell with lead spheres from a wire, such that the two suspended spheres were in proximity to two much larger lead spheres that were fixed. The slight force of gravity between the large spheres and the smaller lead spheres caused the suspended dumbbell to rotate, to torque slightly.

Well, Cavendish knew how much torque it took to twist his wire. He measured that twist, and therefore he was able to measure the force of gravity because he knew how much the two lead masses weighed, and the distance between the weights, and so he could solve G.

Substituting the measured value for G, the gravitational acceleration of the Earth’s surface, and the Earth’s radius all into a modified form of Newton’s equation, yielded the Earth’s mass.

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There are two equivalent descriptions of force—one using Newton’s equation for gravity, and the other using Newton’s second law: force equals mass times acceleration. Because these two equations describe the same force, they can be set equal to each. So the acceleration due to gravity at the Earth’s surface or (g) is 9.8 m/s2 , and this is equal to capital G.

Indeed, the mass of the Earth is equal to little g times r squared over big G [(g)(r2/G)]. Plugging in the numbers, the answer ends up with the mass of the Earth six times 1024 kilograms. The Earth weighs six trillion, trillion kilograms. That number comes from Cavendish’s discovery of the value of the big G, the gravitational constant.

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Cavendish presented this calculation for the first time in his now-classic paper, *Experiments to Determine the Density of the Earth*, published in 1798. That paper stands as a great landmark in geophysical science.

But there were a couple of new ways of determining G as well. There was a group in Zurich that weighed a kilogram mass on an exquisitely sensitive balance.

In one case, they did it with a 1,000 kilogram mass just below sort of a donut-shaped mass, and then they raised that donut-shaped mass and put it just above the kilogram mass, and they looked at the difference in the weight of the object when that 1,000 kilogram was just below, or just above the suspended mass on the balance. A very difficult measurement, but they were able to do it and come up with a value for G.

Another American group tried a similar approach to solve the gravitational constant or G. They measured the time that it took an object to fall. Times also can be measured to millionths or billionths of a second. So if the time it takes an object to fall is measured with a heavy mass below, as opposed to a heavy mass above, a slightly different time would be shown.

All of these techniques now yield similar values for G. For the record, the best estimate of G is now about 6.674 times 10-11 m3/kg/sec2. So it’s a number that people are still converging on, but that’s pretty much the accepted value now.

In the gravity force equation, the capital G refers to the gravitational constant.

Gravity is the energy between any two objects in the universe that attract each other with a certain amount of force. The more massive object attracts the less massive one.

There are two ways to calculate the Earth’s mass. It can be either by Newton’s second law or by Newton’s gravity equation. In both, the answer is exactly the same.

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Isaac Newton was born on Christmas Day in 1642 in Woolsthorpe, a small village in Lincolnshire, East Central England. The newborn was so tiny that doctors thought the chances of his survival were grim.

Newton’s father died three months before he was born. His mother remarried a minister when he was just three years old. The abandoned young Newton grew up with his grandmother until the age of 11.

In 1653, Newton’s mother returned for the first time after his stepfather died. She had three younger children from her second marriage. These experiences probably had an influence on Newton’s aloof personality and the likely reason for his not publishing his scientific ad mathematical discoveries for years.

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Newton attended school from the age of five. He enjoyed drawing and was interested in making mechanical devices. As a child, he showed his ingenuity in making clocks and building working models of windmills.

On her return to the family, Newton’s mother forced him to quit school and, much against his wishes, sent him to work at their Lincolnshire farm. It turned out that the teen was miserable as a farmer. He preferred going to school to farming and was absentminded with his agricultural chores.

Eventually, family and friends convinced Newton’s mother to send him back to school. When in school, Newton studied the contributions of classical scholars and the writings of Kepler and Galileo.

After completing his course-related studies, Newton joined Trinity College in Cambridge in 1661. He graduated by specializing in mathematics and philosophy in 1665.

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During the outbreak of the bubonic plague in 1665 and 1666, Newton was in the prime of his inventions. When the Great Plague ravaged Europe, students at Cambridge University were sent home to prevent further outbreaks. Newton was forced to spend eighteen months at the family farm.

It was during this year and a half that Newton had time for intense personal study and thought. He went on to formulate four important contributions to science and mathematics that provided answers to the problems of scientists of those times. Newton invented the branch of mathematics now known as calculus and discovered many of the laws of optics. He also framed his three laws of motion and derived the universal law of gravitation.

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All this was in the two plague years of 1665 and 1666, for in those days I was in my prime of age for invention, and minded mathematics and philosophy more than at any time since.

In 1667, Newton returned to Cambridge University and furthered his academic work. He continued as a highly respected scholar at Trinity College with illustrious academic positions for the rest of his life.

However, many of the ideas that Newton developed during the plague years were not published for more than twenty years. It was only in 1687 that these mathematical ideas were published in Newton’s great work, *Principia* *Mathematica*.

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Five thousand years ago, humans recognized certain patterns of the Sun, the Moon, and the stars. They predicted the behavior of the Sun, the Moon, and the Earth and created carefully oriented monuments, such as Stonehenge. Scholars continuously monitored planetary movements.

Around A.D. 100, Ptolemy proposed the longest-lasting mathematical model that considered the Earth to be the center of the solar system. The lasting influence of the European Renaissance led to a questioning culture of the previous theories.

That is when Polish astronomer Nicolas Copernicus suggested an alternative to the model of the solar system with the Sun at the center and the Earth orbiting around the Sun.

However, both Copernican and Ptolemaic models had failed to make accurate predictions about the exact positions of planets.

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It was in the 1640s that mathematician Johannes Kepler derived the mathematical basis for describing planetary motions. He proved that the assumptions of circular orbits of celestial bodies were erroneous. Kepler inferred that planets orbit around the Sun in elliptical paths that are somewhat elongated from a pure circle.

And then, Italian physicist Galileo Galilei used mathematical analysis to study how objects fall. He also used his analysis in the study of terrestrial mechanics and the rolling of objects on an inclined plane.

Yet, these studies of terrestrial and celestial mechanics were separate domains as people could not relate the motion of celestial objects to those on the surface of the Earth.

Finally, it was Isaac Newton who synthesized these empirical descriptions into laws of motion that could be applied across the universe.

Sir Isaac Newton‘s mathematical ideas were published in 1687 titled *Philosophiae Naturalis* *Principia Mathematica*.

Newton enjoyed drawing and making mechanical devices. He made clocks and built working models of windmills. He preferred going to school to farming on the family farm.

Sir Isaac Newton is best known for his invention of calculus, formulating the laws of motion, discovering many of the laws of optics, and the theory of universal gravity.

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Isaac Newton classified physical motion into two different categories—uniform and non-uniform motion. This helped him formulate the three laws of motion. Newton considered both an object moving in a straight line at a constant speed and, as a special case, an object at rest as uniform motion.

Newton categorized all other imaginable motion, including that of planets moving in their circular orbits, as non-uniform motion or acceleration.

Newton differed from the earlier belief that planets moving in a perfect circular motion at constant speed were in uniform motion. He defined any change in speed and direction as acceleration and therefore argued that orbital motion is a kind of acceleration.

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Newton’s definition of acceleration describes both positive and negative acceleration. While speeding up is referred to as positive acceleration, an action of slowing down, such as applying the brakes of a car, is negative acceleration.

Mathematically, acceleration is expressed using the concept of the vector. In a mathematical vector, both direction and speed are defined. It can be represented as an arrow, where the arrow denotes the direction, and the length corresponds to the speed.

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Every body continues in its state of rest or of uniform motion in a [straight] line unless it is compelled to change that state by forces impressed upon it.

This means an object will not change its motion unless acted upon by an external force. This law conveys three distinct types of behavior by objects. The first one being that an object moves at a constant speed in the same direction as it goes along. However, this situation is practically impossible in real life as there are forces acting around it all the time.

Another type of behavior is when an object is at rest and continues being at rest without disturbance to both its velocity or direction. This is the special case where the vector is just a point.

And finally, the third and most common type of behavior is when an object accelerates under the influence of a force. Though Newton does not specify the type of force in his first law of motion, he emphasizes that if an object accelerates, then there is a force involved. Thus, Newton’s first law provides an operational definition of force.

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The acceleration produced on a body by a force is proportional to the magnitude of the force and inversely proportional to the mass of the object.

In other words, when the force acting on the object is higher, the acceleration is also higher, but when the mass of an object is increased or higher, the acceleration decreases. Therefore, the more massive the object the greater the force that needs to be applied.

The second law defines the mathematical relationship between three measurable quantities. It can be expressed as force equals mass times acceleration. The unit of measurement is called a ‘newton’, which can be defined as the force required to accelerate a one-kilogram mass by one meter per second per second (m/s^{2}).

The power of mathematics in quantifying the natural world is incredible. These mathematical equations in conjunction with science help to solve many day-to-day problems. The incredibly simple equation of Newton’s second law of motion helps to solve real-life problems such as constructing stable bridges and buildings or calculating the force required to toss a satellite into its orbit.

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For every action there is an equal and opposite reaction.

With this simple yet subtle law, Newton suggests that forces always act simultaneously in pairs. And these forces are equal and opposite.

For instance, when a force is applied to throw a ball, the ball also exerts a force on the hand as the action of throwing is performed.

Similarly, if a car crashes into a tree, the tree exerts the same amount of force on the car as the car on the tree, but the damage is to both of them. In both these examples, the simultaneity of forces acting in pairs is obvious.

Newton’s second law of motion helps to solve real-life problems such as constructing stable bridges and buildings or calculating the force required to toss a satellite into its orbit.

Newton classified physical motion into two different categories—uniform and non-uniform motion. Uniform motion happens when an object moves in a straight line at a constant speed or when an object is at rest. All other motion is classified as non-uniform motion or acceleration.

Newton states that if an object accelerates, then there is a force involved. Newton describes acceleration as both positive and negative. Speeding up is referred to as positive acceleration, and the action of slowing down, such as applying the brakes of a car, is referred to as negative acceleration.

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Isaac Newton analyzed the motion of orbiting objects, a very different approach from that of his contemporaries. According to Newton’s third law of motion, forces act in pairs. For instance, if someone swings a ball around their head, they are exerting a force to hold the ball in place. At the same time, the ball is also exerting a force away from them and these forces are equal and opposite. The former is called centripetal acceleration and the latter is called centrifugal acceleration.

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Newton’s third law of motion manifests itself in subtle ways. For instance, the recoil of a rifle causes an explosion that creates a cloud of gas. While the gas pushes the bullet forward, the bullet pushes the gas. The gas pushes the rifle but the rifle pushes back on the gas. The gun pushes the shoulder of the gunman, but his shoulder pushes the gun.

And despite the relatively larger size of the rifle in comparison to the bullet, the bullet accelerates to a higher velocity. All these are equal and opposite forces that occur more or less simultaneously.

The launching of a rocket is another consequence of equal and opposite forces. While the rocket is being pushed by the expanding gases, it accelerates faster and faster, the gases on the other hand though being pushed by the rocket aren’t physically connected to each other and diffuse outward.

Thus, a rocket can be accelerated by applying a constant force on it. This example also demonstrates that a small but steady force acting over a long period of time could accelerate an object to very high velocities.

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The concept of momentum is a consequence of Newton’s third law of motion. When two objects collide, the objects bumping into each other exert equal and opposite forces on each other. Each of these objects senses unbalanced forces acting on them but the entire system feels no force at all.

According to Newton’s law of motion, the total momentum experienced by the object depends on the force acting on it. The momentum remains unchanged in the absence of external forces.

An important idea of Newtonian mechanics is that when two objects collide, the total momentum remains exactly the same before and after the collision. Mathematically, momentum can be defined as the product of the mass of an object and its velocity. The sum of mass times velocity before and after the collision must be equal.

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When the property of an object remains unchanged, it is said to be conserved. Certain physical quantities do not change for a closed system and these are reflected in aspects of the physical universe as the conservation of angular momentum and momentum, the conservation of mass, and the conservation of energy. These conservation laws provide symmetry and an underlying sense of beauty to the universe.

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The law of the conservation of angular momentum states that when no external force acts on an object, no change will occur in angular momentum. This means that an object which rotates will continue to rotate until it is acted upon by a force. A spinning top is a classic example of conservation of angular momentum, where it will continue to spin unless friction slows it down.

The Earth is a large spinning top that rotates on its axis once in twenty-four hours. But over millions of years, the Earth’s rotation has slowed down by the Moon’s gravitational pull. However, since the angular momentum of the Earth–Moon system has to be conserved, the angular momentum of the Moon has increased over the years.

As a result, the Moon spins slightly faster and the orbit of the Moon has moved farther away from the Earth. These examples illustrate that we live in an amazing interactive system—all of which can be analyzed by Newton’s laws of motion.

To summarize, Sir Isaac Newton made critical advances in understanding the laws of motion. Newton’s three laws of motion together provide a complete framework for investigating and understanding all the forces of motion that occur in our lives and the universe.

According to Newton’s third law of motion, forces act in pairs, and these forces are equal and opposite. For example, when two objects collide, the objects bumping into each other exert equal and opposite forces on each other.

A ball that is swung around someone’s head demonstrates the forces of centripetal and centrifugal acceleration. The force that is exerted to hold the ball in place is the centripetal acceleration. At the same time, the force that the ball is exerting away from them is called centrifugal acceleration.

The law of the conservation of angular momentum states that when no external force acts on an object, no change will occur in angular momentum. An example of this is a spinning top, where it will continue to spin unless friction slows it down.

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