Open Course : Astronomy : Introduction : Lecture 6 : Laws of Motion & Gravity Tension (Cohesion): an attractive force that holds objects together. Cohesion prevents moons and planets from being torn apart by tidal forces (though not always!). Friction: an attractive force that opposes the sliding of objects past each other. Friction between molecules in a gas falling into a black hole will cause it to heat up and emit radiation. Question: if the force of gravity is pulling you downward, what force counteracts it to keep you in place while you are sitting or standing? 6.4 The Universal Law of Gravity (Discovering the Universe, 5th ed., §2-5) In order to complete his study of the motion of the planets, Newton had to combine his general Laws of Motion with a specific description of the force of gravity. Knowing the basic behavior of the planets from Kepler's Laws, Newton was able to determine an appropriate force law, the Universal Law of Gravitation: Here, G is a constant, M and m are two masses, and r is the separation between them. Gravity is an attractive force, and in accordance with Newton's Third Law , the two masses feel equal and opposite forces.

Gravity is relatively weak because of the small value of the gravitation constant G; in metric units, G = 6.7 x 10-11 Nm2/kg2 . Therefore, large masses are required to provide an appreciable force, e.g. the mass of the Earth is 6.0 x 1024 kg. Despite the Earth's large mass, the gravitational force holding you to the surface of the Earth, your weight, is still only a few hundred Newtons. (Note: the distance r in the force law is the radius of the Earth, 6378 Km, as if all of its mass is concentrated at its center.) 6.5 Gravity and Kepler's Laws (Discovering the Universe, 5th ed., §2-6) By combining the Law of Gravitation with his Laws of Motion, Newton was able to mathematically derive all three of Kepler's Laws ! (In the process Newton also had to invent the mathematics of calculus !) Because the Sun is so much more massive than any of the planets, it has a very small gravitational acceleration, and can be taken as essentially motionless.

As described by Kepler, Newton found that all of the planets move around the Sun in circular and elliptical orbits, with the Sun located at a focus of each planet's orbit. Objects with circular and elliptical orbits move around the Sun with a definite period, always between their perihelion and aphelion distances, and sweeping out equal areas in equal times. Newton also showed that Kepler's 3rd Law , relating semimajor axis and period, depends on the mass of whatever is being orbited: As before, a is measured in AU and P is measured in years. But now the mass M appears, and here is measured as multiples of the mass of the Sun. This result provides a powerful tool for determining the mass of the Sun, as well any planet being orbited by a moon, simply by measuring a and P. Question: Newton could immediately calculate the mass of which planets? Circular and elliptical orbits describe objects which are bound to the Sun. Newton also demonstrated that there could be parabolic and hyperbolic orbits! A parabolic orbit describes an object which is marginally bound. Such an object can escape from the Sun's gravity, but it will just barely reach an infinite distance.

Recall that a parabolic orbit has an eccentricity e = 1. Therefore, highly elliptical orbits (e > 0.9) approach a parabolic shape. An object in a hyperbolic orbit travels in a straight line until it nears the Sun and has its path deflected by gravity. Such an object is not part of our solar system, but is instead simply passing through, and can be infinitely far from the Sun while still moving at high speed. An object with a hyperbolic orbit is therefore said to be unbound. A hyperbola has an eccentricity e > 1. 6.6 Energy (Discovering the Universe, 5th ed., §2-6) An important concept that arises from Newton's Laws of Motion is energy. We all have an intuitive idea of what this means. For example, when something moves very fast we say it "has a lot of energy". We might also recognize that heat, electricity, and light have energy as well. In the metric system, the unit of energy is the Joule, whose abbreviation is "J". One Joule is equal to 1 kg·m2/s2, or equivalently 1 N·m.

A unit of energy you may be more familiar with is the food calorie, which is equal to 4184 J. You are probably more familiar with power, the rate of energy production or use (energy per unit time). The metric unit of power is called a Watt, whose abbreviation is "W". One Watt is equal to 1 J/s. Question: where have you seen the Watt appear in everyday usage? 6.7 Potential Energy and Energy Conservation (Discovering the Universe, 5th ed., §2-6) Consider an object which experiences a gravitational force. If the object is thrown upward, it will have some initial speed but it will immediately begin to slow down and eventually stop, i.e. its kinetic energy decreases. The object will then begin to move back downward, rapidly gaining speed as it is accelerated by gravity, and its kinetic energy increases. We intuitively think of an object with greater height as having, "potentially", more energy, because it will be moving faster when it reaches us. We can therefore think of there being a potential energy associated with the object's height, which increases as it rises, and decreases as it falls, the opposite of kinetic energy.

If we define the total energy E as the sum of the kinetic and potential energies, E = KE + PE , then E will not change, i.e. it is conserved. If kinetic energy increases, potential energy must decrease by an equal amount, and vice versa, so that E remains a constant value. We can think of this as one kind of energy being converted into another. The potential energy described above is basically another way to characterize the force of gravity. We can define potential energy for all of the fundamental forces, in such a way that energy is, in general, conserved. As a result, energy conservation and conversion from one form to another are extremely important concepts in physics and astronomy, and we will see many applications, such as planet formation and solar thermal equilibrium. 6.8 Gravitational Potential Energy (Discovering the Universe, 5th ed., §2-6) The mathematical form of gravitational potential energy is very similar to the force law: Note that the potential energy is always a negative number, and reaches its maximum value of zero when the two masses are an infinite distance r apart. For planetary orbits, we can take the Sun to be fixed at position zero, and a planet to be a distance r away from it.

The potential energy of a planet in an elliptical orbit (e ~ 0.36) can then be plotted as shown in the picture at the right. With each orbit around the Sun, the planet will move between its perihelion and its aphelion , and as it does so its energy will convert back and forth between potential and kinetic. At perihelion, kinetic energy is a maximum and potential energy is a minimum; at aphelion, kinetic energy is a minimum and potential energy is a maximum. Question: given that kinetic energy is closely related to speed, where was this characteristic of a planet's motion previously described? Question: what can you say about the speed of a planet in a circular orbit? Notice that, for the elliptical orbit above the total energy is negative (E < 0). This is true for all bound objects (those in circular or elliptical orbits). For marginally bound objects (those in parabolic orbits), the total energy is zero (E = 0). Question: what is the speed of a marginally bound object which has moved an infinite distance from the Sun? You can further explore planetary motion and energy using this Java applet .

We can get an intuitive feel for potential energy by "revolving" the potential energy curve into three dimensions. Potential energy then forms a two-dimensional surface called a gravity well, with the Sun at the bottom and planetary orbits forming curves along it. Imagine walking around the edge of a valley: as you walk higher you slow down, and as you descend you speed up; a planet does the same thing! Question: in the image above you can see three types of orbits; can you tell what they are? 6.9 Escape Velocity (Discovering the Universe, 5th ed., Appendix) The escape velocity of an object such as a rocket is the speed required to depart from some point in a gravity well (such as the Earth's surface) and reach an infinite distance away. This means that the object must be marginally bound or unbound, and so have at least zero total energy: For the surface of the Earth, vescape = 11.2 Km/s ~ 40,000 Km/h. For comparison, at the surface of the Sun, vescape = 618 Km/s, since its mass is 333,000 times that of the Earth!

Newton knew about escape velocity, and used the idea in his Mathematical Principles to illustrate how gravity works; you can explore this yourself with this Java applet from the University of Virginia. 6.10 Conservation of Angular Momentum (Discovering the Universe, 5th ed., §2-5) Another important conservation law arises out of Newton's Laws of Motion, having to do with objects which rotate or revolve. Much like linear momentum , objects have a tendency to keep rotating in the absence of external forces. This "rotational inertia " is characterized by angular momentum, which can be loosely defined as: AM ~ mr2/P where m is the mass of the object, P is its period of rotation or revolution, and r is the distance from the center of rotation or revolution. The "direction" of angular momentum is also important; two rotating objects with the same mass and speed, but different axes of rotation, have different angular momenta. For many forces, including gravity, the angular momentum of a rotating or revolving object will be conserved, i.e. it will be constant.

Conservation of angular momentum is why the Earth always rotates once every 24 hours, and why its rotation axis remains (relatively) fixed in space as it orbits the Sun. Kepler's Second Law , which states that planets sweep out equal areas in equal times, is a consequence of conservation of angular momentum. This can be seen from the above expression for angular momentum by recognizing that area A ~ r2 and time ~ P. So, if AM ~ A/P is conserved, equal areas require equal times. Question: where else have you seen conservation of angular momentum? 6.11 Confirmations of Newton's Laws (Discovering the Universe, 5th ed., §) A contemporary of Newton, Edmond Halley (1656-1742), had been studying comets, bright objects that appear briefly in the sky from time to time and move relative to the stars, like planets (though much faster). Halley noticed that the comets of 1531, 1607, and 1682 had similar characteristics, and were separated by the same period of 76 years.

In 1684, Halley visited Newton in Cambridge, and told him about his suspicion that they were the same comet moving in a periodic orbit around the Sun. It was only then that Halley learned of Newton's unpublished work on planetary motion. Newton advised Halley that the comet's orbit must be elliptical, though much more elongated than a planet's. Halley applied Newton's laws to correctly predict the date and location of the comet's reappearance in 1758. That comet is now known as Halley's Comet; its most recent passage was in 1986. Halley's comet has an orbit with an eccentricity of 0.9673 and a semimajor axis of 17.9 AU (its aphelion of 35.3 AU takes it out beyond the planet Neptune!). It wasn't long before astronomers had applied Newton's Laws to determine the masses of the known planets, by observing their interaction with their moons and with each other. In 1781, an amateur astronomer named William Herschel , who had built one of the most powerful telescopes of the time, noticed "a curious either nebulous star or perhaps a comet".

Subsequent observations revealed that this object moved relative to the stars, although more slowly than a comet. Herschel soon realized that he had discovered a seventh planet, Uranus (and the first in recorded history!). At its brightest, Uranus is barely visible to the naked eye in a dark sky. Because of its slow motion, however, Uranus was always mistaken for a star by earlier observers. Uranus has an orbital period of 84 years, but after 50 years it was clear that it wasn't following its predicted orbit. Astronomers applied Newton's Laws to account for the gravitational pulls of Jupiter and Saturn, but that still did not remove all of the discrepancies. John Couch Adams and Urbain-Jean-Joseph Le Verrier independently realized that a new planet beyond Uranus might cause these deviations. In 1843 and 1845, respectively, they applied Newton's Laws to determine its position. In 1846 Galle and d'Arrest at the Berlin Observatory followed up on Le Verrier's prediction, and quickly identified the eighth planet, Neptune. Neptune moves even more slowly than Uranus, and it has an orbital period of 165 years.

Question: in the picture shown, looking down on the solar system, what effect would the gravity of the outer planet (Neptune) have on the speed of the inner planet (Uranus)? After some years, positional errors in Neptune's predicted orbit again suggested the presence of another large planet further out. In 1905, another amateur astronomer, Percival Lowell , who had built his own observatory in Arizona, began a search for this planet, which he called Planet X. After Lowell died in 1916, his successors at the Lowell Observatory continued the search. Finally, in 1930, Clyde Tombaugh discovered Pluto, but its observation was fortuitous because its mass is so small that it doesn't have a significant effect on Neptune. Better measurements of the outer planets' masses (by the Voyager spacecraft in 1970s and 1980s) have now removed the errors in Neptune's position. Generally speaking, a planetary orbit should be fixed in space. Question: what physical principle requires this? However, another planet's gravitational pull can make a planet's orbit precess around the Sun. Question: where have we already seen an example of a precessing orbit?

In 1845, Le Verrier discovered that Mercury's orbit also precesses around the Sun (note the changing orientation of the semimajor axis in the picture). This is a very small effect, only 0.10 seconds of arc per orbit (43" per century), but even so it could not be explained by the other planets. Le Verrier hypothesized that there might be another planet inside of Mercury's orbit, so close to the Sun that it was difficult to observe. This planet, which Le Verrier called Vulcan, has never been found. So, there was no good explanation for Mercury's precession using Newton's laws, but, like Neptune, the effect was small enough to attribute to measurement errors, and was largely ignored. What Did Isaac Newton Discover? - Universe Today Universe Today What Did Isaac Newton Discover? Article Updated: 18 Oct , 2016 by Matt Williams Isaac Newton – who lived from December 25th, 1642, to March 20th, 1727 – was an English scientist, mathematician, and “natural philosopher”.

In his time, he played a vital role in the Scientific Revolution, helping to advance the fields of physics, astronomy, mathematics and the natural sciences. From this, he established a legacy that would dominate the sciences for the next three centuries. In fact, the term “Newtonian” came to be used by subsequent generations to describe bodies of knowledge that owed their existence to his theories. And because of his extensive contributions, Sir Isaac Newton is regarded as one of the most influential scholars in the history of science. But what exactly did he discover? Newton’s Three Laws of Motion: For starters, his magnum opus – Philosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), which was first published in 1687 – laid the foundations for classical mechanics. In it, he formulated his Three Laws of Motion, which were derived from Johann Kepler’s Laws of Planetary Motion and his own mathematical description of gravity. William Blake’s Newton (1795), depicting him as a divine geometer. Image Credit: William Blake Archive/Wikipedia The first law, known as the “law of inertia”, states that: “An object at rest will remain at rest unless acted on by an unbalanced force.

An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.” The second law states that acceleration is produced when a force acts on a mass – ergo, the greater the mass of the object, the greater the force required to accelerate it. The third and final law states that “for every action, there is an equal but opposite reaction”. Universal Gravitation: He also formulated his law of Universal Gravitation in the Principia, which states that every point mass attracts every single other point mass by a force pointing along the line intersecting both point. According to his calculations, this force is proportional to the product of the two masses and inversely proportional to the square of the distance between them. The formula for this theory can be expressed as: Newton would go on to use these principles to account for the trajectories of comets, the tides, the precession of the equinoxes, and other astrophysical phenomena. This effectively removed the last doubts about the validity of the heliocentric model of the cosmos which argued that the Sun (not the Earth) was at the center of the planetary system.

His work also demonstrated that the motion of objects on Earth and of celestial bodies could be described by the same principles. Sapling of the reputed original tree that inspired Sir Isaac Newton to consider gravitation. Credit: Wikipedia Commons/Loodog Though Newton’s inspiration for his theories on gravity are often attributed to the “Apple Incident” – i.e. where he watched an apple fall from a tree – the story is considered apocryphal by modern sources who argue that he came to his conclusions over time. However, Newton himself described the incident, and contemporaries of his defend this assertion. Shape of the Earth: Additional contributions include his prediction that the Earth was likely shaped as an “oblate spheroid” – i.e. a sphere that experienced flattening at the poles. This theory would later be vindicated by the measurements of Maupertuis, La Condamine, and others. This in turn helped convince most Continental European scientists of the superiority of Newtonian mechanics over the earlier system of Descartes. In terms of mathematics, he contributed to the study of power series, generalized the binomial theorem to non-integer exponents, developed Newton’s method for approximating the roots of a function, and classified most of the cubic plane curves.

He also shares credit with Gottfried Leibniz for the development of calculus. These discoveries represented a huge leap forward for the fields of math, physics, and astronomy, allowing for calculations that more accurately modeled the behavior of the universe than ever before. Optics: In 1666, Newton began contributing to the field of optics, first by observing that color was a property of light by measuring it through a prism. From 1670 to 1672, he lectured at the University of Cambridge on optics and investigated the refraction of light, demonstrating that the multicolored spectrum produced by a prism could be recomposed into white light by a lens and a second prism. Sunlight passing through a prism. Image credit: NASA As a result of his research, he came to theorize that color is the result of objects interacting with already-colored light rather than objects generating the color themselves, which is known as Newton’s theory of color. In addition, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colors (chromatic aberration). As a proof of the concept, he constructed a telescope using a mirror as the objective to bypass that problem.

This was the first known functional reflecting telescope in existence, the design of which is now known as a Newtonian telescope. Other Achievements: He also formulated an empirical law of cooling, studied the speed of sound, and introduced the notion of a Newtonian fluid. This term is used to describe any fluid where the viscous stresses arising from its flow, at every point, are linearly proportional to the rate of change of its deformation over time. Beyond his work in mathematics, optics and physics, he also devoted a significant amount of time studying Biblical chronology and alchemy, but most of his work in these areas remained unpublished until long after his death. So what did Isaac Newton discover? Theories that would dominate the fields of science, astronomy, physics and the natural world for centuries to come. His ideas would go on to influence such luminaries as Joseph-Louis Lagrange and Albert Einstein, the latter of whom is the only scientists believed to have left a comparable legacy. Kepler's Three Laws Circular Motion and Satellite Motion - Lesson 4 - Planetary and Satellite Motion Kepler's Three Laws Energy Relationships for Satellites In the early 1600s, Johannes Kepler proposed three laws of planetary motion.

Kepler was able to summarize the carefully collected data of his mentor - Tycho Brahe - with three statements that described the motion of planets in a sun-centered solar system. Kepler's efforts to explain the underlying reasons for such motions are no longer accepted; nonetheless, the actual laws themselves are still considered an accurate description of the motion of any planet and any satellite. Kepler's three laws of planetary motion can be described as follows: The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses) An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies) The Law of Ellipses Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. An ellipse can easily be constructed using a pencil, two tacks, a string, a sheet of paper and a piece of cardboard.

Tack the sheet of paper to the cardboard using the two tacks. Then tie the string into a loop and wrap the loop around the two tacks. Take your pencil and pull the string until the pencil and two tacks make a triangle (see diagram at the right). Then begin to trace out a path with the pencil, keeping the string wrapped tightly around the tacks. The resulting shape will be an ellipse. An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points is a constant. The two other points (represented here by the tack locations) are known as the foci of the ellipse. The closer together that these points are, the more closely that the ellipse resembles the shape of a circle. In fact, a circle is the special case of an ellipse in which the two foci are at the same location. Kepler's first law is rather simple - all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse. The Law of Equal Areas Kepler's second law - sometimes referred to as the law of equal areas - describes the speed at which any given planet will move while orbiting the sun.

The speed at which any planet moves through space is constantly changing. A planet moves fastest when it is closest to the sun and slowest when it is furthest from the sun. Yet, if an imaginary line were drawn from the center of the planet to the center of the sun, that line would sweep out the same area in equal periods of time. For instance, if an imaginary line were drawn from the earth to the sun, then the area swept out by the line in every 31-day month would be the same. This is depicted in the diagram below. As can be observed in the diagram, the areas formed when the earth is closest to the sun can be approximated as a wide but short triangle; whereas the areas formed when the earth is farthest from the sun can be approximated as a narrow but long triangle. These areas are the same size. Since the base of these triangles are shortest when the earth is farthest from the sun, the earth would have to be moving more slowly in order for this imaginary area to be the same size as when the earth is closest to the sun.

The Law of Harmonies Kepler's third law - sometimes referred to as the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets. Unlike Kepler's first and second laws that describe the motion characteristics of a single planet, the third law makes a comparison between the motion characteristics of different planets. The comparison being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets. As an illustration, consider the orbital period and average distance from sun (orbital radius) for Earth and mars as given in the table below. Planet Check Your Understanding 1. Our understanding of the elliptical motion of planets about the Sun spanned several years and included contributions from many scientists. a. Which scientist is credited with the collection of the data necessary to support the planet's elliptical motion? b. Which scientist is credited with the long and difficult task of analyzing the data? c. Which scientist is credited with the accurate explanation of the data? See Answer Tycho Brahe gathered the data. Johannes Kepler analyzed the data. Isaac Newton explained the data - and that's what the next part of Lesson 4 is all about. 2.

Galileo is often credited with the early discovery of four of Jupiter's many moons. The moons orbiting Jupiter follow the same laws of motion as the planets orbiting the sun. One of the moons is called Io - its distance from Jupiter's center is 4.2 units and it orbits Jupiter in 1.8 Earth-days. Another moon is called Ganymede; it is 10.7 units from Jupiter's center. Make a prediction of the period of Ganymede using Kepler's law of harmonies. a. (T2) / (R3) = 3.16 x 10-16 s2/m3 b. (T2) / (R3) = 3.13 x 10-16 s2/m3 c. (T2) / (R3) = 2.87 x 10-16 s2/m3 d. (T2) / (R3) = 3.03 x 10-16 s2/m3 6. What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support?

See Answer The (T2) / (R3) ratios are approximately the same for each of Jupiter's moons. This is what would be predicted by Kepler's third law! 7. Use the graphing capabilities of your TI calculator to plot T2 vs. R3 (T2 should be plotted along the vertical axis) and to determine the equation of the line. Write the equation in slope-intercept form below. Newton's Law of Gravity - Basic Principles Newton's Law of Gravity Sign Up for Our Free Newsletters Thanks, You're in! What I Learned About Today You might also enjoy: Health Tip of the Day Recipe of the Day There was an error. Please try again. Please select a newsletter. Please enter a valid email address. Did you mean ? Newton did think about gravity watching apples fall from trees, but he didn't have a "eureka" moment by having on fall on his head. That's just not true!. pinstock, Getty Images Updated August 10, 2016. Newton's law of gravity defines the attractive force between all objects that possess mass . Understanding the law of gravity, one of the fundamental forces of physics , offers profound insights into the way our universe functions.

The Proverbial Apple The famous story that Isaac Newton came up with the idea for the law of gravity by having an apple fall on his head is not true, although he did begin thinking about the issue on his mother's farm when he saw an apple fall from a tree. He wondered if the same force at work on the apple was also at work on the moon. If so, why did the apple fall to the Earth and not the moon? Along with his Three Laws of Motion , Newton also outlined his law of gravity in the 1687 book Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy) , which is generally referred to as the Principia. continue reading below our video What Are the Major Laws of Physics? Johannes Kepler (German physicist, 1571-1630) had developed three laws governing the motion of the five then-known planets. He did not have a theoretical model for the principles governing this movement, but rather achieved them through trial and error over the course of his studies. Newton's work, nearly a century later, was to take the laws of motion he had developed and apply them to planetary motion to develop a rigorous mathematical framework for this planetary motion.

Gravitational Forces Newton eventually came to the conclusion that, in fact, the apple and the moon were influenced by the same force. He named that force gravitation (or gravity) after the Latin word gravitas which literally translates into "heaviness" or "weight." In the Principia, Newton defined the force of gravity in the following way (translated from the Latin): Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. Mathematically, this translates into the force equation: FG = Gm1m2/r2 In this equation, the quantities are defined as: Fg = The force of gravity (typically in newtons) G = The gravitational constant, which adds the proper level of proportionality to the equation. The value of G is 6.67259 x 10-11 N * m2 / kg2, although the value will change if other units are being used.

m1 & m1 = The masses of the two particles (typically in kilograms) r = The straight-line distance between the two particles (typically in meters) Interpreting the Equation This equation gives us the magnitude of the force, which is an attractive force and therefore always directed toward the other particle. As per Newton's Third Law of Motion , this force is always equal and opposite. Newton's Three Laws of Motion give us the tools to interpret the motion caused by the force and we see that the particle with less mass (which may or may not be the smaller particle, depending upon their densities) will accelerate more than the other particle. This is why light objects fall to the Earth considerably faster than the Earth falls toward them. Still, the force acting on the light object and the Earth is of identical magnitude, even though it doesn't look that way. It is also significant to note that the force is inversely proportional to the square of the distance between the objects. As objects get further apart, the force of gravity drops very quickly. At most distances, only objects with very high masses such as planets, stars, galaxies, and black holes have any significant gravity effects.

Center of Gravity In an object composed of many particles , every particle interacts with every particle of the other object. Since we know that forces ( including gravity ) are vector quantities , we can view these forces as having components in the parallel and perpendicular directions of the two objects. In some objects, such as spheres of uniform density, the perpendicular components of force will cancel each other out, so we can treat the objects as if they were point particles, concerning ourselves with only the net force between them. The center of gravity of an object (which is generally identical to its center of mass) is useful in these situations. We view gravity, and perform calculations, as if the entire mass of the object were focused at the center of gravity. In simple shapes - spheres, circular disks, rectangular plates, cubes, etc. - this point is at the geometric center of the object. This idealized model of gravitational interaction can be applied in most practical applications, although in some more esoteric situations such as a non-uniform gravitational field, further care may be necessary for the sake of precision. Gravity Index Gravity and Motion - Research Project Website Research Project Website Newton's Laws of Motion and Gravity A cartoon of the tale of how Isaac Newton discovered gravity.

Newton's most well-known work is his laws on motion and gravity. Yet, Newton’s work built upon Galileo’s previous work with vertical and horizontal motion. He synthesized Galileo’s ideas with his own to dictate the three laws of motion. 1. An object in motion stays in motion, and an object at rest stays at rest, unless acted upon by an outside force. 2. The acceleration of an object multiplied by the mass of the object is equal the force applied to it. 3. For every action there is an equal and opposite reaction. Isaac Newton's Laws of Motion defined how objects move on Earth. But he didn’t stop there. The story goes that Newton was sitting under an apple tree and an apple hit him on the head. Then he suddenly formulated the law of gravity. This is sort of true, as Newton did propose that the forces acting on the apple must also be acting on him and everything on Earth. Why not the moon? he thought. This notion, along with his cannon on a mountain, laid the foundation for Newton to mathematically prove gravity. The cannon on a mountain was Newton’s visual representation for how the moon orbited the Earth.

Basically, a cannonball projected at the right height and at the right speed would continue falling around the earth, due to the Earth's curvature, and thus fall into orbit around the Earth. Newton was prompted to continue this work by Edmond Halley. When Halley visited Newton and inquired about the mathematical proof for the orbit of the planets, Newton redid his calculations. He devoted the next three months of his life to writing the Principia, which completely changed man’s view of the universe. In it, Newton outlined his three laws of motion and the theory of gravitation. Newton's cannon on a mountain. It illustrates the different places where a projectile would land if shot at different velocities. "If the Earth is attracting the Moon gravitationally with a certain force holding it in its orbit, then the Moon is attracting the Earth with an equal force. So why isn’t the Earth going around the Moon? The answer is that the masses are so different. The Earth’s mass is more than one hundred times that of the Moon. Consequently, the Earth’s acceleration, “falling” towards the Moon, is very small. What actually happens is that they both circle around a balance point between them, which in fact lies within the Earth.

This motion of the Earth is easily detectable with instruments, but tiny compared with the daily rotation. Of course, it also follows from the above considerations that since the Earth is attracting you downwards with a force equal to your weight, you are attracting the Earth upwards—towards you—with a force of exactly the same strength." ―Michael Fowler, Physics Dept., U.Va. To see more of Michael Fowler's biography of Isaac Newton, click here . Website created by Catherine Paulson Create a free website Who Discovered Gravity? - Universe Today Universe Today by Matt Williams Four fundamental forces govern all interactions within the Universe. They are weak nuclear forces, strong nuclear forces, electromagnetism, and gravity. Of these, gravity is perhaps the most mysterious. While it has been understood for some time how this law of physics operates on the macro-scale – governing our Solar System, galaxies, and superclusters – how it interacts with the three other fundamental forces remains a mystery. Naturally, human beings have had a basic understanding of this force since time immemorial. And when it comes to our modern understanding of gravity, credit is owed to one man who deciphered its properties and how it governs all things great and small – Sir Isaac Newton .

Thanks to this 17th century English physicist and mathematician, our understanding of the Universe and the laws that govern it would forever be changed. While we are all familiar with the iconic image of a man sitting beneath an apple tree and having one fall on his head, Newton’s theories on gravity also represented a culmination of years worth of research, which in turn was based on centuries of accumulated knowledge. He would present these theories in his magnum opus, Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), which was first published in 1687. In this volume, Newton laid out what would come to be known as his Three Laws of Motion , which were derived from Johannes Kepler ’s Laws of Planetary Motion and his own mathematical description of gravity. These laws would lay the foundation of classical mechanics, and would remain unchallenged for centuries – until the 20th century and the emergence of Einstein’s Theory of Relativity . Newton’s own copy of his Principia, with hand-written corrections for the second edition.

Credit: Trinity Cambridge/Andrew Dunn Physics by 17th Century: The 17th century was a very auspicious time for the sciences, with major breakthroughs occurring in the fields of mathematics, physics, astronomy, biology and chemistry. Some of the greatest developments in the period include the development of the heliocentric model of the Solar System by Nicolaus Copernicus , the pioneering work with telescopes and observational astronomy by Galileo Galilei , and the development of modern optics. It was also during this period that Johannes Kepler developed his Laws of Planetary Motion. Formulated between 1609 and 1619, these laws described the motion of the then-known planets ( Mercury , Venus , Earth , Mars , Jupiter , and Saturn ) around the Sun. They stated that: Planets move around the Sun in ellipses, with the Sun at one focus The line connecting the Sun to a planet sweeps equal areas in equal times. The square of the orbital period of a planet is proportional to the cube (3rd power) of the mean distance from the Sun in (or in other words–of the”semi-major axis” of the ellipse, half the sum of smallest and greatest distance from the Sun).

These laws resolved the remaining mathematical issues raised by Copernicus’ heliocentric model, thus removing all doubt that it was the correct model of the Universe. Working from these, Sir Isaac Newton began considering gravitation and its effect on the orbits of planets. A comparison of the geocentric and heliocentric models of the universe. Credit: history.ucsb.edu Newton’s Three Laws: In 1678, Newton suffered a complete nervous breakdown due to overwork and a feud with fellow astronomer Robert Hooke. For the next few years, he withdrew from correspondence with other scientists, except where they initiated it, and renewed his interest in mechanics and astronomy. In the winter of 1680-81, the appearance of a comet, about which he corresponded with John Flamsteed (England’s Astronomer Royal) also renewed his interest in astronomy. After reviewing Kepler’s Laws of Motion, Newton developed a mathematical proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. Newton communicated these results to Edmond Halley (discoverer of “Haley’s Comet”) and to the Royal Society in his De motu corporum in gyrum.

This tract, published in 1684, contained the seed of what Newton would expand to form his magnum opus, the Philosophiae Naturalis Principia Mathematica. This treatise, which was published in July of 1687, contained Newton’s three laws of motion, which stated that: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force. The vector sum of the external forces (F) on an object is equal to the mass (m) of that object multiplied by the acceleration vector (a) of the object. In mathematical form, this is expressed as: F=ma When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. Together, these laws described the relationship between any object, the forces acting upon it and the resulting motion, laying the foundation for classical mechanics. The laws also allowed Newton to calculate the mass of each planet, the flattening of the Earth at the poles, and the bulge at the equator, and how the gravitational pull of the Sun and Moon create the Earth’s tides.

In the same work, Newton presented a calculus-like method of geometrical analysis using ‘first and last ratios’, worked out the speed of sound in air (based on Boyle’s Law ), accounted for the procession of the equinoxes (which he showed were a result of the Moon’s gravitational attraction to the Earth), initiated the gravitational study of the irregularities in the motion of the moon, provided a theory for the determination of the orbits of comets, and much more. Newton and the “Apple Incident”: The story of Newton coming up with his theory of universal gravitation as a result of an apple falling on his head has become a staple of popular culture. And while it has often been argued that the story is apocryphal and Newton did not devise his theory at any one moment, Newton himself told the story many times and claimed that the incident had inspired him. In addition, the writing’s of William Stukeley – an English clergyman, antiquarian and fellow member of the Royal Society – have confirmed the story.

But rather than the comical representation of the apple striking Newton on the head, Stukeley described in his Memoirs of Sir Isaac Newton’s Life (1752) a conversation in which Newton described pondering the nature of gravity while watching an apple fall. “…we went into the garden, & drank thea under the shade of some appletrees; only he, & my self. amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. “why should that apple always descend perpendicularly to the ground,” thought he to himself; occasion’d by the fall of an apple…” John Conduitt, Newton’s assistant at the Royal Mint (who eventually married his niece), also described hearing the story in his own account of Newton’s life. According to Conduitt, the incident took place in 1666 when Newton was traveling to meet his mother in Lincolnshire. While meandering in the garden, he contemplated how gravity’s influence extended far beyond Earth, responsible for the falling of apple as well as the Moon’s orbit.

Similarly, Voltaire wrote n his Essay on Epic Poetry (1727) that Newton had first thought of the system of gravitation while walking in his garden and watching an apple fall from a tree. This is consistent with Newton’s notes from the 1660s, which show that he was grappling with the idea of how terrestrial gravity extends, in an inverse-square proportion, to the Moon. Sapling of the reputed original tree that inspired Sir Isaac Newton to consider gravitation. Credit: Wikipedia Commons/Loodog However, it would take him two more decades to fully develop his theories to the point that he was able to offer mathematical proofs, as demonstrated in the Principia. Once that was complete, he deduced that the same force that makes an object fall to the ground was responsible for other orbital motions. Hence, he named it “universal gravitation”. Various trees are claimed to be “the” apple tree which Newton describes. The King’s School, Grantham , claims their school purchased the original tree, uprooted it, and transported it to the headmaster’s garden some years later.

However, the National Trust, which holds the Woolsthorpe Manor (where Newton grew up) in trust, claims that the tree still resides in their garden. A descendant of the original tree can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. Newton’s work would have a profound effect on the sciences, with its principles remaining canon for the following 200 years. It also informed the concept of universal gravitation, which became the mainstay of modern astronomy, and would not be revised until the 20th century – with the discovery of quantum mechanics and Einstein’s theory of General Relativity . Astronomy Cast has some two good episodes on the subject. Here’s Episode 37: Gravitational Lensing , and Episode 102: Gravity , Sources: Newton's Universal Law of Gravitation | Science | The Guardian Newton's Universal Law of Gravitation How Isaac Newton's encounter with that apple ended up helping send rockets into space Newton's Universal Law of Gravitation: 'a simple equation, but devastatingly effective'.

Newton's Universal Law of Gravitation How Isaac Newton's encounter with that apple ended up helping send rockets into space Sunday 13 October 2013 03.00 EDT First published on Sunday 13 October 2013 03.00 EDT Share on Messenger Close Newton's equation first appeared in the Philosophiæ Naturalis Principia Mathematica, July 1687. It describes why that apple fell from that tree in that orchard in Lincolnshire. Whether or not that apple actually landed on Isaac Newton's head, as some stories would have it, this equation describes why you stay rooted to the ground, what locks the Earth in orbit around the sun and was used by Nasa engineers to send men to the moon. It encapsulates the idea that all the particles of matter in the universe attract each other through the force of gravity – Newton's law tells us how strong that attraction is. The equation says that the force (F) between two objects is proportional to the product of their masses (m1 and m2), divided by the square of the distance between them.

The remaining term in the equation, G, is the gravitational constant, which has to be measured by experiment and, as of 2007, US scientists have measured it at 6.693 × 10−11 cubic metres per kilogram second squared. Newton came to the formula after studying the centuries of measurements from astronomers before him. Stargazers had spent millennia cataloguing the positions of the stars and planets in the night sky and, by the 17th century, the German astronomer and mathematician Johannes Kepler had worked out the geometry of these movements. By looking at the movement of Mars, Kepler had calculated that planets orbited the sun in elliptical paths and, in a kind of celestial clockwork, his three laws of planetary motion allowed astronomers to work out the position of the planets in the future based on data from past records. Kepler's laws explain how the planets moved around the sun but not why. Newton filled in that gap by supposing there was a force acting between the bodies that were moving around each other.

The story goes that Newton saw an apple fall to the ground and it made him wonder why the fruit always fell straight to the ground; why did it not veer off to the left or right? According to his own laws of motion, anything that begins moving from a standing start is undergoing acceleration and, where there is acceleration, there must be a force. The apple started in the tree and landed on the Earth, which means there must be a force of attraction between the apple and the Earth. And even if the apple were higher up in the tree, it would still feel this force of attraction with the Earth, reasoned Newton. In fact, the attraction shouldn't even stop at the top of a tree but carry on way up into the heavens. Which raised the question: if everything around the Earth should feel this force of attraction, including the moon, why doesn't our nearest neighbour fall and crash onto the surface of our planet in the same way as the apple did? Newton concluded that the moon did feel the effect of the Earth's attractive force and that it was indeed falling towards Earth, but there was a very good reason why it didn't crash down.

He used a thought experiment to explain his thinking: imagine you fired a cannonball horizontally from the top of a mountain on Earth. The ball would follow a curved trajectory as it moved forward and was attracted, by gravity, towards the ground at the same time. Fire the cannonball with more energy and it would land further away from the mountain, but it still would follow a curved trajectory in doing so. Newton proposed that, if you fired the cannonball with enough energy, it could fly all the way around the Earth and never land, because the Earth would be curving away underneath the ball at the same rate as the ball fell. In other words, the ball would now be in orbit around the Earth. And this is what happens with the moon – it is in freefall around the Earth but it moves fast enough so that the Earth's surface never quite "catches" it. Newton's law tells us that the strength of the gravitational force between two objects drops off in the same way that a light gets dimmer as you move away from it, a relationship known mathematically as an inverse square law. Another way to visualise the drop-off in the field is to imagine the gravitational field around an object as a series of concentric spheres.

Each sphere represents the same "amount" of gravitational field but the spheres further from the object are bigger, so that same amount of field is spread thinner, over a larger area. The field thus gets weaker as you move away from the object, in proportion to the surface areas of these spheres. The m1 and m2 could be planets and stars or they could be you and the Earth. Compute the equation using numbers for your mass and that of the Earth, and you will get your weight, measured in Newtons. Weight, in true scientific terms, is the gravitational force acting on your mass (which is measured in kilograms) at any point in time. Your mass will stay the same wherever you go in the universe but your weight will fluctuate depending on the mass and position of the objects around you. Newton's law of gravitation is simple equation, but devastatingly effective: plug in the numbers and you can predict the positions of all the planets, moons and comets you might ever want to watch, anywhere in the solar system and beyond. And it allowed us to add to those celestial bodies too, heralding the space age. Newton's formula helped engineers work out how much energy we needed to break the gravitational bonds of Earth.

The path of every astronaut and the orbit of every satellite from which we benefit – whether for communications, Earth observation, scientific research around Earth or other planets, global positioning information – was calculated using this simple formula. Newton's theory of "Universal Gravitation" 22c. Flight (1) The Moon orbits around the Earth. Since its size does not appear to change, its distance stays about the same, and hence its orbit must be close to a circle. To keep the Moon moving in that circle--rather than wandering off--the Earth must exert a pull on the Moon, and Newton named that pulling force gravity. Was that the same force which pulled all falling objects downward? Supposedly, the above question occured to Newton when he saw an apple falling from a tree. John Conduitt, Newton's assistant at the royal mint and husband of Newton's niece, had this to say about the event when he wrote about Newton's life: In the year 1666 he retired again from Cambridge ...

to his mother in Lincolnshire & while he was musing in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon thought he to himself & that if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a-calculating what would be the effect of that superposition... ( Keesing, R.G., The History of Newton's apple tree, Contemporary Physics, 39, 377-91, 1998) If it was the same force, then a connection would exist between the way objects fell and the motion of the Moon around Earth, that is, its distance and orbital period. The orbital period we know--it is the lunar month, corrected for the motion of the Earth around the Sun, which also affects the length of time between one "new moon" and the next. The distance was first estimated in ancient Greece--see here and here .

To calculate the force of gravity on the Moon, one must also know how much weaker it was at the Moon's distance. Newton showed that if gravity at a distance R was proportional to 1/R2 (varied like the "inverse square of the distance"), then indeed the acceleration g measured at the Earth's surface would correctly predict the orbital period T of the Moon. Newton went further and proposed that gravity was a "universal" force, and that the Sun's gravity was what held planets in their orbits. He was then able to show that Kepler's laws were a natural consequence of the "inverse squares law" and today all calculations of the orbits of planets and satellites follow in his footsteps. Nowadays students who derive Kepler's laws from the "inverse-square law" use differential calculus, a mathematical tool in whose creation Newton had a large share. Interestingly, however, the proof which Newton published did not use calculus, but relied on intricate properties of ellipses and other conic sections. Richard Feynman, Nobel-prize winning maverick physicist, rederived such a proof (as have some distinguished predecessors); see reference at the end of the section.

Here we will retrace the calculation, which linked the gravity observed on Earth with the Moon's motion across the sky, two seemingly unrelated observations. If you want to check the calculation, a hand-held calculator is helpful. Calculating the Moon's Motion We assume that the Moon's orbit is a circle, and that the Earth's pull is always directed toward's the Earth's center. Let RE be the average radius of the Earth (first estimated by Erathosthenes) RE= 6 371 km The distance R to the Moon is then about 60 RE. If a mass m on Earth is pulled by a force mg, and if Newton's "inverse square law" holds, then the pull on the same mass at the Moon's distance would be 602 = 3600 times weaker and would equal mg/3600 If m is the mass of the Moon, that is the force which keeps the Moon in its orbit. If the Moon's orbit is a circle, since R = 60 RE its length is 2 π R = 120 π RE Suppose the time required for one orbit is T seconds.

The velocity v of the motion is then v = distance/time = 120 π RE/T (Please note: gravity is not what gives the Moon its velocity. Whatever velocity the Moon has was probably acquired when it was created. But gravity prevents the Moon from running away, and confines it to some orbit.) The centripetal force holding the Moon in its orbit must therefore equal mv2/R = mv2/(60 RE)

Question: Who discovered gravity and proposed the Three Laws of Motion?
Answer: Newton