While this hot gas can be seen, the actual dark matter it masks cannot.The existence of dark matter is known from its gravitational effects on visible matter, radiation, and the large-scale structure of the universe.Although dark matter doesn't absorb, emit or scatter light, the researchers inferred its distribution by charting how its gravitational influence altered the paths of light zooming past.Analysis of the clumpiness of the dark matter in the maps will also allow scientists to probe the nature of the mysterious dark energy, believed to be causing the expansion of the universe to speed up.We used to think that dark matter sits around, minding its own business, " said Dr Richard Massey, a Royal Society research fellow and member of Durham University's Institute for Computational Cosmology.Because dark matter does not reflect, absorb or emit light, it can only be traced indirectly by, such as by measuring how it warps space through gravitational lensing, during which the light from a distant source is magnified and distorted by the gravity of dark matter.They say that the dark matter has scattered due to the gravitational force and an interaction with the photons and neutrinos in the young universe.Kevork Abazajian, Nicolas Canac, Shunsaku Horiuchi and Manoj Kaplinghat analyzed data from NASA's space-borne Fermi Gamma-ray Space Telescope and found that only a narrow range of dark matter models can produce an excess of gamma rays coming from the Milky Way.A detector attached to the International Space Station has so far failed to find any dark matter either.They seem to bear the signature of collisions between atoms of dark matter, the mysterious "stuff" that cannot be seen or detected directly but which binds the cosmos together.After nine years of searching, detectors buried 2, 000ft underground in an old US iron mine registered two "hits" by what could turn out to be dark matter particles.If particles of dark matter somehow could be detected, theoretical advances in physics and astronomy over the past several decades would gain evidentiary support.

]]>A set of 13 measurements of G exhibit a 5.9-year periodic oscillation (solid curve) that closely matches the 5.9-year oscillation in LOD measurements (dashed curve). The two outliers are a 2014 quantum measurement and a 1996 measurement known to suffer from drift. The green dot is an estimate of the mean value of G after the 5.9-year periodicity is removed. Credit: J. D. Anderson, et al. ©2015 EPLA (Phys.org)—Newton's gravitational constant, , has been measured about a dozen times over the last 40 years, but the results have varied by much more than would be expected due to random and systematic errors. Now scientists have found that the measured values oscillate over time like a sine wave with a period of 5.9 years. It's not itself that is varying by this much, they propose, but more likely something else is affecting the measurements. As a clue to what this "something else" is, the scientists note that the 5.9-year oscillatory period of the measured values correlates almost perfectly with the 5.9-year oscillatory period of Earth's rotation rate, as determined by recent Length of Day (LOD) measurements. Although the scientists do not claim to know what causes the /LOD correlation, they cautiously suggest that the "least unlikely" explanation may involve circulating currents in the Earth's core. The changing currents may modify Earth's rotational inertia, affecting LOD, and be accompanied by density variations, affecting . The scientists, John D. Anderson, retired from the California Institute of Technology in Pasadena, and coauthors, have published a paper on the correlation between the measurements of Newton's gravitational constant and the length of day in a recent issue of EPL . As the scientists explained, the main point of the paper is the finding that, while the measured values do vary, they do so in a predictable way. "Once a surprising 5.9-year periodicity is taken into account, most laboratory measurements of are consistent, and are within one-sigma experimental error limits, " Anderson told Phys.org . The solar cycle (monthly mean of the total sunspot number) (black curve) does not consistently align with the data on G. Credit: J. D. Anderson, et al. ©2015 EPLA The constant is essential for our understanding of gravity, appearing in both Newton's law of gravity and Einstein's general relativity. is not an intuitive concept, and not the same as the acceleration of an object due to gravity, , of 9.81 m/s2. The official value of is 6.673889 × 10−11 N·(m/kg)2, but the 13 measurement values analyzed in this study range from approximately 6.672 × 10−11 N·(m/kg)2 to 6.675 × 10−11 N·(m/kg)2, which is a percentage variation of about 10-4. The variations in are generally thought to result from measurement inconsistencies because is very difficult to measure, partly due to the fact that gravity is much weaker than the other fundamental forces. Despite the difficulties in measuring , the new analysis suggests that the measurements are not flawed, but that something in the measurement process varies. One of the scientists' first considerations was that the 5.9-year period is about half of the 11-year period of a solar cycle. Changes in solar activity are caused by changes in the number of sun spots, which affects Earth's atmosphere, and in turn affects Earth's rotational inertia. However, a closer look at the solar cycle shows that it does not consistently align with the data on . Next the scientists turned to a 2013 paper published in Nature that reported a 5.9-year periodicity in Earth's LOD, using data from the International Earth Rotation and Reference Systems Services (IERS) (Holme and de Viron). As the data shows, the length of each day varies slightly, with some days slightly longer and some days slightly shorter than others. The LOD variation is a measure of the speed of Earth's rotation, and the scientists in the current study found that its periodic oscillation aligns almost exactly with the oscillations. (These 5.9-year LOD periodic variations differ from observations that the Earth's rotation is slowing down and the days getting longer due to tidal friction of the Moon, which occurs on a much longer time scale.) Despite the close correlation between LOD and , the scientists note that the maximum percentage variation of the LOD is on the order of 10-9, which is large enough to change by only 10-5 of the amplitude—not enough to explain the full 10-4 percentage variation in . Since this means that the LOD variations cannot cause the variations, the researchers surmise that both variations are caused by changing motions in the Earth's core, or perhaps some other geophysical process. Although the results also raise the possibility that new physics could explain the variations, the scientists believe this is unlikely. One of the 13 measurements of used in this analysis is the first-ever quantum measurement, called LENS-14, performed in 2014. The value obtained by the quantum measurement is the larger of two outliers in the data, with the other outlier being a 1996 experiment that is known to have problems. Further quantum measurements of are needed to understand why the quantum measurement deviates from the classical measurements. The scientists are also not fully convinced that the /LOD correlation is the full story, and they plan to search for other correlations in the future. "We plan to look into the possibility of a connection with the Earth flyby anomaly, which also seems periodic, and perhaps other anomalies, " Anderson said.

]]>(Photo : Getty Images/Peter Macdiarmid ) Scientists may have discovered a new particle in nature - or it could be a glitch. Scientists may have discovered a new particle in nature - or it could be a glitch. A tiny "bump" in datasets from two detectors in the Large Hadron Collider (LHC) has caused excitement in the scientific community, as it could signify the discovery of a new particle, writes Discovery News. Since the discovery of the Higgs boson in 2012, the particle accelerator has been upgraded to accommodate higher energy collisions, known as the "Run 2" phase. The LHC accelerates particles around a 17-mile circumference ring of supercooled electromagnets at 13 teraelectronvolts (TeV) - an energy nearly double that which was used to discover the Higgs boson. Several experiments are situated around the electromagnetic ring. These experiments are building-sized detectors that are highly sensitive to particles by collisions generated when two counter-rotating "beams" of hadrons are forced to collide. Since the counter-rotating beams are traveling at relativistic speeds, any collisions that occur create conditions that have not existed since the Big Bang. According to the Big Bang theory, all energy in the universe was created from an infinitely dense singularity 14 billion years ago. As the universe cooled, the energy was directed into the formation of subatomic particles that eventually condensed to form matter. By recreating Big Bang conditions, physicists can observe the creation of primordial particles by Nature, providing a definitive test for physics theories on the particles that are possible in our universe. Finding the Higgs confirmed that the Standard Model of physics correctly described all particles and forces in the cosmos that we know of. Despite the confirmation of the Standard Model, many mysteries remain - including the mystery of gravity, which cannot be described by this model. Physicists are now looking beyond this model, and entering a realm known as "exotic physics." By exploring this realm, physicists hope to find evidence of dark matter particles as well as other many other mysteries of the cosmos. Inside two of the same LHC experiments that led to the discovery of the Higgs Boson, a small anomaly in energy at around 750 GeV has been detected, according to Run 2 preliminary results from the CMS and ATLAS detectors. "We've been working round-the-clock to understand and triple-check our numbers, and (Dec. 15) was the culmination of the year's worth of work by thousands of people, " said particle physicist James Beacham, a post-doctoral research fellow with the Ohio State University, in an interview with Discovery News. When new particles are produced by the collisions, they typically decay quickly. But they produce other particles as they decay, which might also be detected by LHC experiments. The signature of the signal can act as a fingerprint - revealing the identity of the decaying particle. As more data is collected from the billions of collisions that occur, small bumps in the data could go beyond what the Standard Model is able to predict. The bumps are referred to as "excesses" and often indicate that a new particle has been produced. "The diphoton search, the one that has the most significant excess, is interesting because it could possibly discover things like exotic Higgs bosons or gravitons (the as-yet-undiscovered particles of gravity), " Beacham told Discovery News. "Both of these discoveries would be revolutionary, because they'd be concrete evidence of physics beyond-the-Standard-Model, something we've never seen." While the bump was tiny and could prove insignificant - another detector, The CMS, also picked up on a small signal in the same energy range. The new phase of collisions is still in its infancy, but if the signal is confirmed, it could indicate the presence of something like a bigger Higgs boson particle.

]]>Sichuan University professor Tian Ma, left, and IU Department of Mathematics professor Shouhong Wang have developed a unified theory of dark matter and dark energy they believe could change our view of energy, gravitational interactions and the structure and formation of the universe. (Phys.org)—A pair of mathematicians—one from Indiana University and the other from Sichuan University in China—have proposed a unified theory of dark matter and dark energy that alters Einstein's equations describing the fundamentals of gravity. Shouhong Wang, a professor in the IU College of Arts and Sciences' Department of Mathematics, and Tian Ma, a professor at Sichuan University, suggest the law of energy and momentum conservation in spacetime is valid only when normal matter, dark matter and dark energy are all taken into account. For normal matter alone, energy and momentum are no longer conserved, they argue. While still employing the metric of curved spacetime that Einstein used in his field equations, the researchers argue the presence of dark matter and dark energy—which scientists believe accounts for at least 95 percent of the universe—requires a new set of gravitational field equations that take into account a new type of energy caused by the non-uniform distribution of matter in the universe. This new energy can be both positive and negative, and the total over spacetime is conserved, Wang said. "Many people have come up with different theories for dark energy, " Wang said. "Unfortunately, the mystery remains, and in fact, the nature of dark energy is now perhaps the most profound mystery in cosmology and astrophysics. It is considered the most outstanding problem in theoretical physics. "The other great mystery concerning our universe is that it contains much more matter than can be accounted for in our visible stars. The missing mass is termed as dark matter, and despite many attempts at detecting dark matter, the mystery remains and even deepens." The researchers postulate that the energy-momentum tensor of normal matter is no longer conserved and that new gravitational field equations follow from Einstein's principles of equivalence and general relativity, and the principle of Lagrangian dynamics, just as Einstein derived his field equations. Wang said the new equations were the unique outcome of the non-conservation of the energy-momentum tensor of normal matter. When Einstein developed his theory, dark energy and dark matter had not yet been discovered, so it was natural for him to start his theory using the conservation law of energy and momentum of normal matter, Wang added. "The difference between the new field equations and Einstein's equations is the addition of a second-order covariant derivative of a scalar potential field, " he said. "Gravity theory is fundamentally changed and is now described by the metric of the curved spacetime, the new scalar potential field and their interactions." Tensors provide a concise framework for solving general relativity problems and the energy-momentum tensor quantifies the density and current of energy and momentum in spacetime. The second-order covariant derivative would be the geometric analog of a second order derivative in calculus which measures how the rate of change of a quantity is itself changing. Associated with the scalar field is a scalar potential energy density consisting of positive and negative energies and representing a new type of energy caused by the non-uniform distribution of matter in the universe. The scalar potential energy density varies as the galaxies move and matter redistributes, affecting every part of the universe as a field. Wang said negative energy produces attraction while the positive energy produces a repelling force fundamentally different from the four forces—gravity, electromagnetism, the weak interaction and the strong interaction—recognized in physics today. "Most importantly, this new energy and the new field equations offer a unified theory for both dark energy and dark matter, which until now have been considered as two totally different beasts sharing only 'dark' in name, " he said. "Both dark matter and dark energy can now be represented by the sum of the new scalar potential energy density and the coupling energy between the energy-momentum tensor and the scalar potential field." The negative part of this sum represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies, he said. "In a nutshell, we believe that new gravity theory will change our view on energy, gravitational interactions, and the structure and formation of our universe, " Wang said. Kevin Zumbrun, chair of the Department of Mathematics at IU Bloomington, said the new unified theory looked sound in principle. "It is speculative at the cosmological level, since one must match with experiment, but the math is solid, " he said. "It's a new and elegant angle on things, and if this does match experiment, it is a huge discovery. Quite exciting!" Wang said the new field equations also lead to a modified Newtonian gravitational force formula, which shows that dark matter plays a more important role in a galactic scale at about 1, 000 to 100, 000 light years, but is less important in the larger scale, where dark energy will be significant (more than 10 million light years). "This unified theory is consistent with general characterizations of dark energy and dark matter, and further tests of the theory up to measured precisions of cosmic observations are certainly crucial for an eventual validation of the theory, " Wang added. Explore further: Theoretical Physics: Dark matter and dark energy are different aspects of a single unknown force

]]>A black hole is a point in space with so much gravity that not even light (the fastest thing around) can escape, hence the name. To an observer it would just appear as a sphere of perfect blackness. At the heart of a black hole is an object called a singularity, a point of zero size and infinite density, yes you have read that correctly, Zero Size and Infinite Density. Any object can become a black hole but don’t worry; it would take a hell of a lot of work for something like your car to collapse space, unless of course your car weighed about the same as the sun. A Black Hole is an object for which nothing can get a high enough escape velocity to get away from it. Think of a cannonball being fired straight up in the air. As it goes up it will be slowed down by gravity and come crashing back down. If the speed is high enough however it will keep going until it escapes the gravitational pull. For the earth the escape velocity is 12km/s or 26, 843mph, for something bigger like the sun the escape velocity is 618km/s or 1, 382, 430mph. When the body is outside of the gravitational pull, its kinetic energy and potential energy will be 0, so if we equate them and the rearrange for we get an expression for the escape velocity: (1) Where is the mass of the planet or body, and is the radius you are taking off from. The formula contains no mass of the escaping object, if you wanted to get a space shuttle off the earth you would have to get it to the same speed as if you wanted to get a pebble off the earth, the difference being the amount of energy it would take getting something as heavy as a space shuttle up to the right speed. Cambridge scientist John Michell argued that if you made the value of M big enough in the escape velocity formula, then you could get a value for v that was bigger than the speed of light. We wouldn’t be able to see these objects as no light would be able to reach us, and, as nothing can travel faster than light, no objects would be able to escape their pull once they were close enough. This is a Black Hole. Naturally occurring black holes form when stars collapse. Stars are massive. Our nearest star, the sun, is roughly km wide and weighs about 0kg (2×1030kg). Due to their enormous mass they have a HUGE amount of gravitational force. As you may or may not remember gravity is related to mass via the following equation (2) This is Newton’s Law of Gravitation. The value of the constant is 6.67428×10-11 which is quite small, however when you put in the mass of the sun and the earth and the distance between them the force that comes out is 3.76×1022N, which is equivalent a thousand million million (1 followed by 15 zeros) Saturn V rockets. When the force of gravity from a star becomes bigger than the outwards pressure caused by its temperature then the force starts to make the star collapse, pulling all its mass inwards to a central point. This point gets smaller and smaller and denser and denser as all of the stars mass is squashed into a tiny point. Not all collapsing stars form black holes however. In order for an object to form a black hole it has to be compressed below a certain radius, this radius is given by (3) This radius is known as the Schwarzschild radius, after physicist Karl Schwarzschild who discovered it in 1916 So for example if you wanted to turn the earth into a black hole you would have to compress it all down to about the size of a large mosquito, and if you wanted to turn your car into a black hole you would have to squash it down to the size of a neutrino, which is pretty small (about 1×10-24m wide). Once an object has been compressed to Schwarzschild radius it will continue to collapse until it becomes a singularity. Centred on this singularity will be a sphere of Schwarzschild radius called the Event Horizon. The Event Horizon is the last distance from which light can escape the pull of the black hole. Inside the event horizon, everything, including light, must move inward, getting crushed at the centre. The event horizon itself is not some physical barrier in space, it just represents the last distance at which it is possible to escape the gravitational pull. A person falling into a black hole through the event horizon wouldn’t notice anything different (although they may be preoccupied with the excruciating pain of being crushed and stretched by all that gravity). Due to the extreme nature of gravity around the event horizon some very weird things can happen. As I just stated, someone falling into a black hole wouldn’t notice any changes as he went through the event horizon, however, for someone watching at a safe distance it wouldn’t be that simple. Things moving away from a body get slowed down by the gravitational pull, the bigger the pull the more things get slowed down. Also the closer you are the more you are going to be slowed down. Both of these come from the fact that F∝M and F∝1/r2(from equation 2). As we sit at a safe distance and watch the unlucky person get closer and closer they seem to slow down! This can’t be right can it? Stuff moving away is meant to slow down; stuff moving towards the black hole should speed up! The way we see the person falling in is through photons (particles of light) being reflected off them and into our eye. As they get closer to the black hole the photons get slower and slower due to the increase of gravitational force, so they take longer to reach to reach the observer. The photons given off when the person crosses the even horizon will be slowed down to 0 by the gravity and so an observer will never see them disappear. Despite the fact that black holes just sit there in space sucking things in with their enormous gravity, it is possible for them to radiate, and thus have a temperature. In the vacuum of space particle and antiparticles are continuously created and annihilated randomly. Usually these are just classed as virtual particles as they don’t really interact with anything and can’t usually be detected or measured. But if a virtual particle pair are created outside of the event horizon then it’s possible that one of them falls into the black hole before they can annihilate. The particle that is left can then fly off into space as a real particle. To someone observing from a safe distance, it would appear that the black hole is radiating, and therefore will have a temperature. This temperature was found by Stephen Hawking as (4) where we have the speed of light, Plancks constant, Gravitational Constant, Boltzmanns constant and the mass of the black hole. Notice that this equation contains both and , this indicates that black hole temperature is a ‘quantum-gravitational’ effect. If we have the temperature of a black hole then we can also work out the Entropy , (5) where , , and are the usual constants and is the surface area of the event horizon. Like the temperature equation, the equation for entropy contains both Plancks constant and the Gravitational constant, showing that black hole entropy is a strictly ‘quantum-gravitational’ effect.

]]>Gravity Also called gravitation, gravitationEncyclopædia Britannica, Inc.in mechanics, the universal force of attraction acting between all matter. It is by far the weakest known force in nature and thus plays no role in determining the internal properties of everyday matter. On the other hand, through its long reach and universal action, it controls the trajectories of bodies in the solar system and elsewhere in the universe and the structures and evolution of stars, galaxies, and the whole cosmos . On Earth all bodies have a weight , or downward force of gravity, proportional to their mass, which Earth’s mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects. At ’s surface the acceleration of gravity is about 9.8 metres (32 feet) per second per second. Thus, for every second an object is in free fall, its speed increases by about 9.8 metres per second. At the surface of the Moon the acceleration of a freely falling body is about 1.6 metres per second per second. The works of Isaac Newton and Albert Einstein dominate the development of gravitational theory. Newton’s classical theory of gravitational force held sway from his Principia , published in 1687, until Einstein’s work in the early 20th century. Newton’s theory is sufficient even today for all but the most precise applications. Einstein’s theory of general relativity predicts only minute quantitative differences from the Newtonian theory except in a few special cases. The major significance of Einstein’s theory is its radical conceptual departure from classical theory and its implications for further growth in physical thought. The launch of space vehicles and developments of research from them have led to great improvements in measurements of gravity around Earth, other planets, and the Moon and in experiments on the nature of gravitation . Early concepts Newton argued that the movements of celestial bodies and the free fall of objects on Earth are determined by the same force. The classical Greek philosophers, on the other hand, did not consider the celestial bodies to be affected by gravity, because the bodies were observed to follow perpetually repeating nondescending trajectories in the sky. Thus, Aristotle considered that each heavenly body followed a particular “natural” motion, unaffected by external causes or agents. also believed that massive earthly objects possess a natural tendency to move toward Earth’s centre. Those Aristotelian concepts prevailed for centuries along with two others: that a body moving at constant speed requires a continuous force acting on it and that force must be applied by contact rather than interaction at a distance. These ideas were generally held until the 16th and early 17th centuries, thereby impeding an understanding of the true principles of motion and precluding the development of ideas about universal gravitation. This impasse began to change with several scientific contributions to the problem of earthly and celestial motion, which in turn set the stage for Newton’s later gravitational theory. The 17th-century German astronomer Johannes Kepler accepted the argument of Nicolaus Copernicus (which goes back to Aristarchus of Samos ) that the planets orbit the Sun , not Earth. Using the improved measurements of planetary movements made by the Danish astronomer Tycho Brahe during the 16th century, Kepler described the planetary orbits with simple geometric and arithmetic relations. Kepler’s three quantitative laws of planetary motion are: The planets describe elliptic orbits, of which the Sun occupies one focus (a focus is one of two points inside an ellipse ; any ray coming from one of them bounces off a side of the ellipse and goes through the other focus). The line joining a planet to the Sun sweeps out equal areas in equal times. The square of the period of revolution of a planet is proportional to the cube of its average distance from the Sun. During this same period the Italian astronomer and natural philosopher Galileo Galilei made progress in understanding “natural” motion and simple accelerated motion for earthly objects. He realized that bodies that are uninfluenced by forces continue indefinitely to move and that force is necessary to change motion, not to maintain constant motion. In studying how objects fall toward Earth, Galileo discovered that the motion is one of constant . He demonstrated that the distance a falling body travels from rest in this way varies as the square of the time. As noted above, the acceleration due to gravity at the surface of Earth is about 9.8 metres per second per second. Galileo was also the first to show by experiment that bodies fall with the same acceleration whatever their composition (the weak principle of equivalence).

]]>Is the weakest of the four universal forces which also include nuclear force, weak radiation force, and electromagnetism. Gravity is the force exerted by any object with mass on any other object with mass. Gravity is ubiquitous, omnipresent and causes objects to accelerate towards the centers of other objects exerting gravitational attraction (like the center of the Earth). When shuttle astronauts are in space they experience gravity at approximately 80% of Earth's surface gravity. The missing 20% allows astronauts to float, "seeming weightless. Objects outside of the Earth's gravitational field are held in the Sun's gravitational field. Outside of the solar system, objects are held by the gravity of other stars and the galaxy. Weight is mass being pulled by gravity towards the center of the closest object exerting gravitational pull. Therefore, weight varies from place to place. On Earth, the difference is negligible. But in space, objects are continuously into another object's gravity well (such as the Earth, Sun or Moon) and experience free fall. In this situation, the objects are weightless. On other planets, the objects experience different intensities of gravity, and therefore have different weights. Gravity Table OBJECT ACCELERATION DUE TO GRAVITY GRAVITY Earth 9.8 m/s2 or 32 ft/s 2 1 G the Moon 1.6 m/s2 or 5.3 ft/s 2 24.5 m/s2 or 80 ft/s 2 2.54 the Sun 275 m/s2 or 896 ft/s 2 28 G Newton's Law of Universal Gravitation Newton described gravitational attraction in his Law of Universal Gravitation, which says that the force of gravity between two bodies is directly proportional to the product of the two masses and inversely porportional to the product of the square of the distance between them. Essentially, the pull between two objects directly relates to how massive each object is. Two large objects pull harder than two small objects. Additionally, the inverse square means that every time the distance (R) is increased, the pull of gravity is more than halved. If the distance between two bodies in space is doubled, the pull of gravity would only be one-fourth as strong. Newton's law simply describes in terms humans can use what exists in nature. If the distance relationship was different than inverse square, like inverse cube, there would be no solar system, no Earth, and no life. Humans exist in a universe that is almost completely hostile to life as we know it. Understanding Gravity Gravity affects light, time, matter and biology in a variety of ways. However, there are many questions about gravity that remain unanswered. By producing artificial gravity, humans may be able to understand the force better. Artificial gravity can can be produced through centripetal force and centrifugal force; however, no long-term artificial gravity environment has been produced for experimental purposes. What exactly causes gravity? It appears to be a wavelike kinetic force, but no one knows for sure. Perhaps the next generation will answer that question and others, such as "Does the force of gravity act at light speed?", "Why does gravity's strength or intensity fall off at an inverse square of its distance?" and "How do cells detect gravity?"

]]>In 1687 Isaac Newton published Philosophiae Naturalis Principia Mathematica , a work of immense and profound impact. Newton's pronounced three laws of motion and a law of universal gravitation. They were a united set of principles which applied not only to the heavens but also to the earth in a uniform way. Their simplicity and extremely broad applicability forever changed astronomy. When the string is released, the ball will fly straight away, not along the curve. A body remains at rest, or moves in a straight line (at a constant velocity), unless acted upon by a net outside force. The law of inertia did not originate with Newton, nevertheless it is integral to his system of mechanics. An object in motion will remain in motion unless something acts upon it. Because a planet is moving in an ellipse (i.e. not a straight line) this law states that there must be some “force” acting upon the planet. If there were no force, the planet would fly off in a straight line. The acceleration of an object is proportional to the force acting upon it. The first law says that if no force is acting on an object, it will remain in motion. The second law tells how the motion will change when a force acts upon the object. Velocity is how fast an object is moving (speed or magnitude) and the direction it is moving. Acceleration is a change in velocity. An accelerating object can either change how fast it is moving, the direction it is moving, or both. For every action, there is an equal and opposite reaction. The law can be more fully stated as, “Whenever one body exerts force upon a second body, the second body exerts an equal and opposite force upon the first body.” That is, when the sun pulls on a planet with the force of gravity, the planet pulls on the sun with a force of equal magnitude. But, because the sun is so much more massive than the planet, Newton's second law says that the sun will experience much less acceleration. F = G m1 m2 / r2 Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects. While the law does not explain what gravity is, it does say how the force of gravity works. From this law and his laws of motion, Newton was able to derive all of Kepler's Laws of Planetary Motion.

]]>Fg = force due to gravity between the two objects (N) G = the Gravitational Constant m1 and m2 = the two masses (kg) r = the distance between the two objects’ centres (m) This formula shows that any objects with mass will pull towards each other with a gravitational force. You might have heard the phrase in a Social Studies class. It usually refers to one country having a political or military influence over another. We usually say that an object has a gravitational field around it. Any field is just a sphere of influence around the object. The closer you get, the more you are affected by it. In the case of gravity, the bigger the mass of the object, the bigger the field. The formula also shows that the closer the objects are, the greater the effect of the gravitational field. This is the first formula that you'll see from a family of formulas called the "inverse square formulas". They all look pretty much the same, and lead physicists to believe that there are many common connections and relationships throughout all of physics. Newton then turned his attention to trying to find the value for the Gravitational Constant, “G”. Nope, it isn’t the acceleration due to gravity on Earth, 9.81m/s2. Newton looked for a way of calculating the value for G from the formula above. If we solve that formula for G we get: Let’s look at how we will substitute numbers into this formula. Newton realized that the only thing he could measure a Fg for would be an object on Earth’s surface. An example would be you. We could calculate the force due to gravity on your body easily using Fg = mg. We need to know the distance from the centre of the Earth to your centre… which we do have: 6.38e6 m. And yup, they even had a pretty good estimate of this in Newton's time! We need to know your mass, which would be m1… that’s no problem. The last thing we need, m2, is the mass of the Earth. Oh, oh. That one is a problem. In Newton’s time no one had any idea how heavy the Earth really was. If we knew G, then we could calculate the mass of the Earth, but that’s what we are trying to calculate here! Newton continued to look for some way to calculate G indirectly, but never found a way. Cavendish's Torsion Balance He attached a really heavy pair of metal balls to the ends of a long metal rod, and then hung the rod from a wire. He then brought another pair of really heavy metal balls near the balls on the rod. Cavendish knew that because they had mass they should pull on each other, but very weakly. To measure this weak pull, he carefully measured how much the wire was twisting (torque) whenever he brought the other masses near by. This is why the device he used is called a torsion balance. After a lot of very careful, very tedious tries, he found that G was 6.67e-11Nm2/kg2. Cavendish realized that because he knew the value for G, he could now calculate the mass of the Earth. That’s why he titled the paper that he published “Weighing the Earth.” Example 1: Using values that you now know, Determine the mass of the Earth. We know that the force exerted on my body by the Earth is Fg = mg, where little “m” is my mass. I also know that the force could be found using Newton's big Universal Gravitation Formula, where one mass is a little “m” (my mass), and the other mass is a big “Me” (the mass of the Earth). Fg = Fg Me= 5.99e24 kg Notice that we were able to combine a couple of formulas to get the new formula . Me does not always have to be the mass of the Earth. It could be the mass of the moon, Mars, an asteroid, whatever! It let’s you calculate the acceleration due to gravity on that object if you know the other values. Example 2: The planet Mars has a mass of 6.42e23 kg and a radius (from its centre to the surface) of 3.38e6 m. How much would a 60 kg person weigh on Mars compared to their weight on Earth? Determine How heavy he would “feel” he weighed in kilograms on Mars. On Earth the person has a weight of… Fg = mg = (60kg) (9.81m/s2) Fg = 5.9e2 N Gravity on Mars can be found using the formula shown above. Note: On an exam you need to show how you got this formula. g = 3.75m/s2 So that person’s weight on Mars will be… = (60kg) (3.75m/s2) Fg = 2.3e2 N Remember, mass never truly changes... it's a constant. This is just how much you would feel like, in measurements you can better understand. To figure out how much he would feel like he weighed on Mars in kilograms, remember that we spend our lives here on Earth and our body thinks that 9.81m/s2 is what gravity should always be. Therefore, this person will feel like his mass is… m = Fg / g = (2.3e2 N) / (9.81m/s2) m = 23 kg Example 3: Determine the force of attraction between a 15.0kg box and a 63.0 kg person if they are 3.45m apart. I have to assume that the distance I have been given is the distance between the two centres of the objects.

]]>Starting with the physics equation for the force of gravity, you can plug in the mass and radius of the Earth to calculate the force of gravity near the surface of the Earth. The equation for the force of gravity is and it holds true no matter how far apart two masses are. The gravitational force between a mass and the Earth is the object’s weight . Mass is considered a measure of an object’s inertia, and its weight is the force exerted on the object in a gravitational field. On the surface of the Earth, the two forces are related by the acceleration due to gravity: = mg . Kilograms and slugs are units of mass; newtons and pounds are units of weight. You can use Newton’s law of gravitation to get the acceleration due to gravity, , on the surface of the Earth just by knowing the gravitational constant , the radius of the Earth, and the mass of the Earth. The force on an object of mass 1 near the surface of the Earth is = 1 This force is provided by gravity between the object and the Earth, according to Newton’s gravity formula, and so you can write The radius of the Earth, , is about 6.38 × 106 meters, and the mass of the Earth is 5.98 × 1024 kilograms. Putting in the numbers, you have Dividing both sides by 1 gives you the acceleration due to gravity: Newton’s law of gravitation gives you the acceleration due to gravity near the surface of the Earth: 9.8 meters/second2. Of course, you can measure by letting an apple drop and timing it, but what fun is that when you can calculate it in a roundabout way that requires you to first measure the mass of the Earth?

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