As long as we're talking about one of the greatest scientists who ever lived, let's move on to Newton's other famous laws. His three laws of motion form an essential component of modern physics. And like many scientific laws, they're rather elegant in their simplicity. The first of the three laws states an object in motion stays in motion unless acted upon by an outside force. For a ball rolling across the floor, that outside force could be the friction between the ball and the floor, or it could be the toddler that kicks the ball in another direction. The second law establishes a connection between an object's mass () and its acceleration (a), in the form of the equation F = m a. represents force, measured in Newtons. It's also a vector, meaning it has a directional component. Owing to its acceleration, that ball rolling across the floor has a particular vector, a direction in which it's traveling, and it's accounted for in calculating its force. The third law is rather pithy and should be familiar to you: For every action there is an equal and opposite reaction. That is, for every force applied to an object or surface, that object pushes back with equal force.

In 1665, Isaac Newton recognized that all matter attracts all other matter, but he also recognized that the gravitational attraction of everyday objects for each other was far too small to be measured in his time. Newton tested his theory of gravitation with the large masses of astronomical objects like the moon, Earth, and sun. In 1797, Henry Cavendish succeeded in measuring the tiny gravitational force between two metal spheres. He fastened small spheres on the ends of a rod and hung it from a wire. Then he brought up two larger spheres, as shown in the schematic drawing, so that the gravitational forces twisted the wire slightly. The forces between a small and large sphere are only about a billionth of their weight. Nevertheless, from the amount of twist in the wire, and the physical properties of the wire and suspended spheres, Cavendish measured the tiny force, and it agreed with Newton's prediction. (See drawing at right) Dependence on mass and separation Photo of University of Washington experiment showing polished spheres Newton discovered that all matter in the universe attracts all other matter, with a force that decreases with the square of the separation. If you double the separation of two objects, the force they exert on each other is divided by four. The force is proportional to the mass of each object. Double the mass of one object, and the gravitational force doubles, too. We make an equation. So far we have that for the force of gravity F between two objects, 1 and 2, F is proportional to M1M2 R2 In the above relationship, M1 and M2 are masses, R is the separation between them. To make this relationship into an equation, we need a constant, fondly known as “Big ‘G’”. Here's the equation: Notice that if R gets big, the value of F gets small. Why “Big ‘G’” is important If we know "G" from lab measurements, we can find the mass of Earth by measuring the radius of the moon's orbit and the length of the month, or by measuring the acceleration of gravity on Earth's surface. Likewise, we can find the mass of the sun by measuring Earth's orbit and determining the length of the year. Science Marches Ahead? We expect measurements to get more and more accurate over time, as physicists improve experiments and employ new technologies. With "Big 'G'", however, for a while the accuracy was going down, and fast. Prior to 1987, "Big 'G'" was taken to be accurate to 0.013%. Subsequently, two research groups made measurements that were tenths of a percent from the then-accepted value, and in different directions! Consequently the accepted uncertainty was raised by more than a factor of ten. This unfortunate situation galvanized several other groups into action, including one at the University of Washington, whose measurements are accurate to 0.0015%, nearly 10 times more accurate than the 1987 value. Measuring Big 'G' Big news at an April 2000 scientific meeting was the announcement of a long-awaited higher precision measurement of the gravitational constant (affectionately known as “Big ‘G’”among physicists) by Jens Gundlach of the University of Washington. Although G has been of fundamental importance to physics and astronomy ever since it was introduced by Isaac Newton in the seventeenth century (the gravitational force between two objects equals G times the masses of the two objects and divided by their distance apart squared), it has been relatively hard to measure, owing to the weakness of gravity. Steve Merkowitzz (l) and Jens Gundlach (r) with the Cavendish apparatus developed at the University of Washington. (Credit: Mary Levin, University of Washington)

When you drop an object from some height above the ground, it has an initial velocity of zero. Simple equations allow you to calculate the velocity an object falls after a given period of time and the velocity it reaches at a given displacement. The equations assume that air resistance is negligible. Examples demonstrate applications of the equations. Questions you may have include: What is the equation for the velocity for a given time? What is the equation for the velocity to reach a given displacement? What are some examples of these equations? Velocity with respect to time The general gravity equation for velocity with respect to time is: v = gt + vi Since the initial velocity vi = 0 for an object that is simply falling, the equation reduces to: v = gt where v is the vertical velocity of the object in meters/second (m/s) or feet/second (ft/s) g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2) t is the time in seconds (s) that the object has fallen Velocity of a falling object as a function of time or displacement Velocity with respect to displacement The general gravity equation for velocity with respect to displacement is: v = ±√(2gy + vi2) ± means plus or minus √(2gy + vi2) is the square root of the quantity (2gy + vi2) y is the vertical displacement in meters (m) or feet (ft) Since vi = 0, y is positive because it is below the starting point. Also, v is downward and positive. Only the + term of ± applies. Thus, the equation for the velocity of a falling object after it has traveled a certain displacement is: v = √(2gy) Examples The following examples illustrate applications of the equations. For a given time What will be the velocity of an object after it falls for 3 seconds? Solution Substitute in the equation: If you use g = 9.8 m/s2, v = (9.8 m/s2)*(3 s) = 29.4 m/s. If you use g = 32 ft/s2, v = (32 ft/s2)*(3 s) = 96 ft/s. For a given displacement What is the velocity of an object after it has fallen 100 feet? Since y is in feet, g = 32 ft/s2. Substitute in the equation: v = √[2*(32 ft/s2)*(100 ft)] v = √(6400 ft2/s2) v = 80 ft/s Summary There are simple equations for falling objects that allow you to calculate the velocity the object reaches for a given displacement or time. The equations are: Be a champion Websites - Physics Hypertextbook - Wikipedia - Calculator - Physics Classroom Books Top-rated books on Simple Gravity Science Top-rated books on Advanced Gravity Physics Share Click on a button to bookmark or share this page through Twitter, Facebook, email, or other services: Students and researchers

Yet stick a girl on live telly, and it's as if the cameras exert some weird gravitational pull on her blouse.A star wobbles on its axis when orbiting bodies like planets exert gravitational pull (force of attraction between bodies of matter).The suggestion is the moon's gravitational pull affects the amniotic fluid in the same way it affects the water in the sea.The shipwreck was first revealed when the gravitational pull of the sun, moon and planets led to extreme high and low tides in March.Tides are governed by the gravitational pull of the moon and, to a lesser extent, the sun.As a river basin soaks up water, the satellites record a stronger gravitational pull.Those Lebanese looks have quite the gravitational pull.Without taking into account gravitational pull or structural stress, tons of soil are transported to the roof of the mall, the weight greatly increased by rainwater, and guess what.A key operation called the Trans-Mars Injection (TMI) on December 1 will give Mangalyn enough speed to move out of Earth's gravitational pull and set it on a trajectory for Mars.India's Mars spacecraft has completed the first of a series of engine firings designed to free it from Earth's gravitational pull and propel it towards the Red Planet, scientists said Friday.It is believed 2011 QF99 is part of a larger-than-expected population of transient objects temporarily trapped by the gravitational pull of the Solar System's giant planets.The majority of the gas cloud has escaped from the black hole's gravitational pull but the tail continues to be stretched by the extreme gravity.

I've been reading many clever answers here about dark matter and dark energy that called my attention to this question. Since Einstein's theory relates matter and energy as different states of the same thing, is it valid to think about dark matter and dark energy in the same way? Are they two states of the same dark "thing"? Are they interchangeable? The short answer to your question is that we don't know if dark matter and dark energy are manifestations of the same dark "thing". We know they both must exist to explain certain phenomena, but we still know very little about their make up so we cannot assume they are linked. For now, we think of them as separate, and we believe the cosmos to be composed of roughly 0.03% heavy elements (anything other than hydrogen and helium), 0.3% neutrinos, 0.5% stars, 4% free hydrogen and helium, 25% dark matter, and 70% dark energy. Here is how we define them separately: Dark matter must exist to account for the gravity that holds galaxies together. If the only matter in the universe was matter we could directly detect, galaxies would not have had enough matter to have ever formed. The galaxies we observe today would fly apart because they wouldn't have enough matter to create a strong enough gravitational force to hold themselves together. Dark matter is also responsible for amplifying small fluctuations in the Cosmic Microwave Background back in the early universe to create the large scale structure we observe in the universe today. Dark energy, which also goes by the names of the cosmological constant or quintessence, must exist due to the rate of expansion we observe for our universe. Not only is the universe expanding, but this expansion is also accelerating so the unknown 'anti-gravity' force at work is termed 'dark energy'. Some researchers are searching for an explanation that encompasses both dark matter and dark energy. One example of such a theory uses a form of energy called a scalar field (it is a field because it has magnitude, energy and pressure, but it is scalar so it has no direction). Things would certainly be easier if we didn't need to have separate theories to explain dark matter and dark energy. However, other researchers look at dark matter and dark energy as two separate problems. For example, many string theories use supersymmetric particles to explain dark matter and make no connection to dark energy at all.

Matter is everything around you. Atoms and molecules are all composed of matter. Matter is anything that has mass and takes up space. If you are new to the idea of mass, it is the amount of stuff in an object. We talk about the difference between mass and weight in another section. Matter is sometimes related to light and electromagnetic radiation. Even though matter can be found all over the Universe, you will only find it in a few forms on Earth. We cover five states of matter on the site. Each of those states is sometimes called a phase. There are many other states of matter that exist in extreme environments. Scientists will probably discover more states as we continue to explore the Universe. You should know about solids, liquids, gases, plasmas, and one state called the Bose-Einstein condensate (BEC). Scientists have always known about solids, liquids, and gases. Plasma was a new idea when it was identified by William Crookes in 1879. The scientists who worked with the Bose-Einstein condensate received a Nobel Prize for their work in 1995. What makes a state of matter? It's about the physical state of the molecules and atoms. Think about solids. They are often hard and brittle. Liquids are fluidy, can move around a little, and fill up containers. Gases are always around you, but the molecules of a gas are much farther apart than the molecules in a liquid. If a gas has an odor, you’ll be able to smell it before you can see it. The BEC is all about atoms that are even closer and less energetic than atoms in a solid. Molecules can move from one physical state to another and not change their basic structure. Oxygen (O2) as a gas has the same chemical properties as liquid oxygen. The liquid state is colder and denser, but the molecules (the basic parts) are still the same. Water (H2O) is another example. A water molecule is made up of two hydrogen (H) atoms and one oxygen (O) atom. It has the same molecular structure whether it is a gas, liquid, or solid. Although its physical state may change, its chemical state remains the same. So you're asking, "What is a chemical change?" Let's start with a glass of pure water. If the formula of water were to change, that would be a chemical change. If you could add a second oxygen atom to a water molecule, you would have hydrogen peroxide (H2O2). The molecules would not be water anymore. The reality of creating hydrogen peroxide is more difficult. Chemical changes occur when the bonds between atoms in a molecule are created or destroyed. Changes in the physical state are related to changes in the environment such as temperature, pressure, and other physical forces. Generally, the basic chemical structure does not change when there is a physical change. Of course, in extreme environments such as the Sun, no molecule is safe from destruction. Or search the sites for a specific topic. Alien Matter in the Solar System (NASA Video) Encyclopedia.com: Wikipedia (Matter): Wikipedia (States of Matter):

Newton’s Law of Universal Gravitation is a fundamental physical law. We experience its effects everywhere on this planet, and it is the prime mover in the vast world of astronomy. It can also be expressed in a relatively simple mathematical formula on which SAT II Physics is almost certain to test you. Gravitational Force In 1687, Isaac Newton published his Law of Gravitation in Philosophiae Naturalis Principia Mathematica . Newton proposed that every body in the universe is attracted to every other body with a force that is directly proportional to the product of the bodies’ masses and inversely proportional to the square of the bodies’ separation...

Here I will explain the difference between matter, anti matter, dark matter, and negative matter in a concise and understandable way. I have seen confusion pop up in various online forums and comments on the recent announced trapping of an anti atom by CERN. The first thing to know is that for a physicist there are four fundamental forces of nature which are always at work . These are the familiar Gravity and Electromagnetism, as well as the generally unfamiliar strong and weak atomic forces. The atomic forces work on the length scale of atoms, Electromagnetism and gravity work on the length scale of the universe though in fundamentally different ways. The different kinds of matter interact through these forces in different ways. Normal matter like that which we are all made of interacts via all four forces in the ways which we are familiar with. All of the science and technology we have done to this point is based on normal matter and how it behaves. But for a few experiments and in certain particle accelerators all we have done has been with normal matter. Hence it's name. Anti matter is just like normal matter only the sign of certain properties is different. The classic case would be the electron, which has as it's anti particle the anti-electron also known as the positron. Electrons are negatively charged, and Positrons are positively charged. Yet they are identical in every other way. Then their are particles like neutrons and protons which are made of even smaller particles called quarks. Quarks interact via the strong atomic force, and electromagnetism. Anti Quarks have opposite charges to Quarks in those two forces. Dark matter on the other hand only interacts by way of gravity and the weak atomic force. Dark matter does not interact via either the strong atomic force or electromagnetism hence dark matter cannot be seen and is hard to detect. It only interacts via the weak force which is what keeps neutrons and protons inside the nucleus of atoms together. Such is why experiments to detect dark matter directly rely on a particle of dark matter bumping into a particle of matter dead bang on the nucleus of an atom of normal matter. Most of the reason we think dark matter exists has to do with the fact that it solves problems in cosmology in a very expedient way without us having to alter General Relativity. It is widely agreed that dark matter whatever it turns out to be quantifies how much we really don't know about the matter in the universe. Negative matter is a hypothetical type of matter which if it exist will have negative mass and negative energy. It will in essence have a negative gravitational charge and repel normal matter. Yet it will interact just like any other matter in every other way. This table summarizes the differences in how each type of matter would interact with the different forces. Normal Matter Anti- Dark- Negative- Gravity As usual As usual* Opposite sign Electromagnetism No charge *We assume that antimatter behaves as normal matter under gravity. The truth is we have never seen a large enough mass of it to know for certain it behaves the same. When it comes to Negative matter we know nothing and it may not even exist outside of certain theories. Dark matter is on the edge of being a confirmed real entity.

We have already met gravitational fields, where the gravitational field strength of a planet multiplied by an objects mass gives us the weight of that object, and that the gravitational field strength, of Earth is equal to the acceleration of free fall at its surface. We will now consider gravitational fields that are not uniform and how to calculate the value of for any given mass. Gravity as a field of force [edit] The effects of the Earth's gravity extend far out into space. For example, the Moon is kept in orbit by the Earth even though it is 400, 000km away (where gravity is the centripetal force). The Earth has a gravitational field that will attract any object with mass towards the centre of the planet. Radial Fields [edit] The Earths radial gravitational field is represented by the lines. The Earth has a radial field of gravity, which means that the gravitational field is circular and acts from the centre point. You can see on the diagram that near the Earth's surface the lines are closer together than higher up. The closeness of the lines represent the relative strength of the field, so from the diagram, you can tell that the strength of the field decreases with altitude. Further apart lines represent points where the field is weaker. The arrows show the direction in which the force on an object will act, which is towards the centre of the Earth. Uniform fields [edit] Gravity field lines representation is arbitrary as illustrated here represented in 30x30 grid to 0x0 grid and almost being parallel and pointing straight down to the center of the EarthThe Earth's gravitational field is represented by parallel lines on small scales. A uniform field , however, has the lines perfectly parallel. The Earth's gravitational field can be considered to be uniform on the scale of small things such as cars, balls, and planes. For small heights at this scale (a few dozen kilometres), the strength of the field doesn't change enough to be noticeable. Again, the arrows point towards the centre of the Earth, since that is the way objects fall. Newton's ideas of gravity [edit] Isaac Newton was trying to find a way to explain why objects fell towards the centre of the Earth instead of simply staying put. He began to link the falling of an apple, with the "falling" of the Moon towards the Earth, and came up with his law of gravitation . He suggested that any two objects with a mass would have a force of attraction between them. This force of attraction would be proportional to their masses, so that larger masses would have a stronger force of attraction than a smaller mass. The gravitational field of every object is a radial field, since the mass is concentrated at the objects centre, and as you already know, this is the point at which gravity could be said to act. As you can see, a quarter of lines of force goes through the plane when the distance is doubled. The strength of a radial field decreases as you move further away from it. As you can see on the diagram on the right, the number of field lines going through the plane quarter when the distance is doubled, and it will be of the original value if the distance was tripled. This is called the inverse square law, and is true for anything which is a point source, such a light from a point or the amount of radiation emitted. The inverse square law follows . Using the above, Newton suggested that the force of attraction was proportional to the two masses as well as the distance between them: . This relationship is the basis of how Newton's law of gravitation is often stated: Any two point masses attract each other with a force that is proportional to each of their masses and inversely proportional to the square of the distance between them. However, to make this into an equation, we need to add in a constant of proportionality, G: . Where G is the gravitational constant . There is also a minus sign in the equation, which will be explained in the "electric fields" module, where we will encounter repelling as well as attracting forces. is also sometimes written as , so that capital M represents a large mass such a planet, and lower case m represents a small mass such as a ball or an aeroplane. Defining the gravitational field strength [edit] The gravitational field strength tells us how strong a gravitational field is. You may recall that the gravitational field strength of the Earth near its surface is . This means an object that is near the surface of the earth will accelerate towards it at . We could then define the gravitational field strength as the acceleration an object will experience within that gravitational field. A better definition, however, can be derived from the equation. Making the subject of this gives us , or . From this arrangement of the equation, our definition of gravitational field strength now becomes: The gravitational field strength at a point is the force per unit mass exerted on a mass placed at that point. This means that the gravitational field strength, is equal to the force experienced by a mass of 1kg in that gravitational field. From the new definition, it follows that gravitational field strength is measured in , though it is perfectly acceptable to use for situations where it is treated as an acceleration (such as the acceleration of an object in free fall). Finding the field strength of a mass [edit] Since and , they can be combined to give: (by substituting F for mg) (by cancelling the lower case 'm's) You can use this to find the gravitational field strength of a mass at a particular point, r. Note that the gravitational field strength of the Earth near its surface is numerically equal to the acceleration of free fall.

University of California Hastings College of the Law 2016 Abstract: In the American system of dual sovereignty, states have primary authority over matters of state law. In nonpreemptive areas in which state and federal regimes are parallel — such as matters of court procedure, certain statutory law, and even some constitutional law — states have full authority to legislate and interpret state law in ways that diverge from analogous federal law. But, in large measure, they don’t. It is as if federal law exerts a gravitational force that draws states to mimic federal law even when federal law does not require state conformity. This paper is the first to explore the widespread phenomenon of federal law’s gravitational pull. The paper begins by identifying the existence of a gravitational force throughout a range of procedural and substantive law felt by a host of state actors, including state rulemakers, legislators, judges, and even people themselves. It then excavates some explanatory vectors to help understand and appreciate why federal law exerts a gravitational force. Finally, the paper considers some normative concerns with state acquiescence to the federal gravitational pull. Number of Pages in PDF File: 52 Keywords: gravity, gravitational, federalism, following, federal rules, bowers, marriage, title vii,