In everyday talk, we say things fall because the Earth's gravity pulls on them. We talk as if our weight was a "given". Actually, weight changes when the pull of gravity changes. The Moon is much smaller and the pull of gravity on the Moon is about 1/6th that of Earth. So any object on the Moon weighs 1/6th of its weight on Earth. What does not change is the amount of matter in an object. That is called conservation of mass. On Earth, mass and weight are the same for most purposes, though a sensitive gravimeter can detect the difference. The difference can be very different on another world such as the Moon.
From this we learn two things.
The Earth has mass. Every particle of matter has mass. So the Earth pulls on every object and person, and they pull on the Earth. This pulling force is called "gravity" and it gives weight.
These words mean almost the same thing in everyday use. Sometimes scientists use "gravity" for the force that pulls objects towards each other, and "gravitation" for the theory about the attraction.
According to one of his students, Galileo did a famous experiment about gravity where he dropped balls from the Tower of Pisa. He later rolled balls down inclines. With these experiments, Galileo showed that gravitation accelerates all objects at the same rate regardless of weight.
Johannes Kepler studied the motion of planets. In 1609 and 1616 he published his three laws governing the shape of their orbits and their speed along those orbits, but did not discover why they moved that way.
In 1687, English mathematician Isaac Newton wrote the "Principia". In this book, he wrote about the inverse-square law of gravitation. Newton, following an idea that had long been discussed by others, said that the closer two objects are to each other, the more gravity will affect them.
Newton's laws were used later to predict the existence of the planet Neptune based on changes in the orbit of Uranus, and again to predict the existence of another planet closer to the Sun than Mercury. When this was done, it was learned that his theory was not entirely correct. These mistakes in his theory were corrected by Albert Einstein's theory of General Relativity. Newton's theory is still commonly used for many things because it is simpler and is accurate enough for many uses.
Why does the Earth not fall into the Sun? The answer is simple but very important. It is because the Earth moving round the Sun is in a dynamic equilibrium. The speed of the Earth's movement creates a centrifugal force which balances the gravitational force between the Sun and the Earth. Why does the Earth continue spinning? Because there is no force to stop it.
Newton's first law: "If a body is at rest it remains at rest or if it is in motion it moves at the same speed "until it is acted on by an external force"".
There is a kind of analogy between "centrifugal force" and "gravitational force", which led to the "equivalence principle" of general relativity.
In free fall an object's motion balances out the pull of gravity on it. This includes being in orbit.
The special theory of relativity describes systems where gravity is not an issue; by contrast, gravity is the central issue of the general theory of relativity.
In general relativity "there is no gravitational force" deflecting objects from their natural, straight paths. Instead, gravity is seen as changes in the properties of space and time. In turn, this changes the straightest-possible paths that objects will naturally follow. The curvature is, in turn, caused by the energy–momentum of matter. Spacetime tells matter how to move; matter tells spacetime how to curve.
For weak gravitational fields and slow speeds relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation. Newton's equations are used to plan journeys in our Solar System.
General relativity has a number of physical consequences.
Gravity influences the passage of time. Light sent down into a is blueshifted, whereas light sent in the opposite direction (i.e., climbing out of the gravity well) is redshifted; collectively, these two effects are known as the "gravitational frequency shift".
More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect is known as gravitational time dilation.
General relativity predicts that the path of light is bent in a gravitational field; light passing a massive body is deflected towards that body. This effect has been confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun.
Closely related to light deflection is the gravitational time delay (or Shapiro delay), the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction.
A parameter called γ encodes the influence of gravity on the geometry of space.
Gravitational waves are ripples in the curvature of spacetime. They move as a wave, travelling outward from the source. Einstein predicted them in 1915 on the basis of his theory of general relativity. In theory, gravitational waves transport energy as gravitational radiation. Sources of detectable gravitational waves might include binary star systems composed of white dwarfs, neutron stars, or black holes. In general relativity, gravitational waves cannot travel faster than the speed of light.
The 1993 Nobel Prize in Physics was awarded for measurements of the Hulse-Taylor binary star system. These measurements suggested gravitational waves are more than mathematical peculiarities.
On February 11, 2016, the LIGO Scientific Collaboration and Virgo Collaboration teams announced that they had made the first observation of gravitational waves, originating from a pair of merging black holes using the Advanced LIGO detectors. On June 15, 2016, a second detection of gravitational waves from coalescing black holes was announced. Besides LIGO, many other gravitational-wave observatories (detectors) are under construction.
Centripetal force
Centripetal force is an accelerating force that acts on any body that revolves around a centre. This force contributes to keeping the body in rotation. This force is always directed towards the centre.
The opposite force (by Isaac Newton's third law of motion) is called centrifugal force. This is the force that acts on the body in a direction away from the centre, which contributes to making the body try to fly away. When you hold a rope with a heavy object attached to it, and rotate it around, the rope becomes tight and keeps the body from flying away. This is caused by centripetal force.
An example is a roller coaster which uses centripetal force to accelerate the carts so they will keep going in a circular motion. Even if an object changes direction but maintains at a constant speed it still counts as acceleration.
In the figure to the right we define the displacement vector formula_2 to represent motion in a circle. The magnitude of formula_2 is denoted as formula_4 and represents the radius of the particle's orbit.
Treaty
A treaty is a written agreement between two or more parties that consists international law. The parties may be countries or other important groups. A treaty may be about any subject.
Two countries might agree to stop a war, or declare war on a common enemy. Very common are treaties where a country promises to come to the aid of another country if the other country is attacked. Treaties about trade are also common. They may allow allow each other's citizens or merchandise to cross borders freely. The European Union is set up by treaties between most of the European nations. It arranges that trade is free between members.
In general, treaties are usually used to settle disputes, or to avoid disputes.
Luxembourg