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Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:
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- Newton’s law of gravity
Newton discovered the relationship between the motion of the Moon and the motion of a body falling freely on Earth. By his dynamical and gravitational theories, he explained Kepler’s laws and established the modern quantitative science of gravitation. Newton assumed the existence of an attractive force between all massive bodies, one that does not require bodily contact and that acts at a distance. By invoking his law of inertia (bodies not acted upon by a force move at constant speed in a straight line), Newton concluded that a force exerted by Earth on the Moon is needed to keep it in a circular motion about Earth rather than moving in a straight line. He realized that this force could be, at long range, the same as the force with which Earth pulls objects on its surface downward. When Newton discovered that the acceleration of the Moon is 1/3,600 smaller than the acceleration at the surface of Earth, he related the number 3,600 to the square of the radius of Earth. He calculated that the circular orbital motion of radius R and period T requires a constant inward acceleration A equal to the product of 4π2 and the ratio of the radius to the square of the time:
The Moon’s orbit has a radius of about 384,000 km (239,000 miles; approximately 60 Earth radii), and its period is 27.3 days (its synodic period, or period measured in terms of lunar phases, is about 29.5 days). Newton found the Moon’s inward acceleration in its orbit to be 0.0027 metre per second per second, the same as (1/60)2 of the acceleration of a falling object at the surface of Earth.
In Newton’s theory every least particle of matter attracts every other particle gravitationally, and on that basis he showed that the attraction of a finite body with spherical symmetry is the same as that of the whole mass at the centre of the body. More generally, the attraction of any body at a sufficiently great distance is equal to that of the whole mass at the centre of mass. He could thus relate the two accelerations, that of the Moon and that of a body falling freely on Earth, to a common interaction, a gravitational force between bodies that diminishes as the inverse square of the distance between them. Thus, if the distance between the bodies is doubled, the force on them is reduced to a fourth of the original.
Newton saw that the gravitational force between bodies must depend on the masses of the bodies. Since a body of mass M experiencing a force F accelerates at a rate F/M, a force of gravity proportional to M would be consistent with Galileo’s observation that all bodies accelerate under gravity toward Earth at the same rate, a fact that Newton also tested experimentally. In Newton’s equation F12 is the magnitude of the gravitational force acting between masses M1 and M2 separated by distance r12. The force equals the product of these masses and of G, a universal constant, divided by the square of the distance.
The constant G is a quantity with the physical dimensions (length)3/(mass)(time)2; its numerical value depends on the physical units of length, mass, and time used. (G is discussed more fully in subsequent sections.)
The force acts in the direction of the line joining the two bodies and so is represented naturally as a vector, F. If r is the vector separation of the bodies, then In this expression the factor r/r3 acts in the direction of r and is numerically equal to 1/r2.
Newton discovered the relationship between the motion of the Moon and the motion of a body falling freely on Earth. By his dynamical and gravitational theories, he explained Kepler’s laws and established the modern quantitative science of gravitation. Newton assumed the existence of an attractive force between all massive bodies, one that does not require bodily contact and that acts at a distance. By invoking his law of inertia (bodies not acted upon by a force move at constant speed in a straight line), Newton concluded that a force exerted by Earth on the Moon is needed to keep it in a circular motion about Earth rather than moving in a straight line. He realized that this force could be, at long range, the same as the force with which Earth pulls objects on its surface downward. When Newton discovered that the acceleration of the Moon is 1/3,600 smaller than the acceleration at the surface of Earth, he related the number 3,600 to the square of the radius of Earth. He calculated that the circular orbital motion of radius R and period T requires a constant inward acceleration A equal to the product of 4π2 and the ratio of the radius to the square of the time:
The Moon’s orbit has a radius of about 384,000 km (239,000 miles; approximately 60 Earth radii), and its period is 27.3 days (its synodic period, or period measured in terms of lunar phases, is about 29.5 days). Newton found the Moon’s inward acceleration in its orbit to be 0.0027 metre per second per second, the same as (1/60)2 of the acceleration of a falling object at the surface of Earth.
In Newton’s theory every least particle of matter attracts every other particle gravitationally, and on that basis he showed that the attraction of a finite body with spherical symmetry is the same as that of the whole mass at the centre of the body. More generally, the attraction of any body at a sufficiently great distance is equal to that of the whole mass at the centre of mass. He could thus relate the two accelerations, that of the Moon and that of a body falling freely on Earth, to a common interaction, a gravitational force between bodies that diminishes as the inverse square of the distance between them. Thus, if the distance between the bodies is doubled, the force on them is reduced to a fourth of the original.
Newton saw that the gravitational force between bodies must depend on the masses of the bodies. Since a body of mass M experiencing a force F accelerates at a rate F/M, a force of gravity proportional to M would be consistent with Galileo’s observation that all bodies accelerate under gravity toward Earth at the same rate, a fact that Newton also tested experimentally. In Newton’s equation F12 is the magnitude of the gravitational force acting between masses M1 and M2 separated by distance r12. The force equals the product of these masses and of G, a universal constant, divided by the square of the distance.
The constant G is a quantity with the physical dimensions (length)3/(mass)(time)2; its numerical value depends on the physical units of length, mass, and time used. (G is discussed more fully in subsequent sections.)
The force acts in the direction of the line joining the two bodies and so is represented naturally as a vector, F. If r is the vector separation of the bodies, then In this expression the factor r/r3 acts in the direction of r and is numerically equal to 1/r2.
Aug 1, 2024 · Newton’s law of gravitation, statement that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them. Isaac Newton put forward the law in 1687.
- The Editors of Encyclopaedia Britannica
Jul 30, 2024 · Newton’s laws of motion relate an object’s motion to the forces acting on it. In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration.
- The Editors of Encyclopaedia Britannica
Newton's law of universal gravitation says that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Jun 27, 2024 · What are Newton’s Laws of Motion? An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force. The acceleration of an object depends on the mass of the object and the amount of force applied.
Apr 6, 2022 · Sir Isaac Newton describes the three laws of motion in his 1687 book Philosophiae Naturalis Principia Mathematica. The Principia also outlines the theory of gravity . While the Theory of Relativity applies to objects moving near the speed of light , Newton’s laws work well under ordinary conditions.
