Keith Mack
Newton's law of universal gravitation is a fundamental principle that describes the force of attraction between any two particles in the universe. This law, established by Sir Isaac Newton, states that every object attracts every other object with a force directly proportional to their masses and inversely proportional to the square of the distance between them. Newton's work unified previous observations about gravity on Earth with astronomical behaviours, marking the first great unification. This law helps explain everyday phenomena, like why objects fall to the ground, as well as celestial interactions, such as planetary orbits. While Newton's law was later superseded by Einstein's theory of general relativity, it remains a cornerstone of classical mechanics and modern physics, providing valuable insights into the underlying simplicity and unity in nature.
| Characteristics | Values |
|---|---|
| Force | Directly proportional to the product of their masses |
| Distance | Inversely proportional to the square of the distance between their centers |
| Formula | F = G × (m1 × m2) / r2 |
| Universal Gravitational Constant | 6.672 x 10-11 N2/kg2 or 6.674 x 10-11 N m2/kg2 |
| Scope | All objects with mass, from microscopic particles to massive planets |
| Observations | Falling bodies and astronomical motions, such as planets orbiting the Sun |
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What You'll Learn
The inverse square law
Newton's law of universal gravitation describes gravity as a force stating that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres of mass. This is known as the inverse-square law.
The inverse-square law applies when a force, energy, or conserved quantity is evenly radiated outward from a point source in three-dimensional space. The intensity of radiation passing through any unit area is inversely proportional to the square of the distance from the point source. This means that as the emitted radiation travels farther from the source, it spreads out over an area that increases in proportion to the square of the distance from the source.
The inverse-square relationship can be applied to any physical quantity, including gravitation. Newton's law of universal gravitation follows an inverse-square law, as do the effects of electric, light, sound, and radiation phenomena.
The inverse-square law was first proposed by Robert Hooke in 1670, who stated that the gravitating power decreases with distance. In 1679, Hooke communicated to Isaac Newton that he believed that gravitation had an inverse square dependence. However, when Newton presented his unpublished text to the Royal Society in 1686, Hooke claimed that Newton had obtained the inverse-square law from him, an accusation that was ultimately dismissed.
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Newton's shell theorem
This theorem is a consequence of superposition, the inverse-square law, and the symmetry of a sphere. It is derived from the principle of superposition, which states that to find the net gravitational force, we must sum the vector contributions of individual point masses within the object. However, it is easier to calculate the sum of gravitational potentials and then differentiate to find the force, as gravitational potential is a scalar, not a vector.
The Shell Theorem also has implications for the force experienced by objects inside a spherically symmetric distribution of matter. The potential inside such a sphere is independent of position, and the shell exerts no force on a particle inside it. Therefore, the only gravitational force felt by a particle inside a solid sphere is due to the matter closer to the centre of the sphere.
Thus, Newton's Shell Theorem helps simplify gravitational calculations for objects inside and outside spherically symmetric bodies, making it a valuable tool in understanding the universe.
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Kepler's Third Law
This law is a crucial component of Kepler's laws of planetary motion, which describe how planetary bodies orbit the Sun. Kepler's First Law states that each planet's orbit about the Sun is an ellipse, with the Sun located at one of the two foci. The planet follows the ellipse in its orbit, resulting in a constantly changing distance from the Sun as it moves along its path.
Kepler's Second Law establishes that a planet does not move with a constant speed along its orbit. Instead, it covers the same area of space in the same amount of time, regardless of its position in the orbit. Consequently, when a planet is closer to the Sun, it travels faster, and its speed varies so that the line joining the Sun and the planet sweeps out equal areas in equal intervals of time.
Kepler's laws, particularly the third law, played a significant role in Isaac Newton's development of the theory of universal gravitation. Newton's law of universal gravitation describes gravity as a force, stating that every particle in the universe attracts every other particle with a force proportional to their masses and inversely proportional to the square of the distance between them. By incorporating Kepler's laws, Newton's theory unified previously observed phenomena of gravity on Earth with astronomical behaviours, marking a significant advancement in our understanding of the universe.
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Newton's Second Law of Motion
Newton's Second Law can be applied to calculate the weight, or gravitational force, acting on an object. This is usually represented mathematically as W. For example, when an object is dropped, it experiences acceleration due to the force of gravity, which can be calculated using the Second Law.
In 1666, Newton developed the idea that the laws of planetary motion must also apply to the orbit of the Moon around the Earth and, subsequently, to all objects on Earth. This was a groundbreaking insight, as it proposed that the force of gravity acts as if all the mass of the Earth is concentrated at its centre.
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Newton's Third Law of Motion
Newton's universal law of gravitation describes gravity as a force stating that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This is represented in the equation F=ma, where F is the force, m is the mass, and a is the acceleration.
The universal law of gravitation also explains the motion of planets. Newton realized that the Sun provides a centripetal acceleration to the Earth and all other planets in our solar system, allowing them to maintain their roughly circular orbits. This centripetal acceleration is due to the force of gravity, which is the source of the acceleration.
Newton's laws of gravitation and motion have provided answers to many long-standing questions about nature and have supported the notion of underlying simplicity and unity in nature. They have also helped advance our understanding of the nature and evolution of many astronomical bodies.
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Frequently asked questions
The Universal Law of Gravitation, established by Sir Isaac Newton, states that every particle in the universe attracts every other particle with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them.
Newton's proof was based on empirical observations and what he called inductive reasoning. He connected falling bodies with astronomical motions, realizing that the force of gravity causing objects to fall towards the ground could also be the force that keeps planets in orbit around the Sun.
The formula for Newton's Law of Universal Gravitation is F = G x (m1 x m2) / r^2, where F is the force, G is the universal gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
Newton's law is highly accurate for most everyday applications and has become a cornerstone of classical mechanics and modern physics. However, it has been superseded by Einstein's theory of general relativity for extreme precision or strong gravitational fields, such as those near massive and dense objects.
