Cecily Zamora
Isaac Newton formulated the law of universal gravitation in 1687, in his book 'Philosophiæ Naturalis Principia Mathematica' (Mathematical Principles of Natural Philosophy), also known as the Principia. Newton's law states 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 centres of mass. The law was developed after Newton observed an apple fall from a tree and began to wonder why it fell straight down, rather than sideways or upward.
| Characteristics | Values |
|---|---|
| Name | Isaac Newton |
| Date of Birth | 4 January 1643 |
| Place of Birth | Lincolnshire, England |
| Law of Universal Gravitation | States 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 of mass |
| Equation | F = G(m1m2)/R2 or F = GMm/d2 |
| First Published | 5 July 1687 |
| Book | Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia |
| Inspiration | An apple falling from a tree |
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What You'll Learn
Newton's inspiration: the falling apple
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 that is proportional to the product of their masses and inversely proportional to the square of the distance between their centres of mass. Newton's equation first appeared in the Philosophiæ Naturalis Principia Mathematica, published in July 1687.
The story goes that Newton's theory of gravity was inspired by an apple falling from a tree. According to legend, Newton was sitting under an apple tree when an apple fell and hit him on the head. Newton then wondered why the apple had fallen straight down instead of sideways or upwards. According to his laws of motion, anything that begins moving from a standing start is accelerating, and where there is acceleration, there must be a force. Newton realised that the same force that made the apple fall also keeps the moon falling towards the Earth and the Earth falling towards the sun.
Newton himself recounted this story to William Stukeley, an archaeologist and one of Newton's first biographers. Stukeley recorded the story in his Memoirs of Sir Isaac Newton's Life, published in 1752. Voltaire also wrote about the apple incident in his Essay on Epic Poetry in 1727.
Some have argued that the apple story is a fiction and that Newton did not come up with his theory of gravity in a single moment. Newton did, however, develop his theory of gravity during a period of intense invention, which he described as "the prime of my age for invention". This period began in 1665 when the University of Cambridge, where Newton was a student, temporarily closed due to a bubonic plague epidemic, forcing Newton to return home to Lincolnshire for two years. It was during this time that Newton observed an apple falling and began to ponder the forces that govern such motion. By 1666, Newton had developed the idea that the laws of planetary motion also applied to the orbit of the Moon around the Earth and to all objects on Earth.
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Newton's laws of motion
Isaac Newton is credited with formulating the law of universal gravitation. 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 proportional to the product of their masses and inversely proportional to the square of the distance between their centres of mass. Newton's work, titled 'Philosophiæ Naturalis Principia Mathematica' (Latin for 'Mathematical Principles of Natural Philosophy'), was first published on 5 July 1687.
Now, moving on to Newton's laws of motion:
First Law
The first law, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant speed and in a straight line unless acted upon by an external force. This tendency to resist changes in the state of motion is inertia. If all the external forces cancel each other out, there is no net force acting on the object, and it will maintain a constant velocity.
Second Law
The second law defines force as equal to the change in momentum (mass times velocity) per change in time. Newton's second law talks about changes in momentum (mass x velocity). For objects with a constant mass, the second law states that an object subjected to an external force will accelerate, and the amount of acceleration is proportional to the size of the force. The amount of acceleration is also inversely proportional to the mass of the object.
Third Law
The third law states that when two objects interact, they apply forces to each other of equal magnitude and opposite direction.
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Newton's mathematical formula
Isaac Newton's law of universal gravitation describes gravity as a force by stating 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 centres of mass. Newton's equation first appeared in the Philosophiæ Naturalis Principia Mathematica, published on 5 July 1687.
The equation for universal gravitation takes the form:
> F = G(m1m2)/r^2
Where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centres of their masses, and G is the gravitational constant.
Newton's law tells us that the strength of the gravitational force between two objects drops off in the same way that a light gets dimmer as you move away from it, a relationship known mathematically as an inverse square law. Another way to visualise the drop-off in the field is to imagine the gravitational field around an object as a series of concentric spheres. Each sphere represents the same amount of gravitational field, but the spheres further from the object are bigger, so the same amount of field is spread thinner over a larger area.
Newton's law of universal gravitation was later superseded by Albert Einstein's theory of general relativity. However, the universality of the gravitational constant is intact, and the law is still used as an excellent approximation of the effects of gravity in most applications. Relativity is only required when there is a need for extreme accuracy or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects or at small distances, such as Mercury's orbit around the Sun.
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The universality of the gravitational constant
Isaac Newton's law of universal gravitation, first published in 1687, describes gravity as a force stating 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 centres of mass. Newton's law was later superseded by Albert Einstein's theory of general relativity. However, the universality of the gravitational constant remains intact.
The gravitational constant, also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant, is denoted by the capital letter G. It is an empirical physical constant involved in the calculation of gravitational effects in Newton's law of universal gravitation and in Einstein's theory of general relativity. In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance.
The existence of the constant is implied in Newton's law of universal gravitation, though it is not calculated in his work. The modern notation involving the constant G was introduced by C.V. Boys in 1894 and became standard by the end of that decade. The gravitational constant is a physical constant that is difficult to measure with high accuracy because the gravitational force is extremely weak compared to other fundamental forces at the laboratory scale.
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$8.87
The Cavendish experiment
The apparatus featured a torsion balance: a six-foot wooden rod was suspended horizontally from a wire, with two small lead spheres, each weighing 1.61 pounds (0.73 kg), attached to each end. Two large lead spheres, each weighing 348 pounds (158 kg), were suspended separately and could be positioned away from or on either side of the smaller balls. The gravitational attraction between each larger weight and each smaller one drew the ends of the rod aside along a graduated scale. The attraction between these pairs of weights was counteracted by the restoring force from a twist in the wire, which caused the rod to move from side to side like a horizontal pendulum.
Cavendish placed the apparatus in a sealed room, allowing him to move the weights from outside and observe the balance with a telescope. By measuring how far the rod moved from side to side and how long that motion took, Cavendish could determine the gravitational force between the larger and smaller weights. He then related that force to the larger spheres' weight to determine Earth’s mean density as 5.48 grams per cubic centimetre—close to the modern value of 5.51 grams per cubic centimetre.
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Frequently asked questions
Isaac Newton.
1687.
Newton's law of universal gravitation states 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 centres of mass.
There is a popular story that Newton saw an apple fall from a tree, which made him wonder why the apple fell straight down and did not veer off to the side. This led him to develop his theory of gravity.
The equation for universal gravitation is: F = G(m1m2)/R^2, where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centres of their masses, and G is the gravitational constant.
