Webb's journey to L2 Is nearly complete

On Monday, Jan. 24, engineers plan to instruct NASA's James Webb Space Telescope to complete a final correction burn that will place it into its desired orbit, nearly 1 million miles away from the Earth at what is called ...

Scientists develop novel 'shapeshifting' liquid crystal

Physicists at Case Western Reserve University and Tufts University say they've changed the shape of a flat liquid crystal surface without applying any local stimulus—essentially remotely altering its physical appearance ...

How the Sun affects asteroids in our neighborhood

Asteroids embody the story of our solar system's beginning. Jupiter's Trojan asteroids, which orbit the Sun on the same path as the gas giant, are no exception. The Trojans are thought to be left over from the objects that ...

Exploring quantum gravity and entanglement using pendulums

When it comes to a marriage with quantum theory, gravity is the lone holdout among the four fundamental forces in nature. The three others—the electromagnetic force, the weak force, which is responsible for radioactive ...

Unraveling the mystery of brown dwarfs

Brown dwarfs are astronomical objects with masses between those of planets and stars. The question of where exactly the limits of their mass lie remains a matter of debate, especially since their constitution is very similar ...

Roman Space Telescope will also find rogue black holes

In the past, we've reported about how the Roman Space Telescope is potentially going to be able to detect hundreds of thousands of exoplanets using a technique known as microlensing. Exoplanets won't be the only things it ...

How a ladybug warps space-time

Researchers at the University of Vienna and the Austrian Academy of Sciences, led by Markus Aspelmeyer have succeeded in measuring the gravitational field of a gold sphere, just 2 mm in diameter, using a highly sensitive ...

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Newton's law of universal gravitation

Newton's law of universal gravitation is a general physical law derived from empirical observations by what Isaac Newton called induction. It describes the gravitational attraction between bodies with mass. It is a part of classical mechanics and was first formulated in Newton's work Philosophiae Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. In modern language it states the following:

Every point mass attracts every other point mass by a force pointing along the line intersecting both points. The force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses:

Assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.673×10−11 N m2 kg−2. The value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G). This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton's Principia and 71 years after Newton's death, so none of Newton's calculations could use the value of G; instead he could only calculate a force relative to another force.

Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies. Both are inverse-square laws, in which force is inversely proportional to the square of the distance between the bodies. Coulomb's Law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant.

Newton's law has since been superseded by Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity. Relativity is only required when there is a need for extreme precision, or when dealing with gravitation for very massive objects.

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