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F = G (m1m2)/ R2
- In symbols, the magnitude of the attractive force F is equal to G (the gravitational constant, a number the size of which depends on the system of units used and which is a universal constant) multiplied by the product of the masses (m1 and m2) and divided by the square of the distance R: F = G (m1m2)/ R2.
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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
Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.
For two bodies having masses \ (m\) and \ (M\) with a distance \ (r\) between their centers of mass, the equation for Newton’s universal law of gravitation is \ [ F = G\dfrac {mM} {r^2},\] where \ (F\) is the magnitude of the gravitational force and \ (G\) is a proportionality factor called the gravitational constant.
Newton’s Law of Universal Gravitation states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them. The universal gravitation equation thus takes the form.
- Figure \(\PageIndex{1}\): According to early accounts, Newton was inspired to make the connection between falling bodies and astronomical motions when he saw an apple fall from a tree and realized that if the gravitational force could extend above the ground to a tree, it might also reach the Sun.
- Figure \(\PageIndex{2}\): Gravitational attraction is along a line joining the centers of mass of these two bodies. The magnitude of the force is the same on each, consistent with Newton’s third law.
- Figure \(\PageIndex{3}\): The distance between the centers of mass of Earth and an object on its surface is very nearly the same as the radius of Earth, because Earth is so much larger than the object.
- Figure \(\PageIndex{4}\): The Moon causes ocean tides by attracting the water on the near side more than Earth, and by attracting Earth more than the water on the far side.
Aug 11, 2021 · Newton’s Law of Gravitation. Newton’s law of gravitation can be expressed as \[\vec{F}_{12} = G \frac{m_{1} m_{2}}{r^{2}} \hat{r}_{12} \label{13.1}\] where \(\vec{F}_{12}\) is the force on object 1 exerted by object 2 and \(\hat{r}_{12}\) is a unit vector that points from object 1 toward object 2.
For two bodies having masses m and M with a distance r between their centers of mass, the equation for Newton’s universal law of gravitation is [latex]F=G\frac{mM}{r^2}\\[/latex], where F is the magnitude of the gravitational force and G is a proportionality factor called the gravitational constant.
