Maths in a minute: Newton's law of universal gravitation
Isaac Newton first published his law of universal gravitation in 1687 as part of his monumental work Philosophiæ Naturalis Principia Mathematica (Latin for "Mathematical Principles of Natural Philosophy"). According to legend he was inspired to think about gravity while watching an apple fall from a tree and wondering why it didn't fall upwards or sideways.
According to Newton's theory, gravity is a force that works between two objects. If you have the Earth and the Sun, for example, the Earth feels a force that is exerted by the Sun, and in turn the Sun feels the same force, exerted by the Earth.
The magnitude $F$ of this force is given by the so-called inverse square law $$F=G\frac{m_1 m_2}{r^2},$$ where $G$ is a number known as the gravitational constant, $r$ is the distance between the centres of the two objects, and $m_1$ and $m_2$ are their respective masses.
The forces experienced by the two objects may be equal in magnitude, but the resulting motion is not the same for the two bodies. According to Newton's second law of motion, the magnitude of the acceleration a body experiences when it is subjected to a force is equal to the magnitude of the force divided by the body's mass. Since the Sun's mass is large, the acceleration it experiences due to the Earth's gravitational pull is negligible compared to that experienced by the much less massive Earth. That's why the Sun remains more or less stationary, while the Earth is forced on an orbit around it.
Newton's theory of gravity is remarkably accurate when it comes to most practical purposes. However, it was later superseded by Einstein's theory of gravity, called the general theory of relativity. You can find out more about that in this article.
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