Equation #9: Newton’s law of Universal Gravitation

Probably the most familiar law in science which everyone seems to understand intuitively, the law of universal gravitation is one of the most powerful and useful equation for practical purposes. Before Newton, people knew earth attracted an apple and it attracted the moon, but they didn’t know that both of these phenomena are actually the same! Newton (according to most historians) was the first person to propose the inverse square relation as a law governing all bodies. He declared that the moon is attracted to the Earth in the same way an apple is.
However, it failed to predict the orbit of Mercury accurately. Turns out, gravity is not that simple afterall. Gravity not only affects mass, it also affects energy(and is derived from mass/energy). It took an Einstein to prove that gravity can distort spacetime, or rather, gravity is the curvature of spacetime!

FACT: No evidence of any apple falling on Newton’s head is found. He did observe an apple falling towards the earth and got inspired, according to his biography by William Stukeley :

“After dinner, the weather being warm, we went into the garden and drank thea, under the shade of some apple trees…he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasion’d by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself…”

more info:

For a explanation of what the formula means, see the excellent video by Khan Academy:
For further explanation of gravity in simple terms, see

For more equations, see Famous equations in Physics

Law of Universal Gravitation

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