Newton’s unfortunate close encounter with a fruit may never have happened the way popular science likes to tell it. Nevertheless, the notion of a falling body (or apple) is a useful one to keep in mind for our purpose.
Newton’s Law of Gravitation tells us that every single object in the Universe pulls on every other object with a force that is proportional to their masses and inversely proportional to the square of the distance between them:
where is the gravitational force,
and
are masses,
is the distance, and
is the universal gravitational constant.
This force provides the centripetal acceleration that keeps bodies in their orbits.
Under the influence of the Earth’s mass, any object in freefall experiences a linear downward acceleration due to gravity.
So, a body falling freely near the Earth’s surface, without being impeded by air resistance, accelerates downwards with the acceleration due to gravity of magnitude .
Although the value of the gravity varies slightly from place to place, it is generally accepted to be about
The precise magnitude of this acceleration varies according to location, altitude, the effect of Earth’s rotation and variations in its internal composition.
Nevertheless, gravity is universal – it binds planets to stars, keeps moons into their orbits, and even governs the dance of galaxies.
Newton’s Law is not just a dusty equation. Think of it as a cosmic choreography. Newton showed that the same law governs falling objects and planetary motion, and laid the groundwork for Einstein’s later refinements in General Relativity.
It explains why apples fall to Earth and why Earth itself does not drift away from the Sun. It unifies terrestrial physics with celestial mechanics.
Every star, every planet and comet is part of a grand gravitational symphony. Without it, galaxies would not spiral and tides would not rise.
The whole Universe as we know it would be in a state of chaos…
