A falling apple and the floating Moon are both tied to Earth by the same invisible thread. It stretches between any masses in the Universe: the more massive the bodies, the tighter the thread; the farther apart they are, the weaker the pull.
In practice: Calculating orbits of satellites, planets, and interplanetary trajectories; GPS operation, tide prediction, determining masses of celestial bodies.
Isaac Newton was the first to realize that the force causing an apple to fall is the same one that keeps the Moon in orbit. This was a breakthrough that unified the physics of heaven and earth. He formulated a simple and universal law: any two particles attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
How it works
The law explains why we don't fly off the Earth, why the Moon orbits us without falling, and why the Earth orbits the Sun. It also allows one to calculate a planet's mass from its satellite's orbit and is responsible for ocean tides.
💡 Newton delayed publishing the law for almost 20 years because he needed precise data on Earth's radius to make the calculations match the observed motion of the Moon.
All bodies with mass attract each other. The attraction is stronger if the bodies are more massive, and it sharply weakens with increasing distance. Doubling the mass doubles the force, while doubling the distance reduces it by a factor of four. This rule applies uniformly to everything—from a falling cup to distant galaxies.
How it works
The law explains why we don't fly off the Earth, why the Moon orbits us without falling, and why the Earth orbits the Sun. It also allows one to calculate a planet's mass from its satellite's orbit and is responsible for ocean tides.
💡 The gravitational constant G was first measured by Henry Cavendish in 1798, 71 years after Newton's death. His experiment with a torsion balance literally allowed him to 'weigh' the Earth.
In 1687, in his work 'Mathematical Principles of Natural Philosophy', Isaac Newton published the law that became the foundation of classical mechanics. It states: every point mass attracts every other point mass with a force directed along the line connecting them. The magnitude of the force is proportional to the product of the masses and inversely proportional to the square of the distance, with the proportionality constant being the gravitational constant G.
Discovery
Newton built on the work of predecessors: Galileo studied free fall, Kepler derived the laws of planetary motion from Tycho Brahe's observations, and Robert Hooke suspected an inverse-square dependence. However, only Newton mathematically proved that such a law implies all three of Kepler's laws, and additionally explained tides and the precession of the equinoxes. His 'Principia' became a model for the mathematical description of nature.
How it works
The law applies to any objects with mass, from elementary particles to galaxy clusters, provided speeds are much less than the speed of light and gravitational fields are not too strong. Near neutron stars and black holes, it is superseded by Einstein's general theory of relativity. In practice, the law serves as the basis for celestial mechanics, orbit calculations, and space maneuvers.
Caveats
The law describes how masses attract but does not explain the cause of gravity—why mass creates attraction rather than repulsion.; The formula breaks down at speeds comparable to the speed of light and in strong gravitational fields, where general relativity must be applied.; Seeliger's gravitational paradox: if the Universe is infinite and uniformly filled with matter, the total gravitational force at any point becomes undefined.
F = G\frac{m_1 m_2}{r^2}
F — gravitational attractive force (N), G — gravitational constant, G ≈ 6.67430×10⁻¹¹ N·m²/kg², m₁ and m₂ — masses of interacting bodies (kg), r — distance between the centers of mass (m).
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The discovery of 1I/‘Oumuamua made us wonder: could some interstellar wanderers actually be our own comets, ejected from the Oort cloud and returning millions of years later? Simulations show that such ‘quasi-interstellar objects’ are indeed possible, but they have unique characteristics: extremely
A new study has, for the first time, self-consistently incorporated the recipe of double diffusion into an evolutionary code of planets and traced the fate of Jupiter and Saturn from the moment of formation. It turns out that even a thousandfold enhancement of mixing does not lead to significant sme
Spectrograph NIRSpec aboard the JWST telescope has discerned a complex mosaic of carbon dioxide and carbon monoxide bands on Ariel, Umbriel, Titania, and Oberon. Comparison with laboratory ices at cryogenic temperatures revealed signatures of crystalline CO₂, clathrates, and carbonates. The observed
A model based on exponential technological growth shows: the faster a civilization develops, the shorter the period during which it emits technosignatures we can detect. At rates comparable to Earth's after the emergence of AI, this window could be less than twenty years. Traditional narrowband sear
We've been searching the skies for factory chimney smoke, but we should be looking for blooming gardens. A new approach in astronomy suggests shifting focus from pollution to ecological harmony.