The equivalence principle posits that inertial and gravitational mass are indistinguishable in a gravitational field.Being in an elevator falling in a vacuum is no different from free flight in weightlessness. You will not feel your own weight in both cases. The equivalence principle says: locally, gravity and acceleration are indistinguishable — that very 'happiest moment' in Einstein's life.
Galileo Galilei in the early 17th century showed that all bodies fall with the same acceleration (ignoring air resistance). Isaac Newton in 1687 noted the proportionality of gravitational force to acceleration through the introduction of two types of mass, but considered it a coincidence. Albert Einstein in 1907, reflecting on a man falling from a roof, realized that free fall locally eliminates weight, and formulated the equivalence principle as a basis for extending relativity to gravity. This led him to general relativity (1915). Later, the principle was repeatedly tested: from Eötvös experiments with torsion balances to the MICROSCOPE satellite.
The equivalence principle explains phenomena such as gravitational redshift, the bending of starlight near the Sun, and time dilation in a gravitational field. It is essential for the operation of satellite navigation systems (GPS, GLONASS), where relativistic corrections to clock rates are taken into account. Applicability is strictly local: in sufficiently large regions of spacetime, tidal forces appear, revealing the non-uniformity of the gravitational field.
Aircraft for training cosmonauts fly along a ballistic trajectory and allow passengers inside to experience 20–30 seconds of real weightlessness — this is a direct consequence of the equivalence principle.
| Q | variable | Electric charge of the body — electric charge coulomb |
| M | variable | Mass of the body — mass kilogram |
| k_e | constant | Electrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared |
| G | constant | Newtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| M_J | variable | Jeans mass, minimum mass for collapse — mass kilogram |
| T | variable | Temperature of the gas — temperature kelvin |
| ρ | variable | Mass density of the gas — mass density kilogram per cubic metre |











