# Fundamental Physics/Force/Gravity Force

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## Gravity

The force of attraction between two mass separate at a distance . Gravity Force is denoted as Fg measured in Newton N

${\displaystyle F_{g}={\frac {mM}{r^{2}}}}$


With

${\displaystyle F_{g}}$
${\displaystyle m}$
${\displaystyle M}$
${\displaystyle r}$

## Free Fall

Images of a freely falling basketball taken with a stroboscope at 20 flashes per second. The distance units on the right are multiples of about 12 millimetres. The basketball starts at rest. At the time of the first flash (distance zero) it is released, after which the number of units fallen is equal to the square of the number of flashes.

What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as ${\displaystyle \scriptstyle {\vec {g}}}$ and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth.This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of ${\displaystyle m}$ will experience a force:

${\displaystyle {\vec {F}}=m{\vec {g}}}$

For an object in free-fall, this force is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward.

Newton's contribution to gravitational theory was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion.

Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that the acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law. Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. Combining these ideas gives a formula that relates the mass (${\displaystyle \scriptstyle m_{\oplus }}$) and the radius (${\displaystyle \scriptstyle R_{\oplus }}$) of the Earth to the gravitational acceleration:

${\displaystyle {\vec {g}}=-{\frac {Gm_{\oplus }}{{R_{\oplus }}^{2}}}{\hat {r}}}$

where the vector direction is given by ${\displaystyle {\hat {r}}}$, is the unit vector directed outward from the center of the Earth. In this equation, a dimensional constant ${\displaystyle G}$ is used to describe the relative strength of gravity. This constant has come to be known as Newton's Universal Gravitation Constant, though its value was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of ${\displaystyle G}$ using a torsion balance; this was widely reported in the press as a measurement of the mass of the Earth since knowing ${\displaystyle G}$ could allow one to solve for the Earth's mass given the above equation. Newton, however, realized that since all celestial bodies followed the same laws of motion, his law of gravity had to be universal. Succinctly stated, Newton's Law of Gravitation states that the force on a spherical object of mass ${\displaystyle m_{1}}$ due to the gravitational pull of mass ${\displaystyle m_{2}}$ is

${\displaystyle {\vec {F}}=-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {r}}}$

where ${\displaystyle r}$ is the distance between the two objects' centers of mass and ${\displaystyle \scriptstyle {\hat {r}}}$ is the unit vector pointed in the direction away from the center of the first object toward the center of the second object.

This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the solar system until the 20th century. During that time, sophisticated methods of perturbation analysis

Since then, general relativity has been acknowledged as the theory that best explains gravity. In GR, gravitation is not viewed as a force, but rather, objects moving freely in gravitational fields travel under their own inertia in straight lines through curved space-time – defined as the shortest space-time path between two space-time events. From the perspective of the object, all motion occurs as if there were no gravitation whatsoever. It is only when observing the motion in a global sense that the curvature of space-time can be observed and the force is inferred from the object's curved path. Thus, the straight line path in space-time is seen as a curved line in space, and it is called the ballistic trajectory of the object. For example, a basketball thrown from the ground moves in a parabola, as it is in a uniform gravitational field. Its space-time trajectory (when the extra ct dimension is added) is almost a straight line, slightly curved (with the radius of curvature of the order of few light-years). The time derivative of the changing momentum of the object is what we label as "gravitational force".