Gravity

Weight

An object of mass $m$ in a place where the acceleration of gravity is worth $g$ , appears subjected to a force Verticale, called weight of the object: $P = m g$ .

In 1903, one defined to it kilogram-force as measuring unit forces. It was the weight of a mass of 1 Kilogram in a place where the acceleration of gravity was worth $g_n$ = 9,80665 m s^-2, the acceleration of standard gravity .

The kilogram-force is an obsolete unit, being worth by definition 9,80665 Newton.

Origin of gravity

The first quantitative description of gravity was given by the universal Loi of the gravitation of Newton. Gravity at the distance $R$ of the center of a spherical star isolated formed from layers Homogeneous S, and from total mass $M$ is directed towards the center of the star and is worth $g=G \ frac {M} {R^2}$ According to Newton, there remotely exists an instantaneous force between two masses $m$ and $M$ , being worth $G \ frac {m M} {R^2}$ .

G=6,67259E (- 11) NR. (Kg^ (- 2)). (m^2)

The theory of the General relativity of Einstein describes how the Espace-temps is curved because of the presence of a density of mass. This theory contains the same universal constant of gravitation $G$ that the theory of Newton and coincides with it as long as gravity remains low. The theory of Newton is sufficient to envisage the movement of the Artificial satellite , but the theory of Einstein is essential to ensure the synchronization of the clocks of the satellites GPS.

Terrestrial gravity

The Ground not being a spherical star isolated formed from homogeneous layers, gravity varies according to the place. The value of $g=9,81$ is only approximate, inter alia owing to the fact that the Earth is not not perfectly spherical and its ray thus varies according to the Latitude, and of the existence of forces axifuges. Here one considers the average radius of the Earth, which is worth 6 371 km.

the most obvious variation is the variation due to the Altitude $h$ . For a small variation of $h$ in front of $R$ , the relative variation of the acceleration of gravity is worth $- 2 \ Delta h/R$ , that is to say -3×10^-7 per meter on the surface of the ground.
Because of the flatness of the Ground, gravity notably varies with the Latitude (0,5 % of variation enters the equator and the poles). The not-sphericity induced of the disturbances of the orbits of the satellites, whose precise observation with a few centimetres near by the system of orbitography DORY provides, by “opposite calculation”, of invaluable indications on the variations compared to the spherical form.
the variations of Densité of the basement involve local variations of gravity.
terrestrial Correction of rotation . This correction is due to the daily rotation of the Earth, which is thus not a Référentiel galiléen. This defect is taken into account for a solid at rest by the addition with gravity of a acceleration of drive axifuge, directed perpendicular to the terrestrial axis of rotation, of expression $\ vec {has} _ {IE} = \ left (\ frac {2 \ pi} {T} \ right) ^2d \ \ vec {U} _r$ with $T =$ 86164 S and $d$ the distance enters the object and the terrestrial axis of rotation.
Correction of the forces of Tide , in particular due to the the Moon and the Sun. This correction varies during the day. It is about 2×10^-7 with the latitude of 40 ⁰.

Even thus corrected, the acceleration of gravity is not enough to describe the movement of the fall of the bodies on the surface of the ground.

the friction of the air must be taken into account. It is him which makes that a small ball falls " less vite" that a gross.
the Pushed of Archimedes. If an object is not weighed vacuum, it is necessary to add to its weight measured the weight of the moved volume of air. Without this correction, one kilogram of feather weighs a little less than one kilogram of lead.
If the object is not motionless compared to the terrestrial reference frame in rotation, it is necessary to take into account the acceleration of Coriolis.

Lunar gravity

On the the Moon, gravity is approximately six times less than on Ground. That explains the extraordinary jumps of the Astronaute S of the American space program Apollo, of the historical mission of Apollo 11 (July 21st 1969) with that of Apollo 17, Apollo 13 excluded. The forecast of this phenomenon was popularized in the album of Tintin One went on the Moon …

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