Gravitational acceleration

A gravitational field is in physics and geosciences a force field, which is of a celestial body, such as the earth, caused and expresses itself in the fact that other bodies are attracted to him. This attraction is called weight. The gravitational field is composed of the gravity field of the celestial body ( sometimes referred to in the physics literature itself as a gravitational field ) and one caused by its rotation Zentrifugalanteil together.

Gravimetry is engaged in the exploration of the gravity field.

• 3.1 Earth's gravity on the Earth's surface 3.1.1 standard acceleration
• 3.1.2 German main Gravity Network 1996

Strength and direction of the gravitational field

The field strength of the gravitational field is called gravity, acceleration due to gravity, acceleration of gravity, or (in the case of the Earth) gravitational acceleration. As symbols is common. It is a vector quantity and is the magnitude and direction of the weight of a body based on its mass:

Based on this definition, it has the dimensions of acceleration. With this acceleration on earth about 9.8 m s- 2, a freely falling body starts to move. The magnitude of the acceleration due to gravity is also called spatial factor. This term emphasizes the property of the proportionality factor between weight and mass at each location.

The acceleration of gravity is measured in the SI unit equivalent is a statement in. In the geosciences beyond the Gal unit is widespread. The following applies: 100 Gal = 1 m s -2.

The gravitational acceleration is the vector sum of a gravitational and a Zentrifugalanteil:

• The gravitational acceleration caused by the gravitational field. If you can look at the heavenly bodies as spherically symmetric, the gravitational acceleration is calculated according to the law of gravitation:

• The centrifugal force acts from himself, because it is located on the surface of the celestial body in a co-rotating reference system.

• Tidal forces caused by the influence of other celestial bodies (eg the moon or the sun). Whether these forces are considered part of the gravitational field, is a matter of definition. In this article, they are not counted to the gravitational field.

For the gravitational field of a planet's surface, this results in: The gravitational acceleration is dependent on the level, because according to the law of gravity. Also follows from this relationship that the flattening of the planet, the distance from the planet center to the poles of the smallest, the gravitational effect that is the greatest. Moreover, at the terminals of the celestial body, the centrifugal force disappears, because the distance from the axis of rotation is zero. The weakest gravitational field is thus at the equator: where the centrifugal acceleration is maximum and directed against the action of gravity and the distance from the planet center is the largest.

The direction of the gravitational acceleration is called the perpendicular direction. This includes approximately perpendicular direction towards the Gravizentrum of the celestial body. Deviations occur (apart from gravity anomalies ) in that the centrifugal acceleration to gravity is acceleration at mid-latitudes at an oblique angle. Lines that follow the plumb line, perpendicular lines hot. They are the field lines of the gravity field. A body moving in a gravitational field, so softened with increasing speed from the direction of the effective acceleration of the plumb line. This can be interpreted as the effect of the Coriolis force.

Measurement

In addition to the direct measurement of the acceleration of a freely falling body, one can calculate the gravitational acceleration even from the period of vibration of a string pendulum. In addition, there are modern gravimeters, which utilize the principle of the spring scale advantage and achieve an extremely high precission.

A modern gravimeters can the acceleration of gravity with an accuracy of 0.01 μm/s2 = 0.001 mGal, about 10-9 g to measure. One could thus register a change in height of less than one centimeter. Fluctuations in air pressure cause changes in the same order.

Gravity potential

Since the gravitational force is a conservative force is the acceleration associated Feldstäre as the negative gradient of a potential:

Here is the gravitational potential. It consists - like the gravitational acceleration itself - from a gravitational and a Zentrifugalanteil together:

This is the first term the gravitational potential, the second term the potential of the centrifugal acceleration. The integral extends over the volume of the celestial body. is the density of the volume element and its distance from the start point (the location for which the potential is calculated).

Land on which the gravity potential is constant, hot surfaces or potential level surfaces of the gravity field. They are pierced at right angles from perpendicular lines. Be done during the transition from a level surface to a higher stroke work must, also see potential ( physics ).

Earth's gravity field

Large celestial bodies take under the influence of its gravity field in a form that corresponds to one of the level sets. In the gravitational field of the earth is that equipotential surface which the earth's surface at sea level roughly follows, referred to as the geoid. It is easily flattened by the centrifugal acceleration. Gravity anomalies, ie global, regional and local irregularities, since the mass is not evenly distributed ( in Earth's mantle and core), both in the earth's crust (mountains, continental plates ) as well as deeper, deform the geoid. The gravity anomalies affect the amount of gravity up to 0.01 %, and the plumb line is deflected by up to 0.01 ° from the direction of the center of the earth ( vertical deflection ). As a result, the geoid deviates vertically from up to 100 m from the central Erdellipsoid. Satellite geodesy determined the geoid using the observation of satellite orbits. In the immediate space around the Earth 's gravitational field is only approximately spherical because of gravity anomalies. The differences in magnitude and direction are in the parts per thousand range and influence near-Earth satellite orbits at a few miles or tenths of a degree, there can be variations in the Earth's gravity field of the order of 200 μm/s2 recognize; the latest gradiometry can also significantly smaller perturbations capture (see GRACE and GOCE ).

With the variations of gravity on the earth's surface, the gravity gradient and vertical gradient products take a closer look. Using normal gravity formulas the gravitational acceleration is estimated at a point near the earth's surface.

Earth's gravity on the Earth's surface

The value of the acceleration due to gravity varies due to the centrifugal force, Earth flattening and elevation profile regionally by a few parts per thousand to the approximate value ≈ 9.81 m/s2. The acceleration of gravity is 9.832 m / s ² at the poles and 9.745 m / s ² at the equator. The attraction at the pole is thus larger by about 0.5 % than at the equator, the weight of a man who is at the equator, 800 N, is therefore increased at the Earth's poles to 804.24 N. 2013 it was determined that the acceleration due to gravity with 9.7639 m/s2 on the Nevado Huascaran is the lowest.

Standard acceleration

In 1901, at the third General Conference of Weights and Measures, a default value, the standard acceleration, set to gn = 9.80665 m/s2, a value that had established itself in various state laws and the definition of technical units used (DIN 1305). Basis were ( from today's perspective overtook ) measurements of G. Defforges, Service de l' Armée Géographique, which were extrapolated to a value of 45 degrees latitude, altitude. Due to the later discovered gravity anomalies there is no single value on a Latitude. Accordingly, the standard acceleration of gravity acceleration of gravity is not defined as a specific place or as a kind of calculated average, but a definition.

German main Gravity Network 1996

In Germany the position-dependent acceleration of gravity in the German main Gravity Network 1996 is held ( DHSN 96), which is a continuation of the ( West German ) DHSN 82. It is next to the German main triangle mesh for the place and the German main level network for the height, the third size to clearly define a geodetic reference system. The German gravity network is based on approximately 16,000 measurement points, the severity of fixed points.

Historically significant was that of Bold and Furtwänger from Potsdam Geodetic Institute in 1906 certain value 9.81274 m/s2 in Potsdam. Potsdam in 1906, the fundamental point for determining the local acceleration due to gravity by means of differential determination until the International Gravity Standardization Net was introduced in 1971.

Earth's gravity inside the earth

Gravity curve is considered in the earth under the simplified assumption that the Earth is a homogeneous sphere. Then, a linear increase of the gravitational acceleration from zero at the center of the earth yields up to a maximum at the earth's surface; from that point follows the curve then the inverse square course.

At the center of the earth affects no gravity, and there's zero gravity. In the core of the earth is the gravitational acceleration increases monotonically with distance from the center of the earth. At the core - mantle boundary called ( in about 2900 km depth ), after their discoverers Emil Wiechert and Beno Gutenberg also Wiechert- Gutenberg discontinuity, it reaches a maximum of almost 10.68 m / s ². This effect has its cause in the fact that the predominantly metallic core of the Earth more than twice as dense as the mantle and the crust. From there up to 4900 km, it takes first again slowly up to 9.93 m / s ², rises again at 5700 km to 10.01 m / s ² and then decreases monotonically until at the surface about 9.82 m / s ² achieved.

Could you drill a tunnel through the earth, off friction losses and to counteract the influence of the Coriolis force and would be the density of the soil in each point equal to the mean density of the earth, would one into falling in this slot object in free fall in around 42 minutes to the fall through the other end. The movement of the object would be like a wave with a period length of 84 minutes and the so-called Schuler period.

Earth's gravitational field outside the earth

Near the earth's surface increases by about 3.1 g per μm/s2 from gestiegenem meters.

Outside the Earth, is the gravitational acceleration is proportional to the square of the distance from Earth's center. The Earth's gravity field is thus (like the gravitational field of each celestial body ) principle unlimited, but quickly decreases with increasing distance. In low satellite altitudes of 300 to 400 km, the acceleration due to gravity by 10 to 15 % decreases in 5000 km by about 70 %. Only in the vicinity of a major celestial body, the influence of other celestial bodies can be neglected in practice, because then it is very low - the influence of the nearby body is dominant.

Geopotential

The gravity potential of the earth is also called geopotential. The larger the local acceleration of gravity, the lower the distance between the Geopotentialflächen. The potential difference to the geoid

Is called geopotential. If the geopotential divided by the normal gravity, the result is the dynamic height ( geopotential meters unit, gpm). For mid-latitudes these dynamic heights approximately equal to the metric above sea level.

The geopotential is used in meteorology to describe the potential energy of the air at a certain height. Lines of equal potential energy is called contour lines (also called isopotential ), they are recorded on special weather maps. The Geopotentialtendenzgleichung allows prognostic statements about the geopotential field and is one of the main tools for creating computer models for weather forecasting.

Gravity and gravitational acceleration of selected celestial bodies

The table contains the gravitational, the centrifugal and the resulting gravitational acceleration of the eight planets of our solar system and the moon. The values ​​apply to the surface at the equator and are expressed in m/s2. The negative sign of the centrifugal acceleration to clarify that this acceleration of gravity is opposed.