Gravitational constant

The gravitational constant is that constant of nature that links the mass with gravity. It was introduced by Isaac Newton in the framework of his theory of gravitation and is now fully in the general theory of relativity application. For the description of astronomical sizes and operations it has equally fundamental meaning as for the geosciences. Are common or as symbols. The value of the gravitational constant is:

Definition

After the Newtonian law of gravitation, two spherically symmetric bodies attract with the masses and whose centers are at a distance, each with the power

Of. The proportionality constant occurring in the equation is the gravitational constant.

Value and units

In the International System of Units ( SI) is the value after the current recommendation CODATA 2010:

(ie, with an estimated standard deviation of 0.000 80 × 10-11 )

In the CGS system of units has the value:

The gravitational constant can also be expressed with other constants of nature, for example by means of the reduced Planck's constant and the speed of light ( "natural units"). After CODATA 2010 resulting value:

Compared with other fundamental forces of physics, gravity is a very weak interaction, which is reflected in the small value of the gravitational constant. If one calculates, for example, the relationship between the gravitational force and the electrostatic force between two protons, we obtain:

Accuracy

Under all natural constants is currently the one with the largest relative measurement uncertainty. Reason is the very low strength of the gravitational force between two masses in the laboratory. Even with carefully designed and shielded against interference apparatus has not yet been pressed under 1.2 × 10 -4 of the uncertainty range. By comparison, the Planck constant is known with a relative uncertainty of 1.7 × 10 -7.

Much more accurate, for a celestial body that is orbited by a companion, the so-called gravitational parameters are determined when the orbital radius and circulation angular frequency corresponding exactly known ( for the earth up to 10 digits, see WGS 84). It is up to train third-body perturbations, the equation (see Kepler's laws ). Despite the inaccuracy, is acquainted with the the mass of the celestial body can result from this much more accurate than they can appreciate from its diameter and the density gradient.

Gravity scale

In 1798, Henry Cavendish was measured in a laboratory experiment with a scale gravitational force acting between known masses. The measuring system consisted of two large spheres together = 316 kg and two on a torsion wire rotatably suspended balls together with = 1.46 kg. It has been determined, the power that is required at a distance, so that the gravity force of the ball could not move further together. The necessary torsional stiffness of the wire he determined from the period of the torsional vibration. In addition, he determined the weight of its test mass, so the gravitational force with which the test mass is attracted by the Earth's mass.

Then he sat according to Newton's law of gravitation, the value of its measurement in relation to the corresponding values ​​and the Earth:

This relationship used Henry Cavendish, to determine the density of earth. From his experimental description is not clear whether he has determined the value of the gravitational constant. From his readings, however, a value of the constant can be calculated:

It was only after the value of the gravitational constant was known, the masses of other celestial bodies could be determined.