The Earth and its planetary characterization.

Diverse geometrical models of the Earth were proposed: sphere, spheroid and geoid.

Sphere. It is a specific geometric shape whose surface is everywhere at the same distance from its centre. Sphere is a simple and the most perfect shape from the viewpoint of symmetry. To accept this shape to be the gravitationally stable we need to consider it without the rotation, i.e. assume its isomery, equality of measure, to be invariable. If accept the rotation of this sphere we need postulate it as absolute solid body, so that the centrifugal forces originated by the rotation cannot disturb its shape and internal structure.

According to the modern estimations the radius of this sphere is 6371.116 km and the density is 5.52 g/cm³.

Spheroid. It is a solid geometrical figure generated by rotating an ellipse about its small axis. So spheroid or ellipsoid of rotation, that is the same, has two radii: polar radius R_p and equatorial radius R_e.

In 1946 in ussr the ellipsoid of Krasovsky was accepted as standard. Its parameters are follows:

R_p = 6356.863 km; R_e = 6378.245 km;

polar compression α = (R_e – R_p)/R_e = 1/298.3

Calculated on the base of these parameters the area of the spheroid surface and its volume are equal to 5.1008·10⁸ km² and 1.0833·10¹² km³ correspondingly.

Geoid. This model is used often enough for the description of the Earth surface. However in reality the geoid is not material surface. It is an imaginary surface that coincides with the mean sea level in the ocean and its extension through the continents. Geoid is one of the equipotential surfaces of the gravitational field of the Earth, i.e. the surface where the potential energy of the gravitational field is constant.

The small bodies of the Solar System.

Now we can speak a little about the other bodies of Solar system: asteroids, comets,

and meteoroids.

Asteroid. Asteroid is treated as minor planet. Asteroid is any of the many small rocky or metallic objects in the Solar System. The largest amount of asteroids is situated at 2.3-3.3 AU distance from the Sun forming so-called asteroid belt between the orbits of Mars and Jupiter. Being the result of collisions the uninterrupted processes of breaking, crushing or generally speaking of fragmentation take place in the asteroid belt. The asteroids differ from each other to a considerable degree by mass, shape and composition. Most of asteroid have an irregular shape and only largest bodies are spherical. The largest asteroids Ceres, Pallas, Juno and Vesta have the radius 476, 255, 117 and 265 km correspondingly.

Comets. These are celestial bodies in orbits usually with high eccentricity around the Sun. Comets consist of a central nucleus, so-called head, surrounded by a misty envelope, that may form one or more luminous tails turned away from the Sun. Although a comet may be the brightest object in the night sky, most observed comets are extremely distant objects which may be determined only with the aid of telescopes. Their origin, composition and structure were not definitively determined till now, there are only hypotheses and diverse conceptions.

The period of their revolution round the Sun is very different. For example, for Halley's comet this time is 75-76 years). Nevertheless some comets have periods of revolution equal to several million years. For to-day about 700 comets have been registered. Every year about 5 new comets are registered.

Some astrophysicists assume that the nuclei of comets are constituted with ice (75%) and dust together with stony material (25%). The ice forms the central part of the nucleous and the dust with stony material its external layer. Coming up to the Sun on a distance 3 AU (about 450 million km) the comet begins to be heated that initiates the sublimation of undersurface ice.