The mature inflorescence of sunflowers (Helianthus annuus) orients eastward after its anthesis (the flowering period, especially the maturing of the stamens), from which point it no longer tracks the Sun. Although several hypothetical explanations have been proposed for the ecological functions of this east facing, none have been tested. Here we propose an atmospheric-optical explanation. Using (i) astronomical data of the celestial motion of the Sun, (ii) meteorological data of diurnal cloudiness for Boone County located in the region from which domesticated sunflowers originate, (iii) time-dependent elevation angle of mature sunflower heads, and (iv) absorption spectra of the inflorescence and the back of heads, we computed the light energy absorbed separately by the inflorescence and the back between anthesis and senescence. We found that the inflorescences facing east absorb the maximum radiation, being advantageous for seed production and maturation, furthermore west facing would be more advantageous than south facing. The reason for these is that afternoons are cloudier than mornings in the cultivation areas of sunflowers. Since the photosynthesizing green back of mature heads absorbs maximal energy when the inflorescence faces west, maximizing the energy absorbed by the back cannot explain the east facing of inflorescences. The same results were obtained for central Italy and Hungary, where mornings are also less cloudy than afternoons. In contrast, in south Sweden, where mornings are cloudier than afternoons, west-facing mature inflorescences would absorb the maximum light energy. We suggest that the domesticated Helianthus annuus developed an easterly final orientation of its mature inflorescence, because it evolved in a region with cloudier afternoons.

Space debris larger than 1 cm can damage space instruments and impact Earth. The low-Earth orbits (at heights smaller than 2,000 km) and orbits near the geostationary-Earth orbit (at 35,786 km height) are especially endangered because most satellites orbit at these latitudes. With current technology, space debris smaller than 10 cm cannot be tracked. Smaller space debris fragments burn up and evaporate in the atmosphere, but larger ones fall to Earth's surface.For practical reasons, it would be important to know the mass, composition, shape, velocity, direction of motion, and impact time of space debris re-entering the atmosphere and falling to Earth. Since it is very difficult to measure these physical parameters, almost nothing is known about them. To partly fill this gap, we performed computer modeling with which we studied the dynamics of spherical re-entry particles falling to Earth due to air drag. We determined the time, velocity, and angle of impact as functions of the launch height, direction, speed, and size of spherical re-entry particles. Our results can also be used for semispherical meteoroid particles of the interplanetary dust entering the Earth's atmosphere.

Since the discovery in 1772 of the triangular Lagrange points L4 and L5 in the gravitational field of two bodies moving under the sole influence of mutual gravitational forces, astronomers found a large number of minor celestial bodies around these points of the Sun-Jupiter, Sun-Earth, Sun-Mars and Sun-Neptune systems. The L4 and L5 points of the Earth and Moon may be empty due to the gravitational perturbation of the Sun. However, in 1961 Kordylewski found two bright patches near the L5 point, which may refer to an accumulation of interplanetary particles. Since that time this formation is called the Kordylewski dust cloud (KDC). Until now only a very few computer simulations studied the formation and characteristics of the KDC. To fill this gap, we investigated a three-dimensional four-body problem consisting of the Sun, Earth, Moon and one test particle, 1860000 times separately. We mapped the size and shape of the conglomeratum of particles not escaped from the system sooner than an integration time of 3650 days around L5. Polarimetric observations of a possible KDC around L5 are presented in the second part of this paper.

Telescopes mounted with polarizers can study the neutral points of the Earths atmosphere, the solar corona, the surface of planets/moons of the Solar System, distant stars, galaxies and nebulae. These examples demonstrate well that polarimetry is a useful technique to gather astronomical information from spatially extended phenomena. There are two enigmatic celestial objects that can also effectively be studied with imaging polarimetry, namely the Kordylewski dust clouds (KDCs) positioned around the L4 and L5 triangular Lagrangian libration points of the Earth-Moon system. Although in 1961 the Polish astronomer, Kazimierz Kordylewski had observed two bright patches near the L5 point with photography, many astronomers assume that these dust clouds do not exist, because the gravitational perturbation of the Sun, solar wind and other planets may disrupt the stabilizing effect of the L4 and L5 Lagrange points of the Earth and Moon. Using ground-born imaging polarimetry, we present here new observational evidence for the existence of the KDC around the L5 point of the Earth-Moon system. Excluding artefacts induced by the telescope, cirrus clouds or condensation trails of airplanes, the only explanation remains the polarized scattering of sunlight on the particles collected around the L5 point. By our polarimetric detection of the KDC we think it is appropriate to reconsider the pioneering photometric observation of Kordylewski. Our polarimetric evidence is supported by the results of simulation of dust cloud formation in the L5 point of the Earth-Moon system presented in the first part of this paper.

The escape dynamics around the triangular Lagrangian point L 5 in the real Sun-Earth-Moon-Spacecraft system is investigated. Appearance of the finite-time chaotic behavior suggests that widely used methods and concepts of dynamical system theory can be useful in constructing a desired mission design. Existing chaos control methods are modified in such a way that we are able to protect a test particle from escape. We introduce initial condition maps (ICMs) in order to have a suitable numerical method to describe the motion in high-dimensional phase space. Results show that the structure of ICMs can be split into two well-defined domains. One of these two parts has a regular contiguous shape and is responsible for long-time escape; it is a long-lived island. The other one shows a filamentary fractal structure in the ICMs. The short-time escape is governed by this object. This study focuses on a low-cost method that successfully transfers a reference trajectory between these two regions using an appropriate continuous control force. A comparison of the Earth-Moon transfer is also presented to show the efficiency of our method.