Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube

This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be considered as an extension of previous research work on the dynamics of orbits around simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates with backgrounds in celestial mechanics. In the synodic reference frame, the model of a rotating cube is established, the equilibria are calculated, and their linear stabilities are determined. Periodic orbits around the equilibria are computed using the traditional differential correction method, and their stabilities are determined by the eigenvalues of the monodromy matrix. The existence of homoclinic and heteroclinic orbits connecting periodic orbits around the equilibria is examined and proved numerically in order to understand the global orbit structure of the system. This study contributes to the investigation of irregular shaped celestial bodies that can be divided into a set of cubes.Comment: 29 pages, 16 figures, accepted for publication in Astrophysics & Space Scienc

Dust Devil Tracks

Dust devils that leave dark- or light-toned tracks are common on Mars and they can also be found on the Earth’s surface. Dust devil tracks (hereinafter DDTs) are ephemeral surface features with mostly sub-annual lifetimes. Regarding their size, DDT widths can range between ∼1 m and ∼1 km, depending on the diameter of dust devil that created the track, and DDT lengths range from a few tens of meters to several kilometers, limited by the duration and horizontal ground speed of dust devils. DDTs can be classified into three main types based on their morphology and albedo in contrast to their surroundings; all are found on both planets: (a) dark continuous DDTs, (b) dark cycloidal DDTs, and (c) bright DDTs. Dark continuous DDTs are the most common type on Mars. They are characterized by their relatively homogenous and continuous low albedo surface tracks. Based on terrestrial and martian in situ studies, these DDTs most likely form when surficial dust layers are removed to expose larger-grained substrate material (coarse sands of ≥500 μm in diameter). The exposure of larger-grained materials changes the photometric properties of the surface; hence leading to lower albedo tracks because grain size is photometrically inversely proportional to the surface reflectance. However, although not observed so far, compositional differences (i.e., color differences) might also lead to albedo contrasts when dust is removed to expose substrate materials with mineralogical differences. For dark continuous DDTs, albedo drop measurements are around 2.5 % in the wavelength range of 550–850 nm on Mars and around 0.5 % in the wavelength range from 300–1100 nm on Earth. The removal of an equivalent layer thickness around 1 μm is sufficient for the formation of visible dark continuous DDTs on Mars and Earth. The next type of DDTs, dark cycloidal DDTs, are characterized by their low albedo pattern of overlapping scallops. Terrestrial in situ studies imply that they are formed when sand-sized material that is eroded from the outer vortex area of a dust devil is redeposited in annular patterns in the central vortex region. This type of DDT can also be found in on Mars in orbital image data, and although in situ studies are lacking, terrestrial analog studies, laboratory work, and numerical modeling suggest they have the same formation mechanism as those on Earth. Finally, bright DDTs are characterized by their continuous track pattern and high albedo compared to their undisturbed surroundings. They are found on both planets, but to date they have only been analyzed in situ on Earth. Here, the destruction of aggregates of dust, silt and sand by dust devils leads to smooth surfaces in contrast to the undisturbed rough surfaces surrounding the track. The resulting change in photometric properties occurs because the smoother surfaces have a higher reflectance compared to the surrounding rough surface, leading to bright DDTs. On Mars, the destruction of surficial dust-aggregates may also lead to bright DDTs. However, higher reflective surfaces may be produced by other formation mechanisms, such as dust compaction by passing dust devils, as this may also cause changes in photometric properties. On Mars, DDTs in general are found at all elevations and on a global scale, except on the permanent polar caps. DDT maximum areal densities occur during spring and summer in both hemispheres produced by an increase in dust devil activity caused by maximum insolation. Regionally, dust devil densities vary spatially likely controlled by changes in dust cover thicknesses and substrate materials. This variability makes it difficult to infer dust devil activity from DDT frequencies. Furthermore, only a fraction of dust devils leave tracks. However, DDTs can be used as proxies for dust devil lifetimes and wind directions and speeds, and they can also be used to predict lander or rover solar panel clearing events. Overall, the high DDT frequency in many areas on Mars leads to drastic albedo changes that affect large-scale weather patterns

Periodic orbits in the gravity field of a fixed homogeneous cube

In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different types of symmetry planes of the fixed cube, periodic orbits are obtained using the method of the Poincar\'e surface of section. While in general positions, periodic orbits are found by the homotopy method. The results show that periodic orbits exist extensively in symmetry planes of the fixed cube, and also exist near asymmetry planes that contain the regular Hex cross section. The stability of these periodic orbits is determined on the basis of the eigenvalues of the monodromy matrix. This paper proves that the homotopy method is effective to find periodic orbits in the gravity field of the cube, which provides a new thought of searching for periodic orbits around non-spherical celestial bodies. The investigation of orbits around the cube could be considered as the first step of the complicated cases, and helps to understand the dynamics of orbits around bodies with complicated shapes. The work is an extension of the previous research work about the dynamics of orbits around some simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates.Comment: 23 pages, 10 figures, accepted for publication in Astrophysics & Space Scienc