On the orbital evolution of 2020 AV2, the first asteroid ever observed to go around the Sun inside the orbit of Venus

ABSTRACT The innermost section of the Solar system has not been extensively studied because minor bodies moving inside Earth’s orbit tend to spend most of their sidereal orbital periods at very low solar elongation, well away from the areas more frequently observed by programs searching for near-Earth objects. The survey carried out from the Zwicky Transient Facility (ZTF) is the first one that has been able to detect multiple asteroids well detached from the direct gravitational perturbation of the Earth–Moon system. ZTF discoveries include 2019 AQ3 and 2019 LF6, two Atiras with the shortest periods among known asteroids. Here, we perform an assessment of the orbital evolution of 2020 AV2, an Atira found by ZTF with a similarly short period but following a path contained entirely within the orbit of Venus. This property makes it the first known member of the elusive Vatira population. Genuine Vatiras, those long-term dynamically stable, are thought to be subjected to the so-called von Zeipel–Lidov–Kozai oscillation that protects them against close encounters with both Mercury and Venus. However, 2020 AV2 appears to be a former Atira that entered the Vatira orbital domain relatively recently. It displays an anticoupled oscillation of the values of eccentricity and inclination, but the value of the argument of perihelion may circulate. Simulations show that 2020 AV2 might reach a 3:2 resonant orbit with Venus in the future, activating the von Zeipel–Lidov–Kozai mechanism, which in turn opens the possibility to the existence of a long-term stable population of Vatiras trapped in this configuration.

The role of resonances in the evolution of galactic disks

Resonances play an important role in the evolution of the disks of spiral galaxies, and in particular in the chemical abundance evolution. The dominant effect is that of corotation; this effect can be even used as a tool to estimate the age of the present spiral arm pattern, which are usually found to be long-lived, contrary to a recent common belief. We investigated a sample of galaxies for which the corotation radius is known and for which there are available in the literature measurements of abundance gradients for Oxygen. A very good correlation is found between corotation radii and the radii at which there is a break in the slope of the gradients. The gradients are usually decreasing in the inner regions and become flat or rising at larger radii. In several galaxies, including the Milky Way, one observes not only a change in the slope of the abundance gradient, but also an abrupt step in metallicity, at corotation. This step is due to the fact that corotation separates the disk of a galaxy in two regions (inside corotation and outside corotation) which are isolated one from the other, so that the two sides evolve in an independent way. The barrier between the two regions is produced by the flow of gas in opposite directions in the two sides and by the ring-shaped void of gas observed at corotation. Besides this, an independent effect of corotation is a minimum of star formation associated with the minimum velocity at which the spiral arms (seen as potential wells) are fed with interstellar gas. Still another effect is the scattering of stars by the resonance, which causes their migration to different galactic radii. Other resonances, like 4:1, have properties almost opposite to corotation; they stimulate star-formation, and tend to gather the stars in the resonant orbit, instead of scattering them out, as shown by numerical simulations. Due to this property, one can see arms which have the shape of resonant stellar orbits, which depart from logarithmic spirals.

Basin Boundary Bifurcations and Boundary Crisis in the Twin-Well Duffing Oscillator: Scenarios Related to the Saddle of the Large Resonant Orbit

Bifurcation phenomena in the twin-well Duffing system are considered for such regions of the system parameters, where the saddle DL associated with the two-well T-periodic attractor (large orbit) undergoes homoclinic bifurcation. In particular, a co-dimension-two bifurcation, the bifurcation defined by the intersection of the homoclinic bifurcation of the large orbit with the saddle-node bifurcation of the nonresonant single-well orbit in the system parameter plane is the main point of interest. In the four subdomains around the co-dimension-two point, the manifold structure of the saddle DL and the basins of attractions are studied numerically. The analysis reveals new phenomena and new features of the system behavior. A complex bifurcational structure is observed that includes boundary crisis of the cross-well chaotic attractor, intermittency (subduction) phenomena, and explosion of the basin of attraction of the large orbit. The analysis also explains why, in one of the subdomains, the two-well T-periodic attractor (large orbit) becomes the unique attractor of the system.

Lumped harmonics of 15th and 30th order in the geopotential, from the resonant orbit of the satellite 1971–54A

The satellite 1971–54A entered a near-circular orbit with period 95.9 min and inclination 90.2°. Between 1972 and 1978 the orbit passed slowly through 15th-order resonance, when the track over the Earth repeats after 15 revolutions, and the 15th- and 30th-order harmonics in the geopotential may produce substantial orbital perturbations. The values of orbital inclination and eccentricity from 269 weekly U. S. Navy orbits between November 1972 and January 1978 have been ana­lysed to determine 12 lumped harmonic coefficients of order 15 and 30. The analysis of inclination yields 15th-order coefficients accurate to 1.5 and 2.8%, and 30th-order coefficients accurate to 7 %. The analysis of eccentricity gives two 15th-order coefficients accurate to 3 and 4 %. These lumped harmonic coefficients are used to test the accuracy of the Goddard Earth Model 10B, which is complete to order and degree 36. The agreement with GEM 10B is excellent, for both 15th and 30th order, and shows that GEM 10B is more accurate than was expected. The 12 values of lumped harmonics obtained give 12 linear equations between individual coefficients of order 15 and 30, which will be used in a future solution for the individual coefficients.