On the spacing of meandering jets in the strong-stair limit

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic $\beta$ -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.

The functional relation between three-body mean motion resonances and Yarkovsky drift speeds

ABSTRACT We examined the motion of asteroids across the three-body mean motion resonances (MMRs) with Jupiter and Saturn and with the Yarkovsky drift speed in the semimajor axis of the asteroids. The research was conducted using numerical integrations performed using the Orbit9 integrator with 84 000 test asteroids. We calculated time delays, dtr, caused by the seven three-body MMRs on the mobility of test asteroids with 10 positive and 10 negative Yarkovsky drift speeds, which are reliable for Main Belt asteroids. Our final results considered only test asteroids that successfully crossed over the MMRs without close approaches to the planets. We have devised two equations that approximately describe the functional relation between the average time 〈dtr〉 spent in the resonance, the strength of the resonance SR, and the semimajor axis drift speed da/dt (positive and negative) with the orbital eccentricities of asteroids in the range (0, 0.1). Comparing the values of 〈dtr〉 obtained from the numerical integrations and from the derived functional relations, we analysed average values of 〈dtr〉 in all three-body MMRs for every da/dt. The main conclusion is that the analytical and numerical estimates of the average time 〈dtr〉 are in very good agreement, for both positive and negative da/dt. Finally, this study shows that the functional relation we obtain for three-body MMRs is analogous to that previously obtained for two-body MMRs.

Flip mechanism of Jupiter-crossing orbits in the non-hierarchical triple system

With the discovery of more and more retrograde minor bodies, retrograde orbits’ production mechanism has attracted much attention. However, almost all of the current research on the flip mechanism is based on the hierarchical approximation. In this paper, we study the flip mechanism of Jupiter-crossing orbits in a non-hierarchical Sun-Jupiter triple system. Numerical experiments summarize the characteristics of flipping orbits, and this provides essential guidance for the semi-analytical method. The i − Ω portraits of flipping particles are obtained and verified by numerical integrations. Based on the previous numerical experiments, 200,000 test particles in a particular range are generated and integrated over 1Myr. The flip region on the entire a − e parameter space is obtained. For each grid of the flip area, we plot the i − Ω portrait and measure the corresponding Jupiter’s flip ability. The gaps around the mean motion resonances (MMRs) in the flip region are also investigated. The MMRs protect the particles in these gaps from flips. Different resonant widths cause the differences in the size of these gaps. The flip mechanism is systematically studied in a planet-crossing system. The complete map of Jupiter’s flip ability in the entire flip region is depicted. Given the orbital parameters of the particle, we can assess whether the flip will occur in Jupiter’s presence. Our work can also apply to build the flip maps of other massive planets. And it may help understand the evolution of retrograde minor bodies.

Dynamical evolution of asteroid pairs in the vicinity of resonances

Dynamical evolution of asteroid pairs in close orbits near Jovian mean motion resonances (3 : 1, 4 : 1, 5 : 2, 7 : 3) has been researched by means of numerical integrations of the equations of motion over 1 Myr time interval in the future. Initial orbital elements’ uncertainty and semi-major axis drift due to the Yarkovsky effect significantly affect orbit modification with time, especially for objects originally situated in the vicinity of resonances. Passing through a resonance generally leads to orbital distance growth.

Anisotropy of long-period comets explained by their formation process

<p>Long-period comets coming from the Oort cloud are thought to be<span class="Apple-converted-space"> </span>planetesimals formed in the planetary region on the ecliptic plane.<span class="Apple-converted-space"> </span>We have investigated the orbital evolution of these bodies<span class="Apple-converted-space"> </span>due to the Galactic tide.<span class="Apple-converted-space"> </span>We extended Higuchi et al. (2007) and derived the<span class="Apple-converted-space"> </span>analytical solutions to the Galactic longitude and latitude of<span class="Apple-converted-space"> </span>the direction of aphelion, <em>L</em> and <em>B</em>.<span class="Apple-converted-space"> </span>Using the analytical solutions,<span class="Apple-converted-space"> </span>we show that the ratio of the periods of the evolution of <em>L</em> and <em>B</em> is very close to either 2 or ∞ for initial eccentricities <em>e</em><sub>i</sub>∼1,<span class="Apple-converted-space"> </span>as is true for the Oort cloud comets.<span class="Apple-converted-space"> </span>From the relation between <em>L</em> and <em>B</em>, we predict that Oort cloud comets returning to the planetary region concentrate on the ecliptic plane<span class="Apple-converted-space"> </span>and a second plane, which we call the "empty ecliptic".<span class="Apple-converted-space"> </span>This consists in a rotation of 180<sup>°</sup> of the ecliptic around the Galactic pole. Our numerical integrations confirm that the radial component of the Galactic tide, which is neglected in the derivation of the analytical solutions,<span class="Apple-converted-space"> </span>is not strong enough to break the relation between <em>L</em> and <em>B</em> derived analytically. Brief examination of observational data shows<span class="Apple-converted-space"> </span>that there are concentrations near both the ecliptic and the empty ecliptic. We also show that the anomalies of the distribution of <em>B</em> of long-period comets mentioned by several authors are explained by the concentrations on the two planes more consistently than the previous explanation.</p>

A pair of Jovian Trojans at the L4 Lagrange point

ABSTRACT Asteroid pairs, two objects that are not gravitationally bound to one another, but share a common origin, have been discovered in the Main belt and Hungaria populations. Such pairs are of major interest, as the study of their evolution under a variety of dynamical influences can indicate the time since the pair was created. To date, no asteroid pairs have been found in the Jovian Trojans, despite the presence of several binaries and collisional families in the population. The search for pairs in the Jovian Trojan population is of particular interest, given the importance of the Trojans as tracers of planetary migration during the Solar system’s youth. Here we report a discovery of the first pair, (258656) 2002 ES76 and 2013 CC41, in the Jovian Trojans. The two objects are approximately the same size and are located very close to the L4 Lagrange point. Using numerical integrations, we find that the pair is at least 360 Myr old, though its age could be as high as several Gyrs. The existence of the (258656) 2002 ES76–2013 CC41 pair implies there could be many such pairs scattered through the Trojan population. Our preferred formation mechanism for the newly discovered pair is through the dissociation of an ancient binary system, triggered by a sub-catastrophic impact, but we can not rule out rotation fission of a single object driven by YORP torques. A by-product of our work is an up-to-date catalogue of Jovian Trojan proper elements, which we have made available for further studies.

The functional relation between mean motion resonances and Yarkovsky force on small eccentricities

ABSTRACT This work examines asteroid’s motion with orbital eccentricity in the range (0.1, 0.2) across the two-body mean motion resonance (MMR) with Jupiter due to the Yarkovsky effect. We calculated time delays dtr caused by the resonance on the mobility of an asteroid with the Yarkovsky drift speed. Our final results considered only asteroids that successfully cross over the resonance without close encounters with planets. We found a functional relation that accurately describes dependence between the average time lead/lag 〈dtr〉, the strength of the resonance SR, and the semimajor axis drift speed da/dt with asteroids’ orbital eccentricities in the range (0.1, 0.2). We analysed average values of 〈dtr〉 using this functional relation comparing with obtained values of 〈dtr〉 from the numerical integrations, which were performed in an ORBIT9 integrator with a very large number of test asteroids. We checked the validity of our previous functional relation, derived for asteroids’ orbital eccentricities in the range (0, 0.1), on the present results for eccentricities in the range (0.1, 0.2). Also, we tried to find a unique functional relation for the whole interested interval of asteroids’ orbital eccentricities (0, 0.2) and discussed it.

Short-term stability of particles in the WD J0914+1914 white dwarf planetary system

ABSTRACT Nearly all known white dwarf planetary systems contain detectable rocky debris in the stellar photosphere. A glaring exception is the young and still evolving white dwarf WD J0914+1914, which instead harbours a giant planet and a disc of pure gas. The stability boundaries of this disc and the future prospects for this white dwarf to be polluted with rocks depend upon the mass and orbit of the planet, which are only weakly constrained. Here, we combine an ensemble of plausible planet orbits and masses to determine where observers should currently expect to find the outer boundary of the gas disc. We do so by performing a sweep of the entire plausible phase space with short-term numerical integrations. We also demonstrate that particle-star collisional trajectories, which would lead to the (unseen) signature of rocky metal pollution, occupy only a small fraction of the phase space, mostly limited to particle eccentricities above 0.75. Our analysis reveals that a highly inflated planet on a near-circular orbit is the type of planet which is most consistent with the current observations.

An Age and Space Structured SIR Model Describing the Covid-19 Pandemic

We present an epidemic model capable of describing key features of the present Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic reproduction number, the number of deaths due to the virus and various other statistics. Numerical integrations are used to illustrate the relevance of quarantine and the role of care houses.

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

At the second post-Newtonian (2PN) order, the secular pericenter precession ω ˙ 2 PN of either a full two-body system made of well-detached non-rotating monopole masses of comparable size and a restricted two-body system composed of a point particle orbiting a fixed central mass have been analytically computed so far with a variety of approaches. We offer our contribution by analytically computing ω ˙ 2 PN in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration A 2 PN , and also an indirect part arising from the self-interaction of the 1PN acceleration A 1 PN in the orbital average accounting for the instantaneous shifts induced by A 1 PN itself. Explicit formulas are straightforwardly obtained for both the point particle and full two-body cases without recurring to simplifying assumptions on the eccentricity e. Two different numerical integrations of the equations of motion confirm our analytical results for both the direct and indirect precessions. The values of the resulting effects for Mercury and some binary pulsars are confronted with the present-day level of experimental accuracies in measuring/constraining their pericenter precessions. The supermassive binary black hole in the BL Lac object OJ 287 is considered as well. A comparison with some of the results appeared in the literature is made.