Currently, a surge in the number of spacecraft and fragments is observed, leading to more frequent breakup events in low Earth orbits (LEOs). The causes of these events are being identified, and specific triggers, such as collisions or explosions, are being examined for their importance to space traffic management. Backward propagation methods were employed to trace the origins of these types of breakup events. Simulations were conducted using the NASA standard breakup model, and satellite Hitomi’s breakup was analyzed. Kullback–Leibler (KL) divergences, Euclidean 2-norms, and Jensen–Shannon (JS) divergences were computed to deduce potential types of breakups and the associated fragmentation masses. In the simulated case, a discrepancy of 22.12 s between the estimated and actual time was noted. Additionally, the breakup of the Hitomi satellite was estimated to have occurred around UTC 1:49:26.4 on March 26, 2016. This contrasts with the epoch provided by the Joint Space Operation Center, which was estimated to be at 1:42 UTC ± 11 min. From the findings, it was suggested that the techniques introduced in the study can be effectively used to trace the origins of short-term breakup events and to deduce the types of collisions and fragmentation masses under certain conditions.

The increasing frequency of human launches has led to a dramatic increase in the amount of space debris, especially near sun-synchronous orbits. Most of the fragments are small in size, which may make tracking difficult. Therefore, characterizing the distribution, evolution, and collision risk of small debris has long been a difficult issue. This paper is aimed at investigating the orbital evolution and global dispersion behavior of debris clouds near sun-synchronous orbits. Firstly, the NASA breakup model is used to provide an initial distribution of small fragments after collision events. Secondly, the continuity equation is adopted to propagate the density variation analytically. Furthermore, we introduce some statistical quantities and the entropy of debris clouds to model the randomness and band formation. A theorem concerning the equivalence of the band formation and maximal entropy is presented. The accuracy of the band formation time estimation is also discussed. For noncatastrophic collisions at an altitude of 800 km due to a projectile with a mass of 100 g and a collision velocity of 1 km/s, we compare the analytical and numerical results of space debris density. The results show that the maximal peak error is within 0.17, and the mean square error is about 0.25 at 400 days. Additionally, the entropy of right ascension of the ascending node is 8.5% less than that for debris clouds near an orbit with the same altitude and an inclination of 30 deg. This indicates the concentrating behavior for debris clouds near sun-synchronous orbits.

We investigate the equilibrium points and orbits around asteroid 1333 Cevenola by considering the full gravitational potential caused by the 3D irregular shape. The gravitational potential and effective potential of asteroid 1333 Cevenola are calculated. The zero-velocity curves for a massless particle orbiting in the gravitational environment have been discussed. The linearized dynamic equation, the characteristic equation, and the conserved quantity of the equilibria for the large-size-ratio binary asteroid system have been derived. It is found that there are totally five equilibrium points close to 1333 Cevenola. The topological cases of the outside equilibrium points have a staggered distribution. The simulation of orbits in the full gravitational potential caused by the 3D irregular shape of 1333 Cevenola shows that the moonlet’s orbit is more likely to be stable if the orbit inclination is small.

We are interested in stable periodic orbits for spacecraft in the gravitational field of minor celestial bodies. The stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space exploration, but also for studying the long-time stability of small satellites in the large-size-ratio binary asteroids. The irregular shapes and gravitational fields of the minor celestial bodies are modeled by the polyhedral model. Using the topological classifications of periodic orbits and the grid search method, the stable periodic orbits can be calculated and the topological cases can be determined. Furthermore, we find five different types of stable periodic orbits around minor celestial bodies: (1) stable periodic orbits generated from the stable equilibrium points outside the minor celestial body; (2) stable periodic orbits continued from the unstable periodic orbits around the unstable equilibrium points; (3) retrograde and nearly circular periodic orbits with zero-inclination around minor celestial bodies; (4) resonance periodic orbits; (5) near-surface inclined periodic orbits. We take asteroids 243 Ida, 433 Eros, 6489 Golevka, 101955 Bennu, and the comet 1P/Halley for examples.