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To present a set of trajectories derived from the retrograde periodic orbits around the Lagrangian equilibrium point L1, this paper considers the Circular Restricted Three-body Problem with Earth-Moon masses (CR3BP), the Restricted Bicircular, and Full Four-Body Sun-Earth-Moon-spacecraft Problems (BCR4BP and FR4BP, respectively). These periodic orbits are predicted by the dynamics of the CR3BP. To generate the trajectories of this set, first, slightly different increments of velocity (∆Vs) from those needed to generate periodic orbits around L1 are applied to a spacecraft in circular low Earth orbits in the same direction of their motion when the Earth, the spacecraft, and the Moon are aligned in this order. Thus, translunar trajectories derived from the periodic orbits are obtained and they will lead the spacecraft to the vicinity of the Moon. Depending on the values of the |∆Vs|, which are also functions of the relative positioning between the Sun, the Earth, and the Moon, three types of trajectories of interest are found: Collision with the Moon, escape, and geocentric orbits with large semi-major axes. For a well-defined interval of the |∆Vs|, the trajectories accomplish swing-bys with the Moon and obtain energy to escape from the Earth–Moon system and reach Near-Earth Asteroids (NEAs) between the orbits of Venus and Mars. This procedure reduces the costs of inserting spacecraft into transfer trajectories to a set of NEAs in terms of the required |∆V| by up to 5% when compared to Lambert's problem, for example. This work also presents analyses of examples of transfers to the NEAs 3361 Orpheus, 99942 Apophis, and 65803 Didymos, from 2025 on. [ABSTRACT FROM AUTHOR]

Context: Crude glycerin (CG) is an energetic byproduct that generates glycerol, an energy product that is absorbed by the ruminal wall and conducted to the liver, where it is metabolised and it is converted to glucose, by the action of the enzyme glycerol kinase, in a gluconeogenesis process. Aims: The study objective was to determine the effect of CG inclusion, replacing corn bran, in a total mixed ration to lambs, on carcass traits, physicochemical properties and the fatty acid (FA) profile of lamb meat. Methods: Forty-four uncastrated crossbred Santa Ines × indigenous lambs were distributed in a completely randomised study, with four CG inclusion levels (0, 70, 140 and 210 g/kg in the lamb diet). Key results: The addition of CG up to a level of 70 g/kg to the lamb diets promoted greater slaughter bodyweight, hot and cold carcass weight, carcass traits, and meat lipid content, and improved Warner–Bratzler shear force in meat. Inclusion of CG in the diet did not affect (P > 0.05) the pH and colour parameters (lightness, redness, yellowness and chroma) of meat. The FA composition of the longissimus lumborum of lambs C14:0, C15:1, C16:0, C18:1 cis and ΣFA medium-chain were greater, and FA meat concentration of C14:1, C15:0, C17:1, C18:0, C18:2 n −3, C18:2 n −6, ΣPUFA, ΣFA-old-chain and elongase enzymatic activity were lower in lambs fed without CG and with 70 g/kg CG, compared with lambs mainly fed 140 and 210 g/kg CG. The heath indexes, atherogenicity index and desirable FAs improved by dietary CG inclusion of 210 g/kg to the diet of lambs. Conclusions: CG obtained from biodiesel production can be incorporated in lamb diets up to 70 g/kg total mixed ration, replacing corn bran to improve the weight gain, meat lipid content, Warner–Bratzler shear force and FA profile of lamb meat. Meat fat-related consumers health indices improved from the biggest inclusions of CG to the diet of lambs However, the use of CG at levels 140 and 210 g/kg total mixed ration reduces the performance, carcass weight and morphometric measurements. Implications: It is recommended the inclusion at a maximum level of 70 g of CG/kg DM as total mixed ration replacing corn bran improves the weight gain, cooking weight loss, Warner–Bratzler shear force, meat lipid content and consequently FA meat composition. Crude glycerin is a byproduct of biodiesel production that can be used in the diets of ruminants to replace corn bran, because it has the potential to be a gluconeogenic and, therefore, energetic substrate. Enhancing the diet's energy density may improve the performance of animals, increasing the carcass fat content and thereby improving the physicochemical composition. Meat parameters, such as colour and shear force, generally represent the appearance, sensory traits and fatty acid profile of lamb meat. Other parameters can predict the meat acceptance by the consumer market. [ABSTRACT FROM AUTHOR]