The development of a Russian communication satellite of small class, operating in the geostationary and high-elliptical orbits

In 1994-1995 Lavochkin Association (Russia) together with the other enterprises in accordance with technical requirements of the Russian Space agency, developed a new Russian communication satellite of a small class that will operate in both the geostationary (GSO) and high-elliptical (HEO) orbits. This satellite may be injected into operational orbits using a SOYUZ-2 launch vehicle (LV) and a FREGAT upper stage (US) from Plesetsk and Baykonur space launch sites (SLS).The main reason for creating such a satellite was to decrease the cost of the support and development of the Russian communication geostationary satellites group.Russian satellites Horizont, Express, Ekran and Gals, which operate in GSO, are the basis of the space segment for communications, radio and TV broadcasting. All of these satellites are injected into GSO by the PROTON LV. PROTON is a launch vehicle of a heavy class. The use of a middle class LV instead of a heavy class will allow to reduce considerably the launch cost. The change of a heavy class LV to a LV of middle class determined one economic reason for this project. Besides, the opportunity to launch S/C into GSO from Russian Plesetsk SLS increases the independence of Russia in the domain of space communications, despite the presence of the contract with Kazachstan about the rent of Baykonur SLS. Finally, use of small satellites with a rather small number of transponders is more effective than the use of big satellites. It will allow also to increase a satellite group (by the launch of additional satellites) precisely in accordance to the development of the ground segment.     

State propagation in an uncertain asteroid gravity field

Various spacecraft have been and will be sent to asteroids to characterize them. Generally, an asteroid's gravity field is very irregular and not accurately known when compared to the gravity field of a major planet, Earth in particular. It has been well studied that the irregularity significantly affects the trajectory of an orbiting spacecraft, and causes it to impact or to escape from the asteroid. Complementary to that, this paper focuses on the influence of the limited knowledge of this gravity field on the evolution of the spacecraft's orbit. It develops a general method by which this influence can be quantified. This method comprises specific Monte Carlo simulations with a discrete set of low-altitude orbits, taking into account the uncertainties in the gravity-field parameters. For illustration purposes, it is applied to two different asteroids. Already after three revolutions, the gravity-field uncertainties propagate to significant position uncertainties; this specifically holds for prograde orbits, and around the smaller asteroid. Applying this robust and accurate method helps mission designers and planners to assess the risk posed by gravity uncertainties, and take appropriate measures such as choosing the most favorable orbital geometries and/or lowering the orbit more slowly.     

Earth and Mars observation using periodic orbits

This paper reports the results of a general study carried out on the Periodic Multi-SunSynchronous Orbits (PMSSOs), which the classical Periodic SunSynchronous Orbits (PSSOs) represent a specific solution of. Such orbits allow to obtain cycles of observation of the same region in which the solar illumination regularly varies according to the value of the orbit elements and comes back to the initial condition after a time interval which is multiple of the revisit time. Therefore this kind of orbits meets all the remote sensing applications that need observations of the same area at different local times (for example the reconstruction of the day-nighttime trend of the surface temperature of the planet) and it is particularly suitable to the study of several terrestrial and martian phenomena (diurnal cycle of the hazes and clouds, dynamics of the thermal tides, density variations, meteorology phenomena, etc.). The design of PMSSO is based on the variation of the Right Ascension of the Ascending Node due to the Earth oblateness (referred as basic solution). However, with respect to the basic solution, the analysis of the perturbative effects has demonstrated the need, especially in the case of Mars, to take into account all the superior harmonics of the gravitational field. To this end a corrective factor, to add to the basic equations, has been proposed, allowing a significant saving of propellant (of the order of 2 km/s per year). Besides, single and multi-plane satellite constellations have been taken into account in order to improve the repetition of observation and the ground spatial resolution.     

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

Orbit determination for the GOCE satellite

Precise Orbit Determination (POD) for the Gravity field and steady-state Ocean Circulation Explorer (GOCE), the first core explorer mission by the European Space Agency (ESA), forms an integrated part of the so-called High-Level Processing Facility (HPF). Two POD chains have been set up referred to as quick-look Rapid and Precise Science Orbit determination or RSO and PSO, respectively. These chains make use of different software systems and have latencies of 1 day and 2 weeks, respectively, after tracking data availability. The RSO and PSO solutions have to meet a 3-dimensional (3D) position precision requirement of 50 cm and a few cm, respectively. The tracking data will be collected by the new Lagrange GPS receiver and the predicted characteristics of this receiver have been taken into account during the implementation phase of the two chains.     

Relative motion guidance for near-rectilinear lunar orbits with path constraints via actor-critic reinforcement learning

This paper presents a feedback guidance algorithm for proximity operation in cislunar environment based on actor-critic reinforcement learning. The algorithm is lightweight, closed-loop, and capable of taking path constraints into account. The method relies on reinforcement learning to make the well known Zero-Effort-Miss/Zero-Effort-Velocity guidance state dependent and allow for path constraints to be directly embedded. The algorithm is tested in the circular restricted three-body problem (CRTBP) framework for Near Rectilinear Orbits (NRO) in the Earth-Moon system. It shows promising results in terminal guidance error and satisfies path constraints in constraint scenarios comprising spherical constraints and keep-out-spheres with approach corridors. Furthermore, this approach indicates that reinforcement learning can be effectively used to solve constrained relative spacecraft guidance problems in complex environments and thus can be effective for autonomous relative motion operations in the Earth-Moon dynamical environment.     

Mapping orbits with low station keeping costs for constellations of satellites based on the integral over the time of the perturbing forces

The present paper is concerned with the search for orbits that have potential to require low fuel consumption for station-keeping maneuvers for constellations of satellites. The method used to study this problem is based on the integral over the time of the undesired perturbing forces. This integral measures the change of velocity caused by the perturbation forces acting on the satellite, so mapping orbits that are less perturbed, which generates good candidates for orbits that requires low fuel consumption for station-keeping maneuvers. The integral over the time depends only on the orbit of the spacecraft and the dynamical system considered. The type of engine and the control technique applied to the spacecraft are not considered to search for those orbits. It can be a good strategy to be applied for a first mapping of orbits. For this search, it is analyzed the integral of orbits with different values of the Keplerian elements in order to find the best ones with respect to this criterion. The perturbations considered are the ones caused by the third body, which includes the Sun and the Moon, and the J₂ term of the geopotential. The results presented here show numerical simulations to obtain the integral of those perturbing forces for different orbits. The GPS and the Molniya constellations are used as examples for those calculations.     

Intracellular molecular distributions in spacecraft experiments in orbit around Earth

It is possible that the nucleolous inside the cell plays the role of a “gravity receptor”. Furthermore, cells up to 10 μm in diameter can demonstrate some effect due to the redistribution of mitochondria or nucleolous. Effects of gravity should be present in various cell systems where larger objects such as the ribosomes move from cell to cell. In this paper we study the effects of gravity on cells. In particular, we examine the resulting intracellular molecular distribution due to Brownian motion and the ordered distribution of molecules under the action of gravity, where n₀ is the number per unit volume at certain level, and n is the number per unit volume above that level. This is an experiment that takes place at a certain orbital altitude in a spacecraft in orbit around Earth, where the acceleration due to the central field is corrected for the oblateness and also the rotation of the Earth. We found that equatorial circular and elliptical orbits have the highest n/n₀ ratios. This experiment takes place in circular and elliptical orbits, with eccentricities e = 0, 0.1 and involves a bacterial cell at an orbital altitude of 300 km. We found that n/n₀ = 1.00299 and 1.0037 respectively, which is still a 0.6–0.7 % higher than n/n₀ = 0.0996685 calculated on the surface of the Earth. Examining mitochondria in similar orbital experiments we found that equatorial orbits result to higher n/n₀ ratios. In particular, we found that n/n₀ = 8.38119, where an elliptical orbit of eccentricity e = 0.1 results to n/n₀ = 13.8525. Both are high above 100%, signifying the importance of Brownian motion over gravity. Our results are of interest to biomedical applications. Molecular concentrations are important for various processes such as the embryogenesis, positional homeostasis and its relation to cell energy expenditure, cell torque, cell deformation, and more. These results indicate that statistical molecular distributions play an important role for the recognition of a particular environment by the cell, in biological space experiment to come.     

Analytical long-term evolution and perturbation compensation models for BeiDou MEO satellites

The current paper establishes the analytical models of the long-term evolution and perturbation compensation strategy for Medium Earth Orbits(MEO)shallow-resonant navigation constellation,with application to the Chinese Bei Dou Navigation Satellite System(BDS).The long-term perturbation model for the relative motion is developed based on the Hamiltonian model,and the long-term evolution law is analyzed.The relationship between the control boundary of the constellation and the offset of the orbital elements is analyzed,and a general analytical method for calculating the offset of the orbit elements is proposed.The analytical model is further improved when the luni-solar perturbations are included.The long-term evolutions of the BDS MEO constellation within 10 years are illustrated,and the effectiveness of the proposed analytical perturbation compensation calculation approach is compared with the traditional numerical results.We found the fundamental reason for the nonlinear variations of the relative longitude of ascending node and the mean argument of latitude is the long-periodic variations of the orbital inclination due to the luni-solar perturbations.The proposed analytical approach can avoid the numerical iterations,and reveal the essential relationship between the orbital element offsets and the secular drifts of the constellation configuration.Moreover,there is no need for maintaining the BDS MEO constellation within 10 years while using the perturbation compensation method.