scholarly journals Launch Vehicle Rendezvous to Catalogued Orbital Debris while Injecting into Highly-Inclined Orbits

2020 ◽  
Vol 16 (6) ◽  
pp. 46-55
Author(s):  
A.V. Golubek ◽  
◽  
N.M. Dron' ◽  
Keyword(s):  
Mathematical Model ◽  
Space Debris ◽  
Least Squares Method ◽  
Statistical Processing ◽  
Launch Vehicle ◽  
Orbital Debris ◽  
Relative Distance ◽  
Statistical Characteristics ◽  
Near Earth Space ◽  
The Impact

Introduction. A constant increase in the amount of space debris already constitutes a significant threat to satellites in nearEarth orbits, starting with the trajectory of their launch vehicle injection. Problem Statement. Design and development of various modern methods of protection against space debris requires knowledge of the statistical characteristics of the distribution of the kinematic parameters of the simultaneous motion of a launch vehicle injecting satellite and a group of space debris objects in the area of its trajectory. Purpose. Development of a mathematical model of a launch vehicle rendezvous with a group of observable orbital debris while injecting a satellite into near-earth orbits with an altitude of up to 2100 km and an inclination from 45 to 90 degrees. Materials and Methods. The following methods are used in the research: analysis, synthesis, comparison, simulation modeling, statistical processing of experimental results, approximation, correlation analysis, and the least squares method. Results. The simultaneous motion of a launch vehicle and a group of space debris objects has been studied. The distributions of relative distance, relative velocity, angle of encounter, and moments of time of approach of a launch vehicle to a group of the observed space debris at a relative distance of less than 5 km have been obtained. The dependence of the average rendezvous concentration on the distribution of space debris across the average altitude of the orbit and the inclination of the target orbit of the launch vehicle has been determined. The dependence of the average probability of rendezvous in the launch on the inclination of the target orbit, the number of orbital debris, and the relative distance of the rendezvous has been determined. Conclusions. The obtained mathematical model of rendezvous of a launch vehicle with a group of observed orbital debris can be used while designing means of cleaning the near-Earth space and systems to protect modern satellite launch vehicles from orbital debris. In addition, the results of the research can be used to assess the impact of unobserved orbital debris on the flight of a launch vehicle.

scholarly journals Launch Vehicle Rendezvous to Catalogued Orbital Debris while Injecting into Highly-Inclined Orbits

2020 ◽  
Vol 16 (6) ◽  
pp. 46-55
Author(s):  
A.V. Golubek ◽  
◽  
N.M. Dron' ◽  
Keyword(s):  
Mathematical Model ◽  
Space Debris ◽  
Least Squares Method ◽  
Statistical Processing ◽  
Launch Vehicle ◽  
Orbital Debris ◽  
Relative Distance ◽  
Statistical Characteristics ◽  
Near Earth Space ◽  
The Impact

Introduction. A constant increase in the amount of space debris already constitutes a significant threat to satellites in nearEarth orbits, starting with the trajectory of their launch vehicle injection. Problem Statement. Design and development of various modern methods of protection against space debris requires knowledge of the statistical characteristics of the distribution of the kinematic parameters of the simultaneous motion of a launch vehicle injecting satellite and a group of space debris objects in the area of its trajectory. Purpose. Development of a mathematical model of a launch vehicle rendezvous with a group of observable orbital debris while injecting a satellite into near-earth orbits with an altitude of up to 2100 km and an inclination from 45 to 90 degrees. Materials and Methods. The following methods are used in the research: analysis, synthesis, comparison, simulation modeling, statistical processing of experimental results, approximation, correlation analysis, and the least squares method. Results. The simultaneous motion of a launch vehicle and a group of space debris objects has been studied. The distributions of relative distance, relative velocity, angle of encounter, and moments of time of approach of a launch vehicle to a group of the observed space debris at a relative distance of less than 5 km have been obtained. The dependence of the average rendezvous concentration on the distribution of space debris across the average altitude of the orbit and the inclination of the target orbit of the launch vehicle has been determined. The dependence of the average probability of rendezvous in the launch on the inclination of the target orbit, the number of orbital debris, and the relative distance of the rendezvous has been determined. Conclusions. The obtained mathematical model of rendezvous of a launch vehicle with a group of observed orbital debris can be used while designing means of cleaning the near-Earth space and systems to protect modern satellite launch vehicles from orbital debris. In addition, the results of the research can be used to assess the impact of unobserved orbital debris on the flight of a launch vehicle.

scholarly journals Bias of the Hubble Constant Value Caused by Errors in Galactic Distance Indicators

2021 ◽  
Vol 66 (11) ◽  
pp. 955
Author(s):  
S.L. Parnovsky
Keyword(s):  
Hubble Parameter ◽  
Least Squares Method ◽  
Statistical Processing ◽  
Hubble Constant ◽  
Real Data ◽  
True Value ◽  
Original Dataset ◽  
The Impact ◽  
Distance Indicators

The bias in the determination of the Hubble parameter and the Hubble constant in the modern Universe is discussed. It could appear due to the statistical processing of data on the redshifts of galaxies and the estimated distances based on some statistical relations with limited accuracy. This causes a number of effects leading to either underestimation or overestimation of the Hubble parameter when using any methods of statistical processing, primarily the least squares method (LSM). The value of the Hubble constant is underestimated when processing a whole sample; when the sample is constrained by distance, especially when constrained from above. Moreover, it is significantly overestimated due to the data selection. The bias significantly exceeds the values of the erro ofr the Hubble constant calculated by the LSM formulae. These effects are demonstrated both analytically and using Monte Carlo simulations, which introduce deviations in the velocities and estimated distances to the original dataset described by the Hubble law. The characteristics of the deviations are similar to real observations. Errors in the estimated distances are up to 20%. They lead to the fact that, when processing the same mock sample using LSM, it is possible to obtain an estimate of the Hubble constant from 96% of the true value when processing the entire sample to 110% when processing the subsample with distances limited from above. The impact of these effects can lead to a bias in the Hubble constant obtained from real data and an overestimation of the accuracy of determining this value. This may call into question the accuracy of determining the Hubble constant and can significantly reduce the tension between the values obtained from the observations in the early and modern Universes, which were actively discussed during the last year.

scholarly journals Оцінка впливу похибок БІНС, яка побудована на MEMS-компонентах, на точність виведення ракети-носія надлегкого класу

2021 ◽  
pp. 60-68
Author(s):  
Артём Сергеевич Смирнов ◽  
Александр Вячеславович Голубек
Keyword(s):  
Navigation System ◽  
Statistical Processing ◽  
Satellite Navigation ◽  
Launch Vehicle ◽  
Random Drift ◽  
Modes Of Operation ◽  
Satellite Navigation System ◽  
Orbital Parameters ◽  
Near Earth Space ◽  
Low Earth Orbits

The object of the article is the movement of an ultra-light class liquid-propellant launch vehicle in near-earth space. The subject of the research is the accuracy of launching a spacecraft by a launch vehicle. The article studies the effect of errors in the instruments of a strap-down inertial navigation system built with the use of MEMS sensors on the accuracy of launching a spacecraft into low-earth orbits with an altitude of up to 450 km for two modes of operation: with and without a satellite navigation system. Tasks: to identify the determining disturbing factors, to determine the influence of instrument errors on the trajectory tube, to determine the influence of instrument errors on the insertion accuracy, to perform a comparative analysis of the accuracy characteristics obtained for two modes of operation of the navigation system. Methods used analysis, synthesis, analogy, comparison, factor analysis, statistical modeling, statistical processing of modeling results. Results: a set of defining disturbing factors was revealed, the dependencies of the trajectory tubes on the altitude of the target orbit and flight time were obtained, the dependencies of the limiting deviations of the parameters of the spacecraft's orbit at the time of separation from the launch vehicle on the altitude of the target orbit were obtained. Conclusions. 1. It is shown that the determining perturbing factors are the zero drift of the gyroscope from launch to launch and the zero random drift of the gyroscope. 2. It was determined that the value of the trajectory tube monotonically expands on time and the height of the target orbit. Maximum deviations of the current position and absolute speed in the mode without using a satellite navigation system do not exceed 115 km and 140 m/s. For the mode using a satellite navigation system, these values do not exceed 140 m and 1.5 m/s. 3. It was revealed that the maximum deviations of the parameters of the spacecraft's orbit in the mode with the use of a satellite navigation system do not exceed 27 km in height, 1.8o in inclination, 4.5x10-4 in eccentricity, and 2.7o for the longitude of the ascending node. For the mode with a satellite navigation system - in height - 2.6 km, in inclination and longitude of the ascending node - 0.0003о, in eccentricity - 3.5x10-4. 4. Generally, the use of a satellite navigation system narrows the trajectory tube by twice, and the accuracy increases to four times, depending on the orbital parameters.

scholarly journals Evasive Maneuvers in Space Debris Environment and Technological Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Antônio D. C. Jesus ◽  
Rafael S. Ribeiro ◽  
Alessandro Rossi ◽  
Ernesto Veira Neto
Keyword(s):  
Numerical Model ◽  
Impact Velocity ◽  
Space Debris ◽  
Initial Conditions ◽  
Relative Distance ◽  
Technological Parameters ◽  
Collisional Dynamics ◽  
Relative Dynamics ◽  
The Impact ◽  
Warning Time

We present a study of collisional dynamics between space debris and an operational vehicle in LEO. We adopted an approach based on the relative dynamics between the objects on a collisional course and with a short warning time and established a semianalytical solution for the final trajectories of these objects. Our results show that there are angular ranges in 3D, in addition to the initial conditions, that favor the collisions. These results allowed the investigation of a range of technological parameters for the spacecraft (e.g., fuel reserve) that allow a safe evasive maneuver (e.g., time available for the maneuver). The numerical model was tested for different values of the impact velocity and relative distance between the approaching objects.

Research on Self-Calibration of Circular Artifacts

2013 ◽  
Vol 475-476 ◽  
pp. 167-172
Author(s):  
Xin Mei Liu ◽  
Yun Chen
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Random Noise ◽  
Poor Performance ◽  
Correlation Equation ◽  
System Error ◽  
Calibration Algorithm ◽  
The Impact ◽  
The Mathematical Model

In order to solve the problem of poor performance of the traditional calibration algorithm , the paper proposed a mathematical model under the constraints of nonrotating and nonscale error ,which solved the defects of inconvenience and expensiveness. Moreover, the mathematical model was obtained through the correlation equation based on the least squares method. Meanwhile , the paper discussed the impact of random noise on the model ,and it was simulated by Matlab. The result of the simulation shows that the model can separate the system error of circular artifacts accurately whether the existence of random noise or not. The result of this paper on expanding the application areas of selfcalibration is of great significance.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Analyzing the Impact of Healthy Behavior on Weight Change with a Provable Mathematical Model (Preprint)

2020 ◽  
Author(s):  
Ayan Chatterjee ◽  
Ram Bajpai ◽  
Pankaj Khatiwada
Keyword(s):  
Physical Activity ◽  
Mathematical Model ◽  
Health Behavior ◽  
Weight Change ◽  
Simulated Data ◽  
Negative Behavior ◽  
Healthy Behavior ◽  
Healthy Habits ◽  
Lifestyle Diseases ◽  
The Impact

BACKGROUND Lifestyle diseases are the primary cause of death worldwide. The gradual growth of negative behavior in humans due to physical inactivity, unhealthy habit, and improper nutrition expedites lifestyle diseases. In this study, we develop a mathematical model to analyze the impact of regular physical activity, healthy habits, and a proper diet on weight change, targeting obesity as a case study. Followed by, we design an algorithm for the verification of the proposed mathematical model with simulated data of artificial participants. OBJECTIVE This study intends to analyze the effect of healthy behavior (physical activity, healthy habits, and proper dietary pattern) on weight change with a proposed mathematical model and its verification with an algorithm where personalized habits are designed to change dynamically based on the rule. METHODS We developed a weight-change mathematical model as a function of activity, habit, and nutrition with the first law of thermodynamics, basal metabolic rate (BMR), total daily energy expenditure (TDEE), and body-mass-index (BMI) to establish a relationship between health behavior and weight change. Followed by, we verified the model with simulated data. RESULTS The proposed provable mathematical model showed a strong relationship between health behavior and weight change. We verified the mathematical model with the proposed algorithm using simulated data following the necessary constraints. The adoption of BMR and TDEE calculation following Harris-Benedict’s equation has increased the model's accuracy under defined settings. CONCLUSIONS This study helped us understand the impact of healthy behavior on obesity and overweight with numeric implications and the importance of adopting a healthy lifestyle abstaining from negative behavior change.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Marcos Amaku ◽  
Dimas Tadeu Covas ◽  
Francisco Antonio Bezerra Coutinho ◽  
Raymundo Soares Azevedo ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Vaccination Campaign ◽  
Vaccination Rate ◽  
Sao Paulo ◽  
The State ◽  
São Paulo ◽  
Health Authorities ◽  
The World ◽  
The Moment ◽  
The Impact

Abstract Background At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. Methods We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. Results The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Conclusions Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

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