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Active Debris Removal (ADR) for Mega-constellation Reliability

  • Nikita VelievEmail author
  • Anton Ivanov
  • Shamil Biktimirov
Living reference work entry
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Abstract

Provided that the hazard of space debris in orbit can pose threats to space exploration missions and, thereby, influence the redundancy of Earth observation and telecommunication constellations, this chapter addresses the case for mega-constellation reliability. The space security challenge in this case does not only relate to the regulatory and legal framework thereof but also to the business development of technical solutions for space security. Although the current level of technologies enables active debris removal (ADR), its business applicability remains to be investigated. In this study, a multiparametric mega-constellation model has been developed to take into account orbital motion, coverage, ground communication, reliability, collision risks, and service consumption in the global telecommunication market. The research and simulations performed on the model allowed for the analysis of possible financial metrics (revenue, cash flows, total replenishment cost) of the company who operates the ADR, as well as replacement scenarios and weak points of the mega-constellation. All combined, the chapter provides insights into the market that exists for ADR technologies, by demonstrating the ADR business applicability for mega-constellations.

Introduction

Since the inception of mega-constellation projects, the space debris problem got worse. Despite the fact that the history of spaceflight has witnessed cases of collisions between operating satellites and space junk, space debris objects have not been seriously considered in the business of aeronautics. Provided that the space telecommunication market utilizing low Earth orbit (LEO) and medium Earth orbit (MEO) becomes larger, the demand for new satellite systems and constellations, respectively, grows. Hence, the density of the satellites and other objects in orbit is growing as well. Eventually, by 2030 the number of the manmade objects in LEO and MEO is expected to grow ten times bigger than it is right now (European Space Operations Centre 2019). This definitely has repercussions for the market and as it constitutes a high financial risk.

Accordingly, this chapter examines the problem of space debris and how to potentially tackle it. The solution to the problem is what has been discussed for at least a decade: active debris removal (ADR), which is based on the mechanical process of returning the space object to the Earth atmosphere. Along with a passive debris removal, which is based on the phenomenon of atmospheric drag, active debris removal is one of the main space debris mitigation methods. The approach of this chapter is based on the premise that a satellite constellation operator and a company, aiming at the development of active space debris removal, could create a mutually beneficial situation. This would allow the operator to lower the risks of collisions, increase the stability and quality of the service, and improve its financial indicators while the ADR company would position itself in the market. At the same time, ADR can be of benefit to all mankind by ensuring the sustainably of the outer space environment.

Additionally, the analysis was based on the creation of a simulation environment that could facilitate in general the analysis of business reports for the whole telecommunication market. In particular, the simulation environment could become a quite effective instrument that enables risk assessment, market benchmarking, market specification, and selection of the appropriate business strategy. Hence, the simulation of in-orbit processes and the assessment of the data links were selected as the methodology of this chapter. For this purpose, the sustainable and stable simulation environment was created with valid and verified models. This environment has included different time scales, operating scenarios, constellation types, and satellite types to estimate financial metrics of the operator. As a final stage, the study applied the simulation environment developed to the specific business study. It was produced for the ADR company working along with the first echelon of the SpaceX Starlink constellation.

The results of the simulations and the results of the analysis showed that the loss of satellite could significantly influence the quality of the service reducing the coverage rate up to 20% and lead to extremely high financial losses for the operator (up to one billion dollars for a half of the lifetime of the satellite). That said and taking into account space technology readiness level and existing and developing business strategies, the ADR could successfully enter the space market and become profitable.

Simulation Model for Satellite Mega-constellation Reliability X

Concurrent Engineering Approach for SpaceX Starlink

The first baseline of this study was the research made by the Skoltech Space Center, which applied concurrent engineering methods in practice. The object of the research was the SpaceX company Starlink (Kharlan et al. 2018). The work included assessment of the statements of the company (displayed in Table 1) over its work, methods, service, and implementation process. Thus, the tasks of the team included validation and reverse engineering of the technical part.
Table 1

SpaceX statements regarding service and project characteristics (SpaceX 2017)

Parameter/unit

Value

Mass of the satellite, kg

400

Overall cost of the project, billion US$

<10

Connection speed, MB/s

>512

Service cost, $

<300 per subscription

The concurrent engineering approach assesses the applicability, the main technical parameters, and the evaluation of potential financial metrics of the company, as well as possible bottlenecks of the project (Shishko 1995). Accordingly, a team of ten Space Center researchers and students conducted the breakdown of the SpaceX Starlink satellites to subsystems (Kharlan et al. 2018). The process of concurrent engineering design consisted of seven sessions and five iterations based on the use of a special software. For the purposes of Skoltech Concurrent Engineering Design Laboratory, the CDP4-IME software created by RHEA Group was selected as the best solution because of its open-source code that supports the needed functionality. The research was finalized in a month with results described in the article prepared for the IAC conference in 2018 (Kharlan et al. 2018). Some particular research outcomes are displayed in Fig. 1 exposing the mechanical part 3D model and cost distribution.
Fig. 1

Results of the reverse engineering of the SpaceX Starlink project: mechanical 3D modeling and composition (left), average cost distribution chart (Wertz et al. 2011) (right)

Reliability Simulation Model for Satellite Constellation

Accordingly, the rationale for the simulation model was to understand whether the satellite is operational or not over time. Hence, the evaluation of a satellite’s possible lifetime, which is generated based on the reliability distribution, becomes the most crucial part of the model. The main challenge presented in the process of sampling the lifetime of the satellites is the reliability distribution as the function of time, as that becomes the statistical task. The solution can be found by compiling the data of the launch date and the failure date (if any) of all satellites available in the database of the space objects currently located in orbit. The statistical learning based on the data for satellites and space debris is listed in the SpaceTrack closed database (Castet and Saleh 2009). The overall approximation numerical formula which can be used for the calculations is (Castet and Saleh 2009)
$$ R(t)=0.000120114\ast \frac{\exp \left(0.000265681\ast {t}^{0.4521}\right)}{t^{0.5479}} $$
(1)
where t is time in sec.

The next step of the reliability assessment was to generate the array of satellite states – the matrix describing the status of the satellite during whole lifetime was “1” for operating, “2” for interrupted, “3” for failed, “4” for being on replacement, and “0” for not working. This provided for a simple and obvious understanding of the status of the satellite during every step of the simulation.

Propagation

This study has considered part of the upper echelon of SpaceX non-geostationary orbit (NGSO) satellite system to demonstrate economic feasibility of various ADR strategies. The SpaceX satellite system was expected to be deployed during the first deployment phase (see Table 2). The echelon comprises of 4,425 spacecraft operating in the Ku and Ka bands. According to SpaceX (SpaceX 2017), upper echelon consists of five sub-constellations corresponding to different orbit altitudes and inclinations as shown in Table 2. During this research, the first sub-constellation – corresponding to altitude of 1,150 km above the Earth and 53 degrees – was considered because of the fact that it is planned to be deployed earlier than others. This helps demonstrate operation performance of satellite communication systems. Therefore, it is worth modeling possible advantages and risks of active debris removal technologies at this step.
Table 2

Orbital parameters of the SpaceX NGSO satellite constellation (SpaceX 2017)

Parameter

Initial deployment (1,600 satellites)

Final deployment (2,825 satellites)

Orbital planes

32

32

8

5

6

Satellites per plane

50

50

50

75

75

Altitude

1,150 km

1,110 km

1,130 km

1,275 km

1,325 km

Inclination

53°

53.8°

74°

81°

70°

The satellites in NGSO are located in circular orbits and evenly distributed according to the Walker constellation design pattern (Larson and Wiley 1992). This allows placing the satellite within the constellation in a way that ensures evenly distributed Earth coverage and avoids possible collision between satellites. The main parameters of the constellation according to the Walker design pattern are the total number of spacecraft T, number of orbital planes P, and phasing parameter F (Larson and Wiley 1992). Due to the lack of information regarding the phasing parameter, it was set equal to one, which is suitable for constellation of this size.

The propagation model enables the prediction of satellite’s position and velocity at a required time (Larson and Wiley 1992). Each spacecraft in constellation is equipped with propulsion system for phasing maneuvers and orbit maintenance (SpaceX 2017). Therefore, the effects of atmospheric drag and solar radiation pressure can be omitted because they mostly influence the shape of the orbit, but not the precession (Larson and Wiley 1992). Thus, the perturbation caused by Earth’s oblateness is taken into account. Right Ascension of the Ascending Node (RAAN) velocity is
$$ {n}_{\varOmega}\approx -\frac{3{J}_2{\mu}_G^{1/2}{R}_E^2}{2{R}_0^{7/2}} cosi $$
(2)
where R0 and i are radius and inclination of the orbit, RE = 6378.245 km is the Earth’s mean equatorial radius, μG = 3.986∗105 km3/s2 indicates the gravity parameter of the Earth, and J2 = 1.082626∗10-3 is the first zonal harmonic coefficient.
As it was mentioned earlier, satellites in the constellation have circular orbits. Therefore, in order to describe satellite location in orbit, it is more convenient to use the argument of latitude denoted. The latter is equal to the sum of the argument of latitude and true anomaly. To describe time derivative of argument of latitude, the following expression is used (Vallado 2001):
$$ {\omega}_D={\omega}_o\left[1-\frac{3}{2}{J}_2{\left(\frac{R_E}{R_0}\right)}^2\left(1-4{\mathit{\cos}}^2i\right)\right] $$
(3)
where ωD = 2π/TD; TD is the period of satellite’s revolution around the Earth, also called as draconic period; and ω0 is mean motion of a satellite.
The example of 1-day propagation of the upper echelon satellite is exposed in Fig. 2.
Fig. 2

One-day propagation of the satellite taken from the upper echelon (Larson and Wiley 1992)

To model the ground-track and Earth coverage of a satellite within the constellation, a projection of the satellite position was made. It was calculated in Earth-centered, Earth-fixed (ECEF), coordinate system to Earth sphere. All calculations of satellite motions made according to the previous paragraph are conducted in inertial reference frame such as Earth-centered inertial (ECI). Therefore, it should be converted to ECEF in order to calculate ground track and coverage. Transformation of coordinates is performed according to the International Earth Rotation and Reference Systems Service (IERS) 2010 conventions (Gérard and Luzum 2010) where such effects as precession and nutation of Earth rotation axis are considered.

Simulation Process

The process of simulation starts when the majority of data is prepared for the processing. First the lifetime statuses of the constellation satellites are estimated, then the ABGN is created, and, last, the propagation matrix is ready. The initial parameters of the simulation are:
  1. 1.
    Simulation related parameters:
    1. a.

      The length of the simulation period

       
    2. b.

      The size of the timestep of the simulation – which definitely is supposed to be selected corresponding to the parameters of the preprocessed files

       
     
  2. 2.
    Constellation-related parameters:
    1. a.

      Altitude

       
    2. b.

      Inclination

       
    3. c.

      Accuracy of the ABGN grid

       
     
  3. 3.
    Satellite-related parameters:
    1. a.

      Mass

       
    2. b.

      Volume

       
    3. c.

      Antenna field of view

       
    4. d.

      Coverage rate

       
     
  4. 4.
    Spare strategy type:
    1. a.

      Two options are available: “none” for no strategy and “lod” for launch-on-demand strategy.

       
     
The process of the simulation itself consisted of a method that reads the states of the satellites and is based on information that reveals the coverage of the constellation. Moving forward, the method estimates the possible revenue and the costs for the specific timestep and finally calculates the amount of space debris in the orbit. The simulation requires much resources, including random access memory (RAM), computational power, and hard drive (HD) memory. With all the optimization, the simulation parameters were set to be constant (displayed in Table 3).
Table 3

Optimal simulation parameters based on parameter-sensitivity analysis by the authors

Parameter, units

Value

CPU count, units

40

Step size, s

100

CPU frequency, GHz

3.2

Chunk size, steps

3942

RAM, Gb

200

Replenishment Scenarios

The approach of the simulation considered two types of interactions with spare issues: no strategy at all and launch-on-demand (LOD) strategy assuming that every time the satellite fails in the orbit, the other one is supposed to be launched on its place in the shortest time possible. In that case, the ADR effectiveness is supposed to be evaluated based on satellite costs and the risk of in-orbit collision assessment, which is performed using the growing collision probability formula:
$$ PC=1-\exp \left(- SPD\ast VR\ast AC\ast t\right) $$
(4)
where SPD is spatial density (n/km3), VR is relative velocity (km/s), AC is aerial collision cross section (km2), and t is time (sec).
In Fig. 3, the collision probability along with the growing density of the debris during the 1st year of constellation operation is displayed. As it can be clearly seen, the ADR is supposed to line up the risk management and lower the probability of the chain reaction.
Fig. 3

Space debris density distribution and collision probability distribution based on simulation results of the authors

Marketing Model for Satellite Mega-constellation

As long as the satellite constellation model was created and it became clear how each satellite in the constellation moves and what was the coverage of each satellite, it became available to assess how each satellite influences the connectivity and, consequently, the company operator’s financial metrics. For that purpose, it was necessary to assess the market and allocate marketing data to the coordinates on the Earth surface.

Obviously, as an understanding of the possible business applications of the ADR is based on the financial metrics of the operators, the marketing analysis and model are taking the most important part in the research. It facilitates the calculation of possible revenue for the constellation through the implementation of economics and marketing.

The underlying reasoning of detailed market study was to understand the number of subscribers in every point of the Earth globe and according to the pricing estimations to calculate the potential positive and negative cash flows as a benchmark. The created marketing model consists of two major blocks:
  • Pricing model

  • Population model and market penetration

Pricing Model

The study considered two different types of pricing currently being used by the telecommunication companies worldwide: all-flat and traffic-based tariffs (Deloitte 2019). For the flat plans, the price of the service was calculated as the average price of the flat tariff in the particular country. Figures 4 and 5 show the statistics used for the calculations of the traffic-based subscriber contract.
Fig. 4

Internet user number distribution by region (Statista Inc. database 2019b)

Fig. 5

Internet traffic consumption per month by the region (Statista Inc. database 2019a)

Both calculations were made and verified using the open-source data for telecommunication companies’ statistics in Russia, Statista Inc. database. The average errors for both methods are shown in Table 4.
Table 4

Verification error for different pricing models, based on the simulation assessments of the authors

Method

Error rate, %

Flat

28

Consumption-based

13

Population Map and Market Penetration

The population data is based on the information prepared by the NASA Socioeconomic Data and Applications Center (SEDAC) (Doxsey-Whitfield et al. 2015) based on the gridded population of the world (GPW). The fourth version of the data is the distribution of the human population across the Earth. The statistical data is generated based on the Earth observations and provides globally consistent data for any type of the researches and studies.

The Earth observation data was transferred to the population data values; then the data passed the process of normalization using the official statistic of the countries. This work uses data for 2015 with a resolution of 1 degree. However, increasing the accuracy significantly decreases the calculation speed and affects the overall simulation time, according to Formula 5 (representing the needed number of calculation steps in order to facilitate the whole grid for a single timestep):
$$ {N}_{steps}=\frac{180\mathit{\deg}\ast 360\mathit{\deg}}{A} $$
(5)
where Nsteps is the number of steps, A is accuracy (step size, deg2), and 180∗360 is altitude-longitude degree grid.
The population is not the only thing that is necessary for the calculations though. The other important elements are market penetration and target audience. Both parameters are limited to the number of users interested in the service and able to pay for it. The generic coefficient determining the part of the population that supposed to use the service of the exact provider can be estimated by the formula:
$$ K= MS\ast I\ast IP $$
(6)
where MS is the market share, I is income availability, and IP is Internet penetration.

Theoretical three-parameter model describes three sides of the approach of estimation of the amount of the target audience: economic, marketing, and technical.

The market share of the company is determined dynamically as a function of time, describing the entry of the company to the market with boundary conditions. This is described in the  Federal Communications Commission (FCC) request of SpaceX technical information in 2017, as well as in official forecasts of the SpaceX Starlink stating 40 million subscribers and 30 billion US dollar revenue by 2025 (Harris 2019). As a market acquisition model, the Gompertz curve (Zlatić and Štefančić 2011) has been selected, because the growth speed of the curve is pretty similar to the market share speed. The approximation was used to describe the mobile phone penetration to the population (Islam et al. 2002). The exact formula is presented in Eq. 7:
$$ MS=0.2158\ast {e}^{-3.0716\ast {e}^{-0.00000354\ast t}} $$
(7)
where t is time in sec.
Income availability is the parameter describing price availability of the product on the market. This parameter is being calculated based on the price of the product and the distribution function of the income per capita in each country. According to the fact that the Internet connection payments on average are holding 10% of all spends per month (Visser 2019), selecting the tariff price gives an understanding of the number of people that are able to pay. For most countries, the shape of the curve is described with different data. However, for those countries with no data available for a “rich-poor” curve, the average worldwide curve was used. This curve is displayed in Fig. 6 as an example (OurWorldInData Inc. database 2014).
Fig. 6

The world population income distribution in 2003 and 2013 (OurWorldInData Inc. database 2014)

Agent-Based Ground Network

Considering the output of the economical modeling process, the agent-based ground network (ABGN) has been created. The term ABGN as well as the grid itself was created during the research specifically for the simulation to simplify the process of markets of the Earth-based consumers. The ABGN is the operational set of agents, or in this case subscribers of the Internet service, integrated to the peer-to-peer-linked network distributed by the Earth globe and having a set of parameters, enabling the assessment of the entire system. In the case, when the subscriber is a single user or a household, the agent network could be represented as the grid with number of the subscribers in surrounding area as the nod value.

Each agent can be represented as an object of the “subscriber” class with a set of attributes. This is based on a self-made Python class of objects containing a set of parameters with relative information regarding the selected type of the subscriber. The attributes are:
  1. 1.

    Position. The positional argument, describing the position of the subscriber (or a set of subscribers) on the Earth globe. The distribution could be random, functional – set up with a function of time, evenly weighted – normally distributed nods of the grid, setting up a single subscriber or number of subscribers in the surrounding area, or single-located, the array of coordinate of the subscribers.

     
  2. 2.

    Money capacity. The parameter of money capacity is being calculated based on the amount of the target audience in the nod and the price of the service. This parameter is the permanent base for the calculations of the money flows of the operational company and dynamic coverage methods.

     
  3. 3.

    Traffic demand. The parameter is calculated based on the amount of target audience in the nod and the traffic demand in the location per capita. This parameter hardly influences the link budget and dynamic coverage methods.

     

The agent-based ground network is able to represent not only the large number of users but the single user as well. In other words, this system works with both the business to consumer (B2C) and business to business (B2B) strategy of operation problems. That, in particular, allows to solve the static and dynamic tasks (or a combination of such). This advantage allows the model to be applicable to other scenarios for various companies. The system works on a plug-and-go basis meaning that setting up the type of the ABGN does not require changing code in the core of the simulation.

Model Validation

As soon as the environment is ready, the verification takes place in order to determine the applicability of the model to real scenarios. The validation has been delivered as a two-step process: the first one was the validation of the model itself, performed with running the simulation for the constellation that already exists; the second was the case validation, determining whether the model is applicable to the particular case study.

In the first part, the simulation process was run with the characteristics of and information about the Iridium Inc. constellation (from annual report to Stockholders in 2009) that has been firstly launched in 1997 and consists of 75 active satellites with a coverage of 100% of the Earth globe. The idea was to compare the results of the simulation with company open data (including revenue). The outputs are displayed in Fig. 7, with the error made up to 7%.
Fig. 7

Annual yearly revenues for the Iridium Inc. simulated, where year 1 is the 1st year after main launch in 2003 based on simulation results of the authors

The case validation was based on the open data of the SpaceX company official statements claiming the amount of revenue by 2025 (claiming 30 billion US$ of revenue by the time) (Mosher 2019). The error appeared to be 122%, as the results display in Fig. 8. The big error is corresponding with lack of data.
Fig. 8

Annual yearly revenues for the SpaceX simulated, where year 1 is the 1st year after main launch in 2020 based on simulation results of the authors

Commercialization of ADR and Insurance Strategy

According to the baseline of the simulation, the propagation and coverage footprint were calculated. Based on the coverage and reliability model, the overall constellation coverage was calculated. Along with created ABGN model, the possible market coverage of the operator was calculated for the selected satellite constellation formation. The data for each timestep gave an opportunity to understand main financial metrics of the operator (such as positive cash flow from the servicing, income, and operational expenses).

This, consequently, enabled the research group to run some basic assessment scenarios of the telecommunication segment. The environment and the models have been verified using the existing cases of constellations and open information of the company at hand.

Afterward, the environment was used several times to assess the satellite service to be provided and supported by the SpaceX Starlink company for the simulation periods equaled to 1 month, 1 year, and 3 years. The output data is represented as a time evolution of several important parameters: revenue flow, costs, space debris density in orbit, and coverage. The results are exposed in Figs. 9, 10, and 11.
Fig. 9

Revenue time evolution for the case study: simulated for 1 year (left) and for 5 years (right) based on simulation results of the authors

Fig. 10

Revenue losses for the consequent periods based on simulation results of the authors

Fig. 11

Time evolution of the coverage based on simulation results of the authors

Following the assessments made in the beginning of the work, losing the satellite led to several huge impacts on the constellation operational indicators. It can be seen in Fig. 9 that operating with no replenishment strategy could be followed by revenue decrease (around 1.5 mln USD for the 1st year and nearly 1 bln USD for the first 5 years). In Fig. 10, the same data showed in percentage which is up to 6% revenue loss for the 1st year. Figure 11 also shows that the malfunction satellite can also lead to a coverage loss leading to the quality issues.

The assessment showed that active debris removal is critically important for the company-operator as it allows to increase revenues and decrease the risks of collisions. The main result of the outcome analysis is the fact that ADR is not only practically necessary to tackle the challenges of the mega-constellations, but it can also be commercialized.

Based on the research outcomes, a marketing analysis was followed to create a sustainable business strategy for the ADR company. For that purpose, the company was evaluated from a business perspective. The analysis showed the specifics of the business and possible strategy options. Three major business plans were assessed: the “flat insurance,” the “dynamic flat insurance,” and the “pay-as-you-go tariffs.” For each of the strategy, a separate simulation turn was run in order to understand the applicability of the strategy, its profitability, and positives and negatives of its use.

The flat insurance strategy is based on the business plans of the insurance and reinsurance companies providing the full insurance. This includes the complete ADR services, for a fixed reward. After simulating, this plan, however, appeared to be noncompetitive since the reward calculated is quite high and appears to be not advantageous for the operator.

The pay-as-you-go tariff, on the contrary, means to implement the system of rewarding the ADR company every time the satellite replacement takes place. However, in that case, things can get worse for the company itself. Since the satellite failure is highly connected with the reliability of the satellite, it seems that the company’s financial behavior can turn to be unpredictable. This can subsequently lead to investment overlaps and breaks – the incomes of the company are going to be strictly connected to the satellite loss, which is not equally distributed over time – the cash flow becomes “jumping.”

The compromise lies in merging both of two options and adjusting the details of the strategy. The dynamic flat insurance implements the dynamic rewarding methods and selective ADR use. The rewarding technology is connected with the distribution of the satellite reliability over time, taking into account any kind of collision risks. In Fig. 12, the rewarding scheme is presented. The rewarding scheme based on the business plan enabling dynamic price change; in that case, the price depends on the overall reliability of the constellation. It means that the more time the constellation lives, the less its reliability, the more money the customer supposed to pay to cover the ADR service.
Fig. 12

Reward strategy: base cost multiplicator distribution over time based on simulation results of the authors

Additionally, the simulation showed that the loss of one individual satellite has approximately no influence on the service quality, while the failure of two coherent satellites leads to 1.5 times as big revenue losses. This actually is explained by the fact that the satellite coverage footprints overlap as it can be clearly seen in Fig. 13 (Kharlan et al. 2018) – the blue circles are displaying some of the first echelon satellite footprints. The picture shows that the loss of one satellite leaves relatively small piece of Earth surface, which can lead to predictable and short connectivity losses. At the same time, losing several consequent satellites significantly increases the uncovered surface bringing continuous and unbalanced connectivity failures.
Fig. 13

Footprints of SpaceX lower echelon (SpaceX 20,187) (right) and “street size” description (left)

Conclusions

The objective of this chapter was to analyze a business case connected with an active debris removal (ADR) process. It aimed to understand its applicability and prove the market existence for ADR. In order to pursue this investigation, the analysis was based on the creation of a simulation environment for mega-constellations, the Starlink SpaceX first echelon constellation. The results of the study give insights into the success of an ADR company, being interconnected with the role of operators of these large constellations.

[Can you summarize here a bit more about the results? I think they are very important to highlight in relation to the mega-constellation challenge].

Despite the importance of the results, the limitations of the method are evident due to the study performed for the specific large case of mega-constellations. In order to address these limitations, future research could look into the following proposed directions:
  1. 1.

    Perform a study for different constellation with different orbital parameters.

     
  2. 2.

    Perform a study for different altitudes (MEO and GSO).

     
  3. 3.

    Perform a study for other markets, such as Global Navigation Satellite System (GNSS), Earth observation (EO), or defense applications.

     
  4. 4.

    Apply different optimization methods.

     
  5. 5.

    Assess the replenishment times and the constellation sizing factors.

     

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Nikita Veliev
    • 1
    Email author
  • Anton Ivanov
    • 1
  • Shamil Biktimirov
    • 1
  1. 1.Skolkovo Institute of Science and TechnologyMoscowRussia

Section editors and affiliations

  • Maarten Adriaensen
    • 1
  1. 1.European Space AgencyParisFrance

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