SPACECRAFTS SERVICE OPERATIONS AS A SOLUTION FOR …...artificial spacecrafts are considered as space debris by GOST R 53802 [2]. The number of SC in the Earth orbit constantly increases

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 9, Issue 7, July 2018, pp. 1503–1518, Article ID: IJMET_09_07_160

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=7

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

SPACECRAFTS SERVICE OPERATIONS AS A

SOLUTION FOR SPACE DEBRIS PROBLEM

V. Zelentsov, G.Shcheglov, V. Mayorova and T. Biushkina

Bauman Moscow State Technical University, Moscow, Russia

ABSTRACT

An automatic spacecraft (SC) is probably the only type of an involved engineering

device that is currently devoid of a full system for technical maintenance and repair.

When changing to operation with groups of several spacecrafts, the degree of man-

made pollution of the near-Earth space increases and there is a need in special SC

aimed at removal of space debris. A relevant problem is the choice of the design

parameters of maintenance and repair spacecrafts (MRSC). The purpose of the

present paper is to give the analysis of mass properties and determine the design

layout of a universal multipurpose two-stage inter orbital MRSC capable of

performing the principal service tasks for a group of several spacecrafts.

Keywords: Spacecraft, orbital maintenance, space debris, mass properties, service

operations.

Cite this Article: V. Zelentsov, G.Shcheglov, V. Mayorova and T. Biushkina,

Spacecrafts Service Operations as a Solution for Space Debris Problem, International

Journal of Mechanical Engineering and Technology, 9(7), 2018, pp. 1503–1518.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=7

1. INTRODUCTION

The lifecycle of every product is mostly spent on its operation, including transportation,

storage, intended use, technical maintenance, and repair. According to technical standard

GOST 25866, in the process of operation of a product, its quality should be not only

implemented, but also maintained and recovered, which requires a system for product

operation, involving the product itself, operation facilities, performers, and the required

documentation [1].

The construction of a full system of operations is greatly hindered at present by the nature

of the operational environment of spacecrafts. An automatic spacecraft (SC) is probably the

only type of an involved engineering device that is currently devoid of a full system for

technical maintenance and repair (M&R), even though Russian Standard GOST R 53802

stipulates a special class of maintenance and repair spacecrafts (MRSC) aimed at assembly

and integration activities, technical maintenance and repair of orbital objects [2].

At present, the SC service strategy assumes only the monitoring and control of operation

regimes of onboard systems. The ability of ground control equipment to maintain and resume

Spacecrafts Service Operations as a Solution for Space Debris Problem


SC performance are limited by the capacities of telemetry systems, the degree of redundancy

of the onboard equipment, and the fuel plan for the propulsion system. It should be also noted

that modern SC are non-repairable and that their end-of-service phase is accompanied by

man-made pollution of the near-Earth space, because in the circumterrestrial space all spent

artificial spacecrafts are considered as space debris by GOST R 53802 [2].

The number of SC in the Earth orbit constantly increases since the launch of the very first

satellite. The growth rate was highest in the 1970-80s, when more than 100 launches were

performed each year. At this time, the life time of a spacecraft was at most five years. When

their life time expired, most of such satellites remained in orbit and became space debris. The

nature and characteristic sizes of space debris vary significantly [3, 4]. The total number of

objects of cataloged space debris is approximately 17 000 objects involving healthy SC (as of

2017) [5]. At present, the intensity of launches is not that high, because the average life time

of a SC had increased to 15 years. Also, several documents were accepted requiring the SC

designers to obey constraints on jettison of man-made debris (bolts, covers, etc.) and to

organize SC de-orbiting to disposal orbits. There are several disposal methods: for LEO

spacecrafts this is an entrance into the Earth atmosphere or its transfer to an elliptic orbit with

25-year disposal rule; for GEO spacecraft, the altitude of the disposal orbit is specified

according to GOST R 52925 [6].

Despite of the extended life time and introduction of new constraints, a SC still may go

out of order due to failures of onboard systems. The classified failure statistics of spacecrafts

in orbits for the period 2000--2017 is given in Table 1. The root causes of failures can be

subdivided into three groups: deployment failures of stowed structure elements and

impossibility of establishing a communication link with a SC directly after the injection into

the orbit (ODF); onboard equipment failures (OBEF); mechanical failures and damages of SC

structure elements (DMF). In addition, failures can result in a fatal failure (FF), a partial

failure (PF), and a corrected failure (CF).

The Table 1 shows that the most failures (15% of the total number of injected SC) is

related to onboard equipment failures. Figure 1 shows the graph illustrating the percentage of

onboard equipment failures: radio equipment failures (RE), software failures (SW), power

supply system failures (PSS), mechanical failures and damages of SC structure elements

(DMF), hardware failures (HF), gyro unit failures (GF), propulsion system failures (PSF);

operating personnel mistakes (OPM) are even more rare. Failure of blocks involving

electric/radio components (ERC) can be easily explained, because such elements are highly

sensitive to radiation, vacuum, etc.

Table 1 Distribution of spacecraft subsystems failures in years and types [7, 8]

Year Number

of SC launches

Number of SC failures

ODF OBEF DMF

FF PF CF FF PF CF

2017 21 5 3 3 4 3 3 0

2016 29 1 9 11 5 1 1 0

2015 36 3 3 8 11 1 0 0

2014 21 5 8 6 2 0 0 0

2013 6 2 1 0 1 2 0 0

2012 15 0 8 5 2 0 0 0

2011 14 0 6 6 0 1 0 1

2010 22 2 9 9 2 0 0 0

2009 132 4 2 0 1 0 0 0

2008 114 0 2 1 0 0 1 1

2007 119 1 4 3 2 2 2 0

2006 116 7 5 0 3 0 0 0

2005 2 1 2 1 1 0 0 0



2004 72 0 0 0 1 0 0 0

2003 104 0 0 3 5 0 0 0

2002 103 1 2 2 0 0 3 1

2001 91 2 5 2 3 0 0 0

2000 130 2 0 0 1 0 0 0

Sum 1147 36 69 60 44 10 10 3

Total number of failures

232 (100%)

36 (15,5%)

173 (74,5%) 23 (10,0%)

Failures per the number of launches

20% 3% 15% 2%

So, space debris are composed, in particular, of SC with failed blocks of onboard

equipment but with healthy propulsion system and of SC with healthy onboard equipment but

which cannot perform nominally due to fuel depletion. The end of useful life of a SC due to

fuel depletion is a typical situation for high-altitude satellites, and in particular, for

telecommunication GEO satellites. For example, the Kepler spacecraft (aimed for search of

exoplanets) stopped its work because of fuel depletion [9]. Spent satellites become hazardous

space debris, because an uncontrolled spacecraft may change its position in orbit due to

perturbing factors.

Figure 1 Statistics on root causes of SC onboard equipment [8]

The possibility of life span recovery of a SC in automatic regime has not yet been

implemented, because by now the costs for repairs of a SC with limited service life was found

to be comparable or even exceeding the cost of putting a new spacecraft into service. Until

recently, M&R problems were solved only by manned spacecrafts. One should mention here

the fantastic repair operation of the Salyut-7 orbital station in 1985 and maintenance

operations of the Hubble Space Telescope using Space Shuttles in 1993--2009. Realization of

a project for automatic HRSDM (Hubble Space Telescope Robotic Servicing and De-orbit

Mission) MRSC for servicing the Hubble Space Telescope was found to be unprofitable [10,

11]. At present, considering significant progress in robotic engineering and the appearance of

the so-called cyberphysical systems, the development of unmanned MRSC becomes more

feasible [12]. The first experimental mission of developmental verification of satellites

servicing by a robotic system was implemented in 1997-2002 within the Japanese project

Engineering Test Satellite VII (KIKU-7/ETS-VII) [13]. Another well-known project for

developmental verification of automated servicing is the Orbital Express mission, which was

implemented in 2007 by the Defense Advanced Research Projects Agency (DARPA) [14].

An increase in the nomenclature of services provided by a space segment of information

systems, an increase in demand of such service increase the risk of finance losses in case of

SC failures. For example, a failure in a navigation SC may result in finance losses of many

dozens of customers. In this regard, the return to service rate of SC becomes predominant. In

such conditions, a quick repair of a SC and recovery of its operational life become profitable.

When changing to groups of many spacecrafts, the degree of man-made pollution of the near-



Earth space increases, which requires the use of special spacecrafts for removing space debris.

In other words, no money on maintenance and repair spacecrafts results in money spend for

space debris control.

So, here one faces a complex relevant problem of creation of a unified space service

infrastructure involving the system of commercial operation, the M&R system for SC, and the

system of disposition of space debris. The components of this system (instruments, materials,

and performers) may be ground - or space-based.

2. ANALYSIS OF SC SERVICE PROBLEMS

Economical aspects of operations of SC optimal maintenance have been extensively studied

(see [15 - 18]). All such papers indicate the high degree of uncertainty in estimating the prices

of maintenance missions. The economics of space service is still in a formative stage.

However, at present, the complex of four problems of maintenance service for target SC by

MRSC was formulated pretty clearly [7].

2.1. Transport problem

The purpose of the transport problem is the transfer of objects and means of a service system

for a target SC in space. The principal maneuver here is the rendezvous of objects in orbit:

rendezvous of a target SC and the MRSC, rendezvous of the MRSC with space debris objects,

delivery of consumables to the target SC, etc. This type of maneuvers consists of long range

navigation maneuvers, short long range navigation maneuvers, maneuvers, and docking.

Particular transport problems for service of a target SC may include the orbit formation,

trajectory correction, transfer of a target SC to the place of repair (for example, to the orbital

station or to the Earth), and de-orbiting of a target SC into disposal orbits.

By using an MRSC one can when required execute an involved maneuver requiring large

fuel consumption, which saves the fuel of a serviced target SC [19, 20]. For example,

injection failures may result in the appearance of the target SC on an off-nominal orbit, whose

change is either impossible or involves excessive fuel consumption and shorter life of the

target SC. With the help of an MRSC one can recover such a target SC by transferring it to

the operational orbit. Space debris handling by transferring into disposal orbits with the help

of an MRSC is another example of the transport problem. The difference here is that in the

first example the rendezvous and docking is made with a controlled object, while in the

second example an object is non-cooperative [21].

2.2. Monitoring problem

The purpose of the monitoring problem is to acquire and process the information required for

servicing the target SC. In this problem, an MRSC can be used as an element of control of the

space and a diagnostic tool of an unhealthy target SC.

Particular monitoring problems may include the continuous monitoring of the near-Earth

space for operational evaluation and forecasting of hazardous situations on flight routes of

serviced target SC created by various objects and fragments of space debris; recognition of

space orbits, including the selection, identification, and determination of their target purpose;

visual inspection [22] and health assessing of serviced target spacecrafts in off-nominal

situations; formation and delivery of information to the mission control center (MSC) about

space objects, state, and changes in the space situation.

Solution of the monitoring problem may involve the solution of the transport problem for

close range diagnostic testing of a serviced target SC. Based on the results of the monitoring,

the MCC may take a solution about the SC repair or its transfer to a disposal orbit.



2.3. M&R problem

The purpose of the solution of the M&R problem is the quality assurance and recovery of the

target SC. Here an MRSC is used as a remote performer for maintenance and repair operating

in fully automated or telemetry controlled regime (from the Earth-based MCC or from an

orbital station). Particular M&R problems are the performance recovery of an unhealthy target

SC directly on the working orbit, for example, releasing of elements from their stowed

configurations, refueling, replacement of modules and separate equipment blocks.

Repair of an unhealthy target SC with the help of MRSC involves the solution of both the

monitoring and transport problems. A solution of M&R problems is most efficient in the case

when a SC is fit for servicing from the beginning (being equipped with the docking module

and admits a unit modular repair).

Considering the M&R spacecraft activities from the point of view of standard GOST

18322, one may single out the following basic provisions, for example, as this was done for

the ground power support equipment [23, 24].

Technical maintenance (TM) of a SC is the main preventive measure required for

assurance of reliable operation of the equipment between scheduled repairs and for reduction

of the total scope of repair activities. TM calls for the performance control of equipment,

keeping equipment in good working order, provision of scheduled technical inspections and

tests.

TM can be also unregulated, when the monitoring and control of operational regimes of

onboard systems is performed by means of traditional telemetry and remote monitoring and

control means within the onboard control complex of a SC in operation. All the pinpointed

failures are recorded for planning repair activities.

A regulated TM of the SC onboard equipment is carried out with the help of an MRSC

with given periodicity, which can be smaller than or equal to that of the routine repair of

smallest scope. This type of TM is realized in the form of scheduled technical inspections,

checkouts, and tests, which may reveal operational defects (for example, damage of surfaces

by meteoroid particles) and which may result either in a failure or equipment failure; they also

refine the composition and the scope of activities to be fulfilled under a successive repair. The

deviations from the normal state of equipment, as detected during a scheduled TM and which

do not call for immediate refurbishment, should be formalized for repair activities planning.

The periodicity of a regulated TM may be equal to that of the planned orbit corrections

(similarly to ISS orbital corrections conducted by cargo ships). In this case, TM is aimed at

saving the fuel of the onboard propulsion system or rejuvenation of an SC not equipped with

altitude control thrusters.

For some types of onboard equipment, a test can be provisioned with the aim of

monitoring the operational reliability of equipment in the period between two successive

planned repairs, timely detection and prevention of the occurrence of contingency situations.

The principal purpose of the SC repair is to restore the performance and life time of

onboard equipment, correction of failures and defects appearing in the course of operation or

detected during a TM.

A SC repair can be either scheduled (a routine or complete repair) or emergency. For SC

maintenance, an important thing is that under a schedule repair the SC acts as a cooperative

object for the repair performers of the SC. Under an emergency repair, the SC can be a non-

cooperative object, which increases the difficulty of docking with it. Depending on the

production importance of equipment, the effect of its failures on safety and stability of

engineering processes, a strategy for scheduled maintenance and repair activities is



implemented in the form of a regulated repair, a technical condition repair, or as their

combination.

A routine repair is performed in the process of operation for providing the health and

operational integrity of equipment up to the next repair. On this stage, inoperable units are

replaced, preventive actions are taken, and single faults are corrected.

The purpose of a full repair is the correction of failures and compete or nearly complete

(at least 80%) recovery of equipment life with replacement or reconditioning of any

equipment parts, including the base elements, by verification and regulation of repaired

elements of equipment in whole.

The most promising method of repair of onboard equipment of an automatic SC is the unit

modular repair, under which unhealthy components or units are replaced by new or repaired

ones. Such a repair method should be based on a scientifically grounded decomposition of

equipment into replaceable repair elements, determination of optimal replacement times,

formation of the product range, and establishment of the reserve of replaceable elements.

For a unit modular repair it is required that the SC be of block-modular type according to

a certain design-layout scheme according to the so-called open architecture as single modules

with a common interface. Up to now, such scheme was used only for manned space

complexes (Almaz, Salyut, Mir, ISS). However, one can also mention examples of heavy

telecommunication satellites of open architecture [25], as well as projects of modular

automatic SC implemented so far [26, 27].

Modules of onboard equipment can be made of separate blocks or as a cluster block, in

which each subsystem is a cluster embedded into the block body. Under the cluster approach,

one can replace not the entire block, but rather separate clusters that most frequently get out of

order. With such architecture it is possible to replace the required number of modules or

separate blocks in case they break down or become obsolete during the flight.

The configuration of blocks of onboard equipment designed for unit modular repair

should satisfy the following requirements.

1. The blocks of onboard equipment, which statistically break most often, are

manufactured as separate blocks with quick-release mechanical interface (the

docking unit) for automatic installation and removal of a block (see, for example,

the Kaber bracket used on the outer platform of the Japanese Kibo module on the

ISS [28]);

2. A block should be equipped with the electrical power transformer supplying the

necessarily voltage and current to onboard equipment after hooking to the SC

interface circuit.

3. A block should have an individual thermal regulation system (if required).

4. Accommodation of onboard equipment blocks with high failure probability should

have an unhindered access for dismantling and assembly operations.

5. A block should be equipped with a docking module that can be gripped by a

robotic arm and transferred to its place of installation.

It is clear that the SC onboard equipment and its accommodation satisfying the above

requirements calls for a unification approach, which is most efficient for a group of several

SC. Because of this, it seems most efficient to create serviceable systems of spacecrafts, for

example of GLONASS or GPS-type satellites, etc, which are produced in cooperation.

Another approach is the introduction of a united standard for interfaces of SC configuration

items, which is a matter for the future.



2.4. Disposal problem

The aim of the disposal problem is to reduce the man-made pollution of the near-Earth space.

Particular problems of the disposal problem are the de-orbiting of a target SC into disposal

orbits (using the MRSC main engine) or by equipping a disposable object with a thruster de-

orbiting kit (TDK) [29] and demounting of healthy blocks from disposable SC to continue

their use on a different SC.

A target SC is disposed either if its operation concludes or if it cannot be repaired. The SC

disposal calls for the solution of a complex of above service problems: the monitoring

problem, M&R problems (rendezvous with a disposable object and its capture, installation of

a thruster de-orbiting kit), and the transport problem for transferring the object into the

disposal orbit or to a place of processing.

The choice of design MRSC parameters is an actual task for the purpose of construction of

space service infrastructure. The aim of the present article is to give the analysis of mass

properties and find the design layout of a universal multipurpose inter orbital MRSC capable

of fulfilling the above tasks for a group of several target SC.

3. SURVEY OF MRSC ANALOGUES

Unmanned MRSC for solving the above problems have been designed for quite a long time.

In particular, in NASA the spacecraft service problems are dealt with by the special SSPD

subdivision [30]. A description of approaches to the SC orbital service problem for the period

up to 2010 can be found in the conference proceedings [31]. At present, the Restore-L

precursor servicing mission for automated service for refueling the Landsat 7 SC after 2020 is

being developed [32]. The spacecraft shall be made based on the Space Systems Loral SSL-

1300 bus with the launch mass varying in the range from 5500 to 6700 kg. American

company DARPA develops an MRSC for service of geosynchronous satellites on the base of

engineering solutions verified in the course of the Orbital Express mission. The mission is

aimed at solving service problems in 2020-2021 using a single MRSC [33].

The DOCTOR project [34] is aimed in particular at problems of replacement of SC blocks

(Orbital Replacement Unit, ORU) on geostationary satellites. Such approaches involve the on-

demand replacement of blocks (with an injection of an MRSC in case of a failure on a

serviceable SC) and replacement of blocks as required (involving an MRSC on duty equipped

with replaceable units on a service orbit until a repair is required). A prototype of an MRSC

of mass 2500 kg is considered; this MRSC is equipped with ion engines to deliver a modulus

of mass 260 kg. To supply the required amount of block, the project calls for launches of

small modules to an MRSC (the Piggyback Platform) as a piggyback payload for GEO

launches. Such MRSC can dispose a spent SC by transferring it to a disposal orbit. However,

the use of electric propulsion engines decreases substantially the response speed to off-

nominal situations requiring the repair of a target SC.

In the method of orbital maintenance of several spacecrafts, as proposed by the American

Space Infrastructure Services company [35], an automatic MRSC is used, which performs the

above service problems transferring during 2-4 years between 5 communication Intelsat

spacecrafts. For other servicing projects of similar satellites, the reader may consult the survey

prepared by Intelsat [36, 37]. The project of the MDA Corporation [38] is mainly concerned

with refueling satellites, for which purpose up to 2000 kg of propellant components is placed

onboard. The above prototypes of MRSC are designed for service of already operational

satellites, which were not designed initially for servicing: they are not equipped with docking

units and are non-cooperative objects, they are unfit for refueling or replacement of blocks.

The above features of a target SC drastically reduce the service efficiency.



More rational is the following approach to SC service proposed in Russia at NPO

Mashinostroeniya [39]. In this approach, one has an interacting system of target spacecrafts

and a servicing SC equipped initially with necessary units and systems for docking and active

maneuvers. Under this approach, spacecrafts are assumed to have standard interfaces and a

possibility of reallocation of equipment and power sources between the target SC in the

course of M&R by the unit modular method. For the purpose of disposal, an MRSC removes

healthy blocks and residues of fuel from a spent target SC and mates two or more unhealthy

target SC with the MRSC or between each other for subsequent de-orbiting.

Under this approach, it is assumed that an MRSC, which is in the same orbital plane with

a group of target SC, is a service center, onto which target spacecrafts will be docked using

controlled maneuvers for M&R activities. Once a target SC underwent service, it is de-mated

from the MRSC and transferred into the nominal orbit position by a controlled maneuver. The

MRSC executes a rendezvous maneuver only with an inoperable target SC for its repair or

disposal. For this approach, it is assumed that a target SC has a heavy weighted propulsion

system, which in turn reduces the relative mass of the payload, and hence, decreases the

efficiency of the target SC.

It seems more rational to equip an MRSC with small spacecrafts for service operations.

Such service spacecrafts (SSC), which can be accommodated on a single base block, should

be capable of solving the entire spectrum of the above problems. Such a scheme of

accommodation of several SSC on a base MRSC is known both for M&R problems [40, 41]

and for space debris disposal problem [42, 43].

However, in the available studies the principal energy-intensive rendezvous dynamical

operations with the target object are performed by the base MRSC, which implements the

increment of the principal fraction of the delta-V budget, and hence, the fuel consumption. In

turn, an SSC executes only maneuvers near the target SC requiring small fuel consumption.

Such allocation of functions may prove insufficiently efficient from the point of view of the

MRSC mass structure. It seems more rational to construct an MRSC as a multi-stage system

to save fuel.

4. A TWO-STAGE MRSC FOR SERVICING A GROUP OF

SATELLITES

We first consider the mass MRSCM of a single-stage MRSC aimed at multi objective

maintenance of a target SC requiring repair. Assume first that the mission involves long range

navigation maneuvers, short range navigation maneuvers, maneuvers, and docking, as well as

the MRSC de-orbiting after the completion of activities.

In this paper, we consider in detail only long range navigation maneuvers. We assume that

the mass of the payload equipment on MRSC (involving the power supply, thermal control

and control systems, as well as robotic arms, equipment blocks of the target SC for

replacement, fuel for refueling the target SC, etc), as well as the mass of fuel, tanks, and

structures required for short range navigation maneuvers, orbital maneuvers, docking and

disposal constitute in sum some given quantity (the mass of the repair module M0).

A long range navigation maneuver can in simplified form be looked upon as a transfer

between circular coplanar orbits: the support orbit with altitude h1 (into which an MRSC is

launched) and the support orbit of the target SC with altitude h2. A rendezvous maneuver of

an MRSC with a target SC requires, for an optimal phase, the approximate delta-V budget

0201 RhRhV

, 1



where 0, R is the gravitation parameter and the average Earth radius, respectively.

The mass of fuel for the propulsion system with the specific impulse I0 is calculated by

Tsiolkovsky’s formula as follows

)/exp()());(1( 0IVVJVJMM MRSCT 2

The mass of the liquid propellant engine is denoted by MD. The mass of tanks and

structure are expressed in terms of the corresponding dimensionless weight coefficients as

MRSCKKTBB MgMMgM ; 3

The total mass of an MRSC for long range navigation is given by the formula

,)(

0

0Vz

MMMMMMMM D

KBTDMRSC

4

where the denominator reads as

)()()1()( KBB ggVJgVz 5

Assume now that for a group of satellites one should perform N equal maintenance

operations. The required total mass of payload to be injected from the Earth is

,)(

0

Vz

MMNNMM D

MRSCN

6

Let us consider the formula for the mass of an MRSC consisting of a base SC of mass

MBSC carrying N servicing SC (SSC) of mass MSSC. We assume that the base SC acts as an

upper stage to transfer the SSC stack to an intermediate orbit of altitude

h1 ≤ hα ≤ h2. This maneuver, as performed by the main liquid propellant engine of the base

SC of mass MDB, requires some part of the total delta-V budget

ΔV1= ΔV(1‒α), where the coefficient lies in the range 0 ≤ α ≤ 1. The altitude of the

intermediate orbit for the known α can be found by the formula

021 ))1((

RVV

h

, 7

where 01

1Rh

V

is the motion velocity along the support orbit.

On the intermediate orbit, the base SC is on the stand-by mode. If there is a need for

maintenance, one SSC is deployed from it and flies to the target SC using a liquid propellant

thruster of mass DBDS MM . This maneuver requires the delta-V budget VV 2 .

Assuming that the weight coefficients for the SSC are the same as for a single-stage

MRSC, the mass of an SSC is given by

,)( 2

0

0Vz

MMMMMMMM DS

KSBSTSDSSSC

8

and the mass of a base SC is given by



,)()(

)()(

))(1)(1()(

21

20

1

2

0

VzVz

VzMMMN

MgVJgMMVz

MMN

MMMMNMM

DBDS

BSCKBBSCDB

DS

KBBBTBDBSSCBSC

9

The positive mass difference

0 BSCN MMM 10

shows the efficiency of a two-stage MRSC both from the point of view of the reduction of

mass injected from Earth to orbit, and from the viewpoint of the reduction of the pollution

degree of space by spent MRSC.

Transforming, we get the following expression for the difference of masses, as defined in

terms of the mass of the repair module and the mass of the liquid propellant engine

DBDBDSDSDD MKMKMKMKNM )( 00 11

where the coefficients are given by the formulae

)()()(

)()()(

21

210

VzVzVz

VzVzVzK

, 12

)(

1

VzK D

, 13

)()(

1

21 VzVzK DS

, 14

)(

1

1VzK DB

15

With the same (for the two one- and two- stage MRSC under consideration) weight

coefficients, specific impulse, and the delta-V budget, we get constKD , while the other

coefficients depend on 10 (i.e., on the separation of the total delta-V budget between

the base SC and the SSC). By analytic transformations one easily verifies that the coefficients

)(DSK and )(DBK have an extremum with 2/1 .

In case when the mass of the main liquid propellant engine of the base SC depends

linearly on the number of SSC accommodated on it, for example, in the simplest case when

DSDB NMM , 16

we see that the gain in mass for a two-stage MRSC depends linearly on the number of

SSC accommodated on it

QNMMKKMKMKNM DSDBDSDD 000 ))(( , 17

besides, the expression for the unit gain in mass

DSDBDSDD gKKgKKQ )()( 0 18



shows that with the given weight coefficient 0M

Mg D

D the coefficient 0M

Mg DS

DS

should assume its smallest value. The function )(Q has a maximum with some max .

The gain in mass for a base SC can be used to accommodate additional equipment on it,

for example, equipment for electric power supply and testing of SSC, monitoring of a target

SC from the group, and to place the control system for the base SC. The mass of such

equipment AM enters the expression for the total mass of the base SC as follows:

,)()(

)()()(

21

20

*

VzVz

VzMMMMN

MMMMMNMM

ADBDS

KBBBTBADBSSCBSC

19

For the case DSDB NMM , equating to zero the difference of masses, we calculate the

maximal mass of additional equipment on the base block

*00

00 ))(

( QNMK

QNM

K

MKKMKMKNM

DBDB

DSDBDSDDA

20

The function )(* Q assumes its maximum value at some *max . The expressions for Q

and *Q are smooth functions on the interval 10 , and so their maxima can be easily

found numerically.

Consider an example of a two-stage MRSC carrying four SSC ( 4N ). A general view of

this spacecraft is shown in Fig. 2a. Figure 2b shows the separation of an SSC from the base

block. A general view of an SSC is given in Fig. 3. An SSC on the base block is in transport

configuration (Fig. 3a), after separation it is configured in the work configuration (Fig. 3b).

a b

Figure 2 General view of a multi-stage MRSC: 1 attitude control thrusters of the base block; 2 solar

arrays of the base block; 3 structure of the base block; 4 SSC accommodation



a b

Figure 3 General view of an SSC: a) in transport configuration; b) in work position: 1 manipulator for

docking; 2 replacementequipment block for a target SC; 3 tanks with fuel for refueling of a target SC;

4 pressurization tank; 5 attitude control thrusters; 6 liquid propellant engine of the main propulsion

system; 7 SSC body; 8 fuel tanks of the propellant system; 9 long range antenna; 10 solar array panel;

11 servicing manipulator no. 2; 12 docking unit (with the system for recharging and refueling); 13

short range antennas; 14 equipment bay; 15 servicing manipulator no. 1

5. NUMERICAL EXAMPLE FOR AN MRSC

Let us consider a numerical example for an MRSC aimed at servicing navigation GLONASS-

type satellites within the same orbital position. For such target SC the orbit altitude is about

200001 h km. Choosing 2002 h km for the altitude of the support orbit, we get the

required delta-V budget 3901V m/s. The specific impulse of liquid of a liquid propellant

engine on storable propellant components like UDMH/ nitrogen tetroxide is taken to be

31200 I m/s. According to statistical data, the weight coefficients for such SC can be taken

to be 05.0,07.0 BK gg . Assuming that the mass of the repair module is 5000 M kg and

the mass of the liquid propellant engine is 80DM kg, 20DSM kg we get the weight

coefficients 04.0,16.0 DSD gg . For these values, the graphs of the coefficients are shown

in Fig. 4.

Figure 4 Graphs of the coefficients )(0 K (solid line), constKD (the dash line), )(DSK (the

pointed line), )(DBK (the dash-dotted line)

A unit gain in mass is 005.1max Q with 524.0max . For four SSC, the gain in mass is

2010005.15004 M kg. The altitude of the intermediate orbit is 4959h km. The

0.2 0.4 0.6 0.8 1.0

1

2

3

4

5

6

K

α



maximum 549.0*max Q is attained with 727.0*

max . So, the base spacecraft, which carries

four SSC, can carry at most 1098549.05004 AM kg of additional onboard equipment.

As a consequence of this, the altitude of the intermediate orbit decreases to 2446h km.

Table 2 gives the mass properties of an SSC and a base SC for this example. Here, by a

payload (PL) one means the repair module (for MRSC and SSC) and the four transported SSC

(for the base SC). The table shows that the SSC mass with the two-stage scheme is relatively

small. This SSC can be made more maneuverable and efficient. This offers the prospects for

further mass-optimization of the repair modules.

Table 2 Mass characteristics of variants of maintenance SC

Parameter One-stage

MRSC

Variant 1 Variant 2

SSC Base SC SSC Base SC

Payload mass, kg 500.0 500.0 4889.7 500.0 7962.0

Mass of the liquid propellant engine, kg

80.0 20.0 80.0 20.0 80.0

Mass of the additional equipment, kg

0.0 0.0 0.0 0.0 1098.0

Mass of propellant components, kg

2290.3 587.5 4857.7 1024.65 3711.9

Mass of tanks, kg 114.5 29.4 242.9 51.2 185.6

Mass of the structure, kg 224.7 85.6 758.0 120.1 898.7

Total mass, kg 3209.4 1222.4 10828.2 1716.0 12838.2

6. CONCLUSION

1. The available MRSC and their future advanced projects are one-stage SC for long

range navigation to a target SC with the help of the main propulsion system. However,

this variant is not optimal with respect to mass, especially when solving service

problems for groups of target SC of artificial Earth satellites for communication or

navigation at high altitude orbits.

2. More advantageous is to use a two-stage MRSC consisting of a base SC

accommodating several SSC used for servicing satellites clusters.

3. The maximal gain in MRSC mass is obtained by analyzing long range navigation

maneuvers; it is obtained with the optimal breakout of the delta-V budgets between

the SSC and the base SC (the impulses are separated as approximately 1/2, the gain in

mass may depend linearly on the number of SSC). The gain in mass increases as the

mass of the SSC engine decreases.

4. Placing additional equipment on a base SC changes the optimal distribution of

impulses so that the major part of the impulse is given from an SSC. The altitude of

the orbit of the base SC decreases as the mass of additional equipment increase. An

estimate for the maximal mass of additional equipment that can be installed on a base

SC is given.

ACKNOWLEDGMENTS

The research was performed at Bauman Moscow State Technical University with the financial

support of the Ministry of Education and Science of the Russian Federation under the Federal

Target Program "Research and development on priority directions of scientific and

technological complex of Russia for 2014-2020". Agreement # 14.574.21.0146 (unique

identifier RFMEFI57417X0146).



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