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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
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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
V. Zelentsov, G.Shcheglov, V. Mayorova and T. Biushkina
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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-
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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.
V. Zelentsov, G.Shcheglov, V. Mayorova and T. Biushkina
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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
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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.
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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.
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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
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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
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,)()(
)()(
))(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
V. Zelentsov, G.Shcheglov, V. Mayorova and T. Biushkina
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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
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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
V. Zelentsov, G.Shcheglov, V. Mayorova and T. Biushkina
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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).
Spacecrafts Service Operations as a Solution for Space Debris Problem
http://www.iaeme.com/IJMET/index.asp 1516 [email protected]
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