1 Introduction

As the number of orbiting objects around Earth is constantly rising, it is necessary to develop new strategies to manage the space environment. For this purpose, it is crucial to study the space objects in situ with a close observation for future in orbit-servicing missions that will allow to extend the operative life of functional satellites. This statement is driven by the fact that in first approximation, with an equal number of operational satellites, in order to reduce space debris, it is necessary to first decrease satellite traffic. This translates into seeking to maximise the operational lifespan of satellites as much as possible instead of simply substituting them; this approach could also be more sustainable from the economic and environmental point of view and it is already under investigation by the space industry [1]. Examples of in orbit-servicing missions are: Seeker, a 3U CubeSat used to complete autonomous mocking inspections [2] and AeroCube-10, a 1.5U CubeSat created to demonstrate precision satellite-to-satellite pointing [3]. Both missions were launched on April 17th, 2019. However the number of space missions involving CubeSats meant to inspect other satellites remains low. The aim of this work is to contribute to this field studying the preliminary design of a CubeSat inspired by SROC (Space Rider Observer Cube), a future mission designed by ESA in conjunction with Politecnico di Torino and Tyvak International, that aims to carry on inspections and docking manoeuvres with its mothership Space Rider (SR), a reusable robotic spacecraft. In fact, SROC will reach its operative orbit inside Space Rider cargo bay and then will be deployed by it [4, 5]. Currently, SROC has been approved and it is in the project Phase B. During the development of this work (March–July 2023), it was in pre-Phase A.

This project has been developed during a university class, and it started from the definition of the system requirements based on the mission objectives of performing inspection manoeuvres and automatic docking manoeuvres employing a CubeSat. Functional, performance, design and operative requirements have been formulated through a series of trade-offs following the workflow reported in Fig. 1. These have been particularly important for the following selection of components and sizing of the subsystems.

Fig. 1
figure 1

Work procedure followed to reach the preliminary design

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The CubeSat has two payloads, an imaging payload and a docking mechanism, supported by all the classical subsystems: OBC (On Board Computer), TTC (Telemetry Tracking and Control), ADCS (Attitude Determination and Control Subsystem), EPS (Electric Power Subsystem), TCS (Thermal Control Subsystem) and the Propulsion System. Moreover, since manoeuvres are a consistent part of the operative life of the CubeSat, it has been clear from the beginning that the orbit path would have been one the most important drivers of the work.

This has led to the preliminary design of the system that has been validated through a series of simulations using software like GMAT [6], for the orbit estimation; SYSTEMA [7], especially for the thermal simulation; MATLAB [8], again for the orbit and for the TTC, EPS and Propulsion System activities.

Furthermore, in case of failure the CubeSat shall comply with the ESA Space Debris Mitigation Compliance Verification Guideline [9]. For this purpose, many possibilities have been considered leading to the choice of a drag sail.

In the remainder of this paper, the discussion will proceed to cover the orbit description and manoeuvres. The central section will be dedicated to the design of subsystems, providing detailed descriptions for each.

2 Requirements and Preliminary Definition

Starting from the mission objectives of performing safe inspection and docking manoeuvres and transposing them into mission requirements, all the subsystems with their performance level have been defined.

Afterwards, the design and operational requirements have been considered to formulate an initial set of requirements. Since the CubeSat is inspired by SROC, it has some similarities that have been included in the requirements such as its 12U structure, an imaging payload and a docking payload. It has been established that Space Rider model orbit should be a 600 km dawn dusk 6 a.m. Sun Synchronous Orbit, its parameters are resumed in Table 1. Initial operations date June 21st, 2024 has been chosen to ensure a continuous in light environment.

Table 1 SR orbit parameters
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3 Inspecting Spacecraft Orbit Definition

The orbit must position SR in an illuminated environment to accommodate the camera operations within the visible spectrum and enable continuous inspection of SR surface. Another crucial consideration is maintaining an optimal distance between the camera and SR to ensure that images meet resolution requirements, avoiding excessive distance that could compromise resolution.

Three reference frames have been designed to define the dynamics of the CubeSat: the Earth inertial frame MJ2000Eq, for SR motion around the planet (Fig. 2a); the radial in-track crosstrack (RIC) frame centred in SR (Fig. 2a) and the CubeSat body-fixed frame to describe its relative orbit, with x-axis pointing along the line of sight of the camera (Fig. 2b, c).

Fig. 2
figure 2

a MJ2000EQ and RIC frame system representation. b CAD model of the CubeSat. c CAD model of the CubeSat

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The CubeSat will fly near SR, so precautions to avoid collisions have been considered. During the inspection phase (see Sect. 3.1) around SR, there will be a no-fly zone sphere of 100 m radius around SR geometrical centre. This has been derived from the International Space Station (ISS) 200 m keep out sphere [10], scaling by a factor of 2. This solution has been deemed acceptable as an initial approximation, particularly considering the smaller size of Space Rider compared to the ISS [11]. Another sphere of 50 m radius around SR geometrical centre has been considered to keep SR safe during the orbital transfers. To comply with these limits, transfer orbits and the inspection orbit have been modelled to not intersect the spheres as well as the burns are directed away from SR. In case of propulsive system malfunctions, the CubeSat flight path must be designed to move away from SR at every stage of the mission. Other non-nominal scenarios have not been considered. Moreover the CubeSat shall inspect the entire SR surface with a resolution of 4.8 mm (see Sect. 4.2.1). A distance between 100 minimum and 200 m maximum allows the resolution required from imaging payload (Fig. 3).

Fig. 3
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Mass loss of the CubeSat due to burn manoeuvres

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Given these constraints, a nonstatic orbit relative to SR has been modelled during the Inspection Phase (see Sect. 3.1): the Walking Safety Ellipse (WSE), an orbit derived from the Fly-Around one, defined in the RIC reference frame [12]. The geometrical centre of this orbit moves along the SR in-track axis, generating a spiral path. The WSE centre moves between the back of SR and its frontal geometrical point, in order to cover all its surface. The WSE has been modelled with a 200 m semi-major axis, 100 m semi-minor axis and an inclination of 28° with respect to SR reference frame. Other inclination configurations lead to a partial coverage of the surface, often leaving the front and the back of SR unreachable or too much angled for the camera sensor to have a clear image (SR nose ever pointing in-track axis has been considered). The WSE orbital period is the same of SR around the Earth.

The criteria based on which the WSE has been chosen are:

  • To satisfy the previous constraints.

  • In case of failure, the CubeSat shall not intersect SR flight direction, avoiding a collision; the CubeSat shall also advance continuously along the in-track axis of SR, moving away from SR and lowering the collision probability.

3.1 Mission Phases

The CubeSat will spend about 25 days in space, divided in six phases as shown in Tables 2, 3 and 4. The period of each phase, and by extension the total flight time in space, is based mainly on the time:

  • needed from the ADCS to reorient the CubeSat by 90° in the worst-case scenario (5.12 h) (see Sect. 4.5);

  • required by the imaging payload and TTC subsystems to, respectively, perform the scanning of the entire SR and to communicate with ground stations (see Sect. 4.2.1 and 4.4).

Table 2 Values of DeltaV, relative propellant mass consumption and burning time for the requested manoeuvres per phase. DeltaV and Spent Mass values for Inspection phase must be multiplied by 10 because they are referred to transfer manoeuvres needed every end cycle. All manoeuvres are performed by thrusters with a thrust level of 1.3 N
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Table 3 Initial and final positions and time of the CubeSat in RIC reference frame
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Table 4 Mission flight scheduling
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Below each phase is described:

  1. 1.

    Departure from SR: this phase includes the separation from SR and the orientation of the CubeSat for the first manoeuvre. The initial position considered for the analysis of the CubeSat is 2 m away from SR centre of mass, with a relative velocity of 1 m/s departing from SR. Initial velocity has been assumed in line with literature of Canisterized Satellite Dispenser (CSD) [13], which can eject a payload of 12 U with a DeltaV from 0.5 to 5 m/s.

  2. 2.

    WSE entering phase: this phase includes a first burn (Burn2a Fig. 4a), that in 3 orbits moves the CubeSat towards the coordinates of the WSE initial point, 200 m away from SR with a 28° inclination with respect to the SR RIC frame; then a second burn (Burn2b Fig. 4a) regulates the velocity to enter in the WSE.

  3. 3.

    WSE/Inspection–communication phase: the CubeSat spends about 583 h inspecting SR (about 96% of the total flight time), following this cycle eleven times:

    1. 1.

      moving forward in the WSE for 2 days, which correspond to 30 orbits around SR. Performing in total 5 orbits of visual inspection and 25 orbits of communication with Ground Stations (Table 4);

    2. 2.

      performing an orbital manoeuvre (comeback manoeuvre) (Burn3a and Burn3b Fig. 5a) to return to the WSE initial position, with a transfer period of 5 h (see Tables 3 and 4), 200 m away from SR.

      At the eleventh cycle only the first part will be executed and the CubeSat will start the following phase. Camera payload would scan 100% of SR surfaces during one cycle (without taking into account dark zones). The comeback manoeuvre is motivated by the CubeSat distancing from SR and the consequent loss of resolution of the images taken during the inspection. Another issue for inspection, and that justifies the comeback manoeuvres, is that SR has been considered ever pointing nose in flight direction (in-track axis), therefore a part of the surface is ever in dark, but SR could change attitude to support other payload missions [14], so dark surfaces could be enlightened and scanned.

  4. 4.

    WSE departure: the CubeSat is brought to a stationary point HP1 (Burn4a and Burn4b Fig. 6a), 100 m far from SR with 5 h transfer time. Another 5 h of parking in HP1 have been considered to make sure the CubeSat is ready and safe for docking. At this stage the no-fly zone sphere of 100 m radius around SR voids.

  5. 5.

    Hold Point approach: the CubeSat reaches a hold point (HP2) at 50 m from SR model (Burn5a and Burn5b Fig. 6a) in 2.8 h.

Fig. 4
figure 4

a Relative distance between the CubeSat and SR centre of mass of the orbit phases 1&2. b 3D visualisation in RIC frame of the orbit phases 1&2

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Fig. 5
figure 5

a Relative distance between the CubeSat and SR centre of masses during one cycle of the Inspection phase, the upper and lower black lines represent the boundaries of the WSE. b 3D visualisation in RIC frame during one cycle of the Inspection phase. Positions of burns are not shown because they would be overlapped but are reported in final (Burn3a) and initial (Burn3b) coordinates of Table 3 phase 3

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Fig. 6
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a Relative distance between the CubeSat and SR centre of masses of the orbit phases 4&5. b 3D visualisation in RIC frame of the orbit phases 4&5

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6. Rendezvous phase: the CubeSat arrives at a 2 m distance from SR through a bang–bang technique. The values for the burning time and DeltaVs for the rendezvous phase are just an estimation in case of a continuous manoeuvre as shown in Fig. 7. To increase the safety of the manoeuvre there are six hold points in which the CubeSat can be stopped in case of anomalies, so the time, DeltaVs and burning time of the manoeuvre could change in the real case.

Fig. 7
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CubeSat path in the Rendezvous phase

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3.2 Simulations

MATLAB and GMAT software have been used to simulate the dynamics of the CubeSat around SR and the cost in velocity (DeltaV) required to perform the orbital manoeuvres described above. The initial departure date of the CubeSat from SR has been set to the summer solstice (June 21st, 2024), chosen to reduce the umbra periods and increase the electric power generated by the solar panels. Initial CubeSat orbit parameters are shown in Table 5.

Table 5 Postdeployment initial CubeSat absolute orbit parameters with respect to Earth
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MATLAB simulations have been implemented using Clohessy–Wiltshire (CW) equations, described by Gaylor [15] and Naasz [16] and referred to SR RIC frame, to extrapolate the DeltaV needed for the CubeSat manoeuvres in a nonperturbed environment. Then the MATLAB results have been set in GMAT and propagated for 25 days with a RugeKutta89 propagator. JGM2 (Joint Gravity Model) with fourth-order harmonics has been chosen to define the simulation environment in GMAT: these harmonics are predominant during the period in which the spacecraft will be in activity. Therefore, a two-body dynamical problem has been implemented. In case of a possible de-orbit phase, the Solar Radiation Pressure (SRP) and the Drag Model have been considered.

In particular, the GMAT program inputs are:

  • the MATLAB DeltaV results;

  • the positions (Table 3) the CubeSat has to follow throughout the phases;

  • the transfer times (Table 4).

The last two inputs have been considered as constraints, the first instead can vary when the simulation runs.

Outputs of simulation are DeltaVs corrected of the environmental perturbations.

The results are shown in the following figures and in Table 2.

Figure 5a shows that the CubeSat passes through the no-fly zone during the Inspection phase (minimum distance about 90 m) and exceeds the 200 m of maximum distance. This might be due to gravitational harmonics, which lead the WSE to have a clockwise rotation around the RIC Z-axis (Fig. 5b). Furthermore, no corrective manoeuvres have been implemented for this phase. Regarding Fig. 5b, the WSE helicoidal form is not visible due to the low advance of its geometrical centre (0.269 m/orbit), which corresponds to the advance needed to cover the 8 m length of SR in 2 days.

The paths of the CubeSat are visible in Figs.4b, 5b, 6b and 7. Their features aim to maintain the minimum time for the transfer orbits of 5 h (phases 1, 2, 4, 5) due to ADCS attitude change worst-case scenario (see Sect. 4.5). All the manoeuvres have out of plane displacements and need to accelerate or decelerate the CubeSat, to maintain the SR safe zones. The CubeSat trajectory also aims to optimise the Inspection phase giving the imaging payload the required distance and time to totally scan SR, tuning the number and the geometry of orbits around SR per cycle. Note that phases 1, 4 and 5 are the most critical in terms of safety, because the CubeSat intersects the path of SR even if the CubeSat is moving away from SR. Other simulations have been implemented increasing the transfer orbit time, but these exceeded the total DeltaV of 11.0920 m/s storable in the satellite with ESA safety margins, due to overall tank and other subsystems dimensions, which could not fit in a CubeSat if the value was greater, with the propellant chosen (see Sect. 3.3). Phase 1 path, instead, is defined by the chosen initial conditions, changing them should result in other paths with possible trajectories not intersecting the SR flight trajectory.

The total DeltaV required to complete the mission is 5.5460 m/s. The remaining extra fuel stored could be used for orbital keeping manoeuvres or for the possible de-orbiting phase.

3.3 Propulsion System

The propulsion system allows the CubeSat to carry out the orbital manoeuvres described in Sect. 3.1 The DeltaV and the combustion time of each individual manoeuvre has been calculated using the CW equations (note that the orbit maintaining manoeuvres will be performed 10 times). The CubeSat is equipped with a propulsive system based on the cold gas thrusters. In particular, the B1 cold gas engine manufactured by Dawn Aerospace [17], which uses nitrous oxide as propellant, has been chosen for the following reasons:

  • It has small dimensions (108 × 79 × 40 mm);

  • It has a low power demand during activation and at nominal functioning as compared to other motors (14.4 W and 0.75 W, respectively);

  • Nitrous oxide is a self-pressurising oxidizer, so the propulsion system does not require a pressurising tank. The propellant in the tank will be at a pressure of 60 bar and will have an operating temperature between 0 °C and 25 °C (liquid phase);

  • It has a minimum total impulse of 0.005 Ns;

Following the ESA directives on safety margins for orbital manoeuvres, using a safety coefficient of 2 [18], the required mass of propellant has been estimated to be 0.3 kg together with a tank volume of 729 cm3.

The CubeSat has been equipped with 3 motors as shown in Fig. 8. This configuration has been designed in order to:

  • do not apply moments to the body during injection (assuming assembly without misalignments), because the nozzles are aligned with the CubeSat inertia principal axis;

  • have the camera pointed towards SR during the rendezvous phase and therefore have injections only in the relative x–y orbital plane.

Fig. 8
figure 8

Representation of the three cold gas thrusters and the fuel tank (on the right)

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During all manoeuvres (except for rendezvous), only the negative x axis thruster is utilised. Directional adjustments are accomplished using the ADCS prior to engine ignition. For the rendezvous phase, both the aforementioned engine and the one along the y axis are employed. The secondary engine along the x axis is redundant, in the event of the first engine's failure, resulting in altered rotation angles required by the ADCS. During the rendezvous phase, from the results obtained from CW equations, the required DeltaV adjustments necessitate only the first engine along the x axis and the one along the y axis. The spacecraft approaches in increments of 10 m during the rendezvous phase, pausing after each step to ensure safe approach. Therefore, engines are switched on twice during each step: once to initiate movement and again to halt.

4 CubeSat Design

In this section an overview of the preliminary design of the CubeSat and its subsystems is presented.

4.1 External Frame

The CubeSat has the standard dimensions of a typical 12U CubeSat with a mass of 16 kg. The skeleton of the external structure is made of Aluminium 6061, closed by graphene panels. Two other panels are added to the internal structure to create different zones inside the satellite and facilitate the storing of the components.

4.2 Payloads

The satellite has two payloads: optics plus the detector for the VIS (visible) imaging payload [19], that fits 2U and a partially external docking mechanism, whose dimensions are 1U.

4.2.1 Optics and Detector for the VIS Imaging Payload

The imaging payload has been designed in order to guarantee a resolution of 4.8 mm per pixel, as a compromise between the precision given by the ADCS pointing and the desired coverage area. The 150 mm Techspec lens [20] has been chosen considering the following parameters:

  • focal length: the selected lens has a focal length of 143.3 mm that fits 2U together with the detector;

  • field of view: the selected lens has a horizontal field of view of 5.36°, a vertical one of 4.03° and a diagonal one of 6.68° necessary to reach the desired resolution;

  • observable wavelengths: it has been stated that the imaging payload must take images in the visible bandwidth since the main goal is to observe the surface of SR.

Also the presence of a shutter is needed to avoid the saturation of the camera every time it is directed toward the Sun.

As concerns the camera sensor there were mainly two possibilities: a CCD (Charge Coupled Device) sensor and CMOS (Complementary Metal Oxide Semiconductor) sensor.

It has been decided to integrate a CMOS sensor, since the CCD has a higher power consumption (three times the CMOS sensor) and a high thermal noise generated which implies the need of a dedicated thermal control.

Consequently, to choose the camera, the compatibility with the lens has been considered as well as the presence of a CMOS sensor with the fewer number of pixels among the commercially available to not reduce the resolution given by the lens. Moreover, since SR is mostly black and white, the camera could be monochromatic, so the weight of images would be lower. The camera should also occupy not more than 0.5U, so at the end the camera M 2590 from Teledyne Dalsa [21] has been chosen as the best trade off.

Because the goal of the mission is to take as many images of SR as possible in order to cover the entire area and so to recreate its surface, the activation of the imaging payload has been designed as follows: knowing that the CubeSat will perform 30 orbits around SR during an inspection phase, only 5 orbits (the first one, the 10th, the 15th, the 20th and the 30th) are active for images acquisition. During the first orbit, the spacecraft will be precisely aimed at SR centre. Subsequent orbits will undergo a slight shift of ± 2 m from the centre, a margin necessitated by the ADCS accuracy. This adjustment enables image acquisition exclusively during the specified orbits, optimising resource utilisation without requiring the use of all available orbits. During each designated active orbit, a total of 6 photos will be captured across SR velocity, resulting in a cumulative data volume of 318 Mbit. This calculation has been derived based on the camera specifications, which include a resolution of 5.30 MegaPixels and a pixel depth of 10 bits in the worst-case scenario:

$${\text{data volume}} = {\text{resolution}} \cdot {\text{pixel depth}} \cdot {\text{number of photos}} = 318\,{\text{Mbit}}$$

This data will subsequently be transmitted for download. Once again, this decision was purposeful, with the aim of minimising the volume of data to be transmitted to Earth. This consideration is particularly crucial given that the communication channel utilised is the UHF, as detailed in Sect. 4.4.

4.2.2 Docking Mechanism

The docking mechanism has been considered as a black box. It has been designed to comply with the given constraints: it occupies 1U, it consumes 1 W during the entire mission and 2 W during the docking manoeuvres and it should be switched on automatically at a 2 m distance from SR. It has been assumed that there are some proximity sensors for the docking and a NavCam for proximity operations [22, 23].

The CubeSat and SR configurations and attitudes have been considered as known through information coming from the Ground Stations (GS). During the approach phase, the CubeSat has been designed to maintain a continuous contact with SR using GNSS (Global Navigation Satellite System) and the Attitude Control System to correct the misalignments with the body frame. The misalignments on each axis [24] are:

  • Yaw < 10°

  • Roll < 8°

  • Along x and z < 10 mm

Figure 9 illustrates the placement of the docking mechanism in relation to the camera and two visible thrusters. This positioning has been intentionally selected to align the docking mechanism on the same face as the camera, facilitating its utilisation during the approach to SR.

Fig. 9
figure 9

location of the docking mechanism, camera and thrusters

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4.3 OBC

The images are taken and then transferred to the OBC to be processed and then sent to Earth by the TTC antennas.

The DATAPATTERN DP-OBC-0402 [25, 26] has been chosen based on the requirements. The payload of the CubeSat is an imaging payload, so it requires a high level of computing power: it is important for the computer to be able to process and store all its data. For this reason, the COTS OBC chosen has a SD memory card of 8 GB. The external memory size has been determined during the requirement definition phase aligned with the TTC subsystem, striking a balance between data downlink capacity and the necessity for backup data storage in the event of transmission failure.

When considering the nominal orbit of the CubeSat, simulations using the software SPENVIS [27] have been performed, since one of the major causes of failures in an OBC are the Single Events. The simulations have considered the following parameters:

  • Mission duration: 30.0 days;

  • Account for solar radiation pressure “no”;

  • Account for atmospheric drag “no;

  • Orbit start: 21 June 2024 00:00:00;

  • Semi-major axis: 6978.14 km;

  • Eccentricity: 3.4024e−05;

  • Inclination: 97.8°;

  • R.asc. of asc. node: 0.1428;

  • Argument of perigee: 0;

  • True anomaly: 0.

In addition, for the calculation of the Single Event Upset (SEU) these parameters have been selected:

  • Particle spectra: AP-8 MIN trapped protons.

  • Spacecraft shielding thickness (Al equivalent): 0.55 cm.

  • Device material: Si (CREME-86);

  • Shape Sensitive Volume: 38.70 × 38.70 × 2.00 (μm3);

  • Heavy ion method: critical charge. Qc: 1.13E−02 pC.

  • Proton method: Bendel function. A = 4.88 MeV B = 7.09 MeV.

From the results of the simulations it has been possible to calculate that a SEU will occur once in about 80 days. Considering that single events are still quite unpredictable, the OBC has an error correction code and watchdogs for all the memories. Furthermore, in the requirements it has foreseen a “Safe Mode” which must be implemented in the flight code, which guarantees the basic survival functions of the satellite if an error that could seriously compromise the survival of the CubeSat occurs.

As far as the software is concerned, two valid options that could work on the microprocessor of the chosen OBC (e200 PowerPc) have been taken into account: eCos [28] and VxWorks [29]. The first one is likely to be the best option since it is open source.

4.4 TTC

The TTC communicates with ground stations using UHF band, through which the satellite also transmits telemetry data and receives commands. Downlink and Uplink Communication is not a trivial issue: a trade-off between almost all the subsystems is necessary to properly design the TTC. The selected communication band might seem unusual considering that images shall be downloaded but due to limitations on power budget, a less power expensive system is necessary.

A fundamental parameter to be determined for the dimensioning of the TTC is the downlink bit rate necessary for the accumulated data to be correctly transmitted in compliance with the requirements. To accomplish this task, a MATLAB code has been implemented using as main input the number of bits generated during a cycle of the Phase 3 corresponding to 30 orbits or two sidereal days (1.67686e + 09 bits); the entire mission produces 2.01 GB overall; as observable in the operation scheduling it was chosen to totally divide imaging activities and transmission ones to avoid overlapping operations problems. At this point, the bit rate required for the downlink can be derived with the following equation:

$$R\left( {{\text{bps}}} \right) = \frac{{{\text{compression factor}} \cdot \left( {{\text{n}}^\circ \,{\text{bit two days}}} \right) \cdot 1.3}}{{\left( {2 \cdot {\text{sidereal time}}} \right) \cdot \left( {{\text{link availability}}\,[\% ]} \right)}}$$

where 1.3 coefficient takes into account protocol efficiency and channel coding.

Due to limitations on power budget, it has been decided to use only one communication channel: the UHF band, in particular the frequency range between 434 and 438 MHz.

The system consists of 3 main elements highlighted in Fig. 10:

  • An ISISpace antenna [30] placed on the 4U face opposite the payload module.

  • An UHF Transceiver from Sputnix [31]; observing its elevated transfer data rate values selectable up to 57,600 bps, it represents the ideal candidate for the mission.

  • A redundant UHF Transceiver from ISISpace [32] with a limited data transfer rate up to 9600 bps.

Fig. 10
figure 10

From top to bottom: the ISISpace antenna, the Sputnix and the ISISpace UHF Transceivers

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For conservative reasons communication occurs directly with Earth, in this way the CubeSat is independent from SR simplifying the space segment and making it simpler, more reliable and able to operate also in case of problems of SR.

The huge amount of collected data requires to increase the ground visibility as much as possible.

The chosen ground stations are equally distributed around the globe (Fig. 11) and divided between existing ground station facilities, COTS telecommunications systems (GS Alenspace kits for UHF band [33]) and a series of antennas provided by the global SatNOGS Network [34]. The entire infrastructure provides an average link availability of 34,600 s per day (40.23% of a sidereal day); this value is conservatively simulated on GMAT considering a minimum elevation angle of 10°.

Fig. 11
figure 11

The chosen ground stations projected on a planisphere are located in Barrow, Alert, SvallSat, Hawaii, Oregon, Florida, Azores Islands, Padua, United Arab Emirates, Japan, Brasil, TrollSat, Malaysia, Camberra and Mc Murdo

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By combining the information presented above, the following diagram has been obtained (Fig. 12). A particularly interesting result is that only the Sputnix Transceiver with its highest downlink bit rate can transfer all the images without compression in a sidereal day. This proposed communication design constitutes only a first iteration and additional optimization studies can be foreseen to reduce communication time and the ground stations used.

Fig. 12
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Logarithmic diagram presenting different downlink bit rate as function of the compression rate and performances of the chosen transceivers

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4.5 ADCS

The CubeSat operates around SR, which is in a high inclination circular LEO orbit with an altitude of 600 km, so the orbital environment used for the disturbances evaluation of the CubeSat is the same. A preliminary calculation between gravity gradient, solar radiation pressure, atmospheric drag and magnetic field, highlights the dominant effects of the latter; in fact, the mean magnetic torque (Tm) acting on the spacecraft is determined by the product of the residual dipole moment (D) of the vehicle, measured in Ampere square metres \(\left[ {{\text{Am}}^2 } \right]\), and the Earth's magnetic field (B):

$$T_{\text{m}} = D \cdot B = 1.88 \cdot 10^{ - 5} \,{\text{Nm}}$$

The ADCS integrates data from onboard sensors for attitude determination and control. These sensors include the Inertial Measurement Unit (IMU) (STIM377H [35]), the three-axis magnetometer (MAG-3 [36]), and four two-axis sun sensors (NanoSSOC-D60 [37]). GNSS (Global Navigation Satellite System) [38] and GNSS antenna (piPATCH L1E1 [39]) have been chosen to determine the relative position of the CubeSat with respect to SR position. They are utilised primarily throughout the inspection phase, to reconstruct the state vector during the approach to SR.

An additional GNSS antenna (external from to the GNSS system) has been selected for redundancy purposes, due to the high criticality during the departure from SR and the rendezvous manoeuvres. For simplicity, the mission dynamics have been segmented into two distinct phases: the inspection orbits, characterised by stringent requirements, and the communication orbits.

Independently from the phase, at least one sun sensor and one magnetometer are active through the entire mission. The GNSS system has a key importance during inspection to evaluate relative position from SR, so it is active primarily during the inspection orbits, with the addition of the GNSS system and antenna. For approach and departure, the IMU and magnetometer are crucial for relative position determination.

The number of sensors is sufficient to always ensure information on the CubeSat attitude, both during illumination and eclipse phases, without ambiguity. Other types of instrumentations, such as horizon sensors, have been discarded since the continuous rotation around SR during the WSE phase causes fast changes in the horizon position.

Except during the eclipse period, at least one sun sensor has to be always functioning and pointing to the Sun: consequently sun sensors have been positioned on every edge of the CubeSat. Furthermore, the chosen orbital dynamics relative to SR aim to minimise the eclipse period as much as possible, estimated to be less than 1 min. The IMU platform and magnetometers become crucial in determining the CubeSat attitude during this brief interval. Possible attitude ambiguities will subsequently be managed by the on board software.

During the inspection orbits, precision is fundamental, leveraging the principle of gyroscopic rigidity provided by a Momentum Wheel (MW) [40] mounted along the z-axis of the CubeSat. This configuration ensures stability and precise pointing on the orbital plane relative to SR. The attainment of such stringent requirements necessitates the utilisation of high-authority actuators, which consume a considerable amount of power. Consequently, its usage is restricted. The main challenge that has been encountered by the ADCS involved harmonising performance requirements with mission-specific requirements within the size restrictions imposed by the facility. Indeed, the degree of accuracy required to achieve adequate observation while scanning the SR surfaces, even at the maximum distances achieved by the mission dynamics, necessitated a significantly larger momentum wheel. However, this solution would have resulted in a violation of the size limits set for a 12U structure. It has been then necessary to make a trade-off, decreasing performance requirements and containing alignment errors with other actuators, thus arriving at the current solution: with a maximum torque of 0.25 Nm, the momentum wheel (17 × 17 × 7 cm) maintains deviations within 2.19 m at 200 m of distance.

In the initial sizing calculations, the deviations account for the Worst-Case Scenario (WSO) conditions of the attitude control system, considering a pointing error requirement of Δθ = 0.35°. The MW is capable of achieving this precision by counteracting a constant disturbance of 10–5 operating at maximum speed possible. In addition, the phenomenon of nutation effect on the CubeSat axis was incorporated, resulting in a total error of \(\Delta \theta_{{\text{total}}} = 0.35^\circ + 0.25^\circ = 0.60^\circ\), which, through trigonometric relationships, translates into an uncertainty of 2.19 m at the maximum predicted distance.

During the communication phase, characterised by a reduced precision requirement, the use of the MW is not necessary. Instead, Reaction Wheels (RW) can be utilised to counteract satellite disturbances. Four reaction wheels (RW400 [41]) aligned on the three body axes, supplemented by redundancy and three magnetorquer (MTQ 400 [42]) handles wheel desaturation to guarantee continuous rotation. RWs are employed to maintain the CubeSat attitude, being \(T_{{\text{RW}}} > T\) magnetic field. The maximum momentum storage, accumulated over a quarter orbit (SR orbits), is \(h_{{\text{D}} } = 0.01924\,{\text{Nms}}.\) To address this, the magnetorquers are employed, generating a torque of 3.75·10−5 Nm, allowing for a desaturation period of 9 min every 24 min.

Approach and departure manoeuvres combine thrusters and reaction wheels to control the trajectory until the docking system activation. In this context, orbit manoeuvres and their corresponding control system have been outlined through qualitative considerations. Three main activation phases of the ADCS have been identified:

  1. 1.

    Insertion into the WSE: occurs post-deployment from SR due to post-deployment orientation uncertainty.

  2. 2.

    Re-positioning: this occurs during the transition from an inspection orbit to a communication orbit or vice versa, involving manoeuvres along the y and z axes of the CubeSat using a combination of RWs in speed mode and the MW.

  3. 3.

    Insertion into the approach manoeuvre towards SR: these manoeuvres involve a series of DeltaV applications by the propulsion system followed by re-alignments, akin to docking operations with SR.

Each phase is further broken down into specific actions:

  • Pre-manoeuvre orientation with the activation of MW.

  • Thruster activation for orbital transfer.

  • Attitude maintenance or manoeuvring during transfer is facilitated by RW or MW (if necessary).

  • Thruster activation for arrival positioning.

  • Post-manoeuvre orientation adjustments, if necessary, are managed using the MW.

This manoeuvring scheme is orchestrated by the satellite flight control software based on operational conditions and mission requirements. Accurate positioning is paramount for subsequent phases, particularly if the inspection phase follows. Therefore, efforts are made to maximise the utilisation of the MW, which, from initial assessments, allows for a maximum precision of 0.35°.

From conducted calculations, it is estimated that the maximum manoeuvring time in the Worst-Case Scenario (WCS), utilising RWs in speed mode for a 90° rotation of the CubeSat, is approximately 5.12 h. This estimation ensures a comprehensive understanding of the time allocated for manoeuvring phases.

4.6 EPS

The Electric Power Subsystem includes a set of body mounted solar panels [43] covered with a 125 μm Kapton layer to provide protection from erosion caused by atomic oxygen. The satellite has been designed to mount four 6U panels upon all the 6U faces of the system surface and two 2U panels on the 4U face opposed to the one which houses the camera, capable of producing a maximum power output of 21.72 W. In order to account for situations in which solar panels power output is not enough to sustain the satellite power requests (i.e. during the inspection–communication cycles, see Fig. 14), the subsystem has been integrated with a Li-ion battery of 80 Wh [44] which can be recharged:

  • When the power produced by solar panels is greater than the request from the other subsystems;

  • When the satellite is in idle mode.

In case of excess produced power, it can be damped by using an external resistance.

Considering that the CubeSat follows a dawn dusk orbit along with SR, as shown in Fig. 13 the illuminated surfaces are, referring to the body reference system already introduced:

  1. 1.

    Phase 1–2: the one normal to z axis;

  2. 2.

    Phase 3: the one normal to z axis and the one normal to x axis on the opposite side respect to the camera face,

  3. 3.

    Phase 4–5–6: the one normal to z axis.

Fig. 13
figure 13

Visual representation of the CubeSat illuminated surfaces: a during the inspection orbits, b during all the other phases

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The other faces (except the payload one) have also been covered with solar panels as a safety measure in case of deviations from ideal attitude caused by random disturbances or anomalies in ADCS actuators/sensors nominal functioning.

For what concerns the power budget, Fig. 14 shows the histogram containing both produced power and requested power for each phase and for one cycle of inspection–communication orbits as all cycles would have weighted down the chart.

Fig. 14
figure 14

Histogram for the power budget (represented only one cycle of inspection-communication orbits)

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This configuration has been reached after two previous iterations:

  • The first one used two deployable 6U solar panels with a mechanical joint to track down the sun’s position, but considering the type of the mission that would have been impractical.

  • The second one used a single 6U body mounted panel positioned on the 6U surface opposed to the camera one (supposing the camera positioned on a 6U face) combined with 2 deployable 6U solar panels connected to the body mounted one, but, as the CubeSat must dock with SR at the end of the mission, it was imperative that the deployable solar panel had a closing system, thus different solutions were explored, from electric motors, to multiple hinges to memory shaped alloys. The last one was the more practical solution, but tests are needed in order to assess their reliability.

4.7 TCS

The environmental analysis (both external and internal) has been conducted using SYSTEMA 8.4.2. The results indicate that a passive Thermal Control Subsystem (TCS) is adequate to ensure the maintenance of the operational temperature for individual components. In particular, the goals is:

  • to demonstrate that (1) the temperature range of the satellite surface shall be included between − 65 ÷  + 125 °C, in accordance with the LEO altitude of its orbit; (2) the temperature range of the internal components shall be included between − 5 ÷  + 45 °C.

  • to show the temperature variations of the internal components.

To verify the feasibility of the mission, before proceeding with the thermal analysis on SYSTEMA, a preliminary balance of the external surfaces has been carried out, with the following assumptions [45]:

  1. (a)

    Earth is a blackbody with a temperature of 290 K. The view factor between Earth and the CubeSat is 0.4.

  2. (b)

    The albedo factor is a = 0.34.

  3. (c)

    The albedo coefficient is k = 1.

  4. (d)

    The solar flux is JS = 1361 W/m2.

  5. (e)

    To evaluate the temperature in the worst hot case (WHC), the surface most affected by the solar radiation, measuring 3 × 2 units, has been selected.

  6. (f)

    To evaluate the temperature in the worst cold case (WCC) the surface less affected by the solar radiation, equal to 2 × 2 units, has been chosen. Both the albedo flux and the planetary flux have been assumed to be zero.

  7. (g)

    The SR is a black body with a temperature of 300 K.

  8. (h)

    Given that SR and CubeSat dimensions are nearly comparable, it has been determined that the most effective method to describe the radiation fluxes between the two is the following: SR has been treated as an infinite plate, while the CubeSat has been modelled as a regular rectangle inclined at an angle of β = 28° relative to the plate. Therefore, the view factor between the plate and the rectangle is [46]:

    $$F_{{\text{SR}}} = \frac{1 - \cos \beta }{2}$$

    The results are 0.94 for the front face, 0.186 for the back face.

  9. (i)

    The components internal generation, as specified in their datasheets, is 16.81 W in the WHC and 5.17 W in the WCC.

Consequently, the thermal balance equation can be expressed as follows:

$$q_{{\text{s}} } + q_{{\text{p}} } + q_{{\text{a}} } + q_{i } + \sigma \varepsilon A_{{\text{cubesat}}} F_{{\text{SR}}} T^4_{{\text{SR}}} = \sigma \varepsilon A_{{\text{cubesat}}} T^4_{{\text{cubesat}}}$$

From the solution of this balance, it appears that the temperature of the external surfaces is 78.35 °C in the WHC, while in the WCC the temperature does not drop below − 14.09 °C, in accordance with the imposed requirement.

The analysis on SYSTEMA has been conducted to verify the variation of incident power (solar, planetary, and albedo) on the external surfaces (especially solar panels, structure, and surfaces protecting the docking system and optics), and the resulting variation in external temperature and individual internal components.

Because of the limitation of SYSTEMA, internal and external components, as well as the various layers forming the panels, have been connected solely through radiation. The simulation has been conducted considering the entire satellite throughout each phase. The results presented in this paragraph pertain to the most critical nodes, where multiple components converge. Other nodes fall within the expected range. The satellite has been divided as follows: the solar cells, modelled one by one on the panel substrate as will be described later, have been divided into 1 × 1 × 1 meshes, the covers of the optics and other external surfaces into 3 × 3 × 3, as well as the internal components. A higher number of meshes would have caused the analysis to become excessively slow and onerous for the software. Each mesh represents a node; for the thermal analysis the central node has been chosen as the reference.

As mentioned earlier, the CubeSat orbits around SR during its inspection. Since replicating this motion accurately in SYSTEMA, where the possible kinematic configurations are limited, is challenging, it has been decided to replicate the trajectory of SR, extended by 15 m, which represents the average distance between the CubeSat and SR. The satellite framework, designed in SYSTEMA, features an Aluminium 6061 structure enclosed by carbon fibre reinforced polymer (CFRP) [47] panels coated with Kapton. FR4 printed circuit board (PCB) layers [48] have been mounted on these panels. To enhance the realism of the thermal conduction simulation on the solar panels, a 0.003 m graphene layer [49] has been applied as a Thermal Interface Material (TIM) between the FR4 and the Zerodur cover. Without the TIM, SYSTEMA has demonstrated temperature increases of up to thousands of degrees Celsius; therefore, solar cells have been selected as a coating. The distances between the individual layers are detailed in Table 6.

Table 6 Thermal and mechanical characteristics of the solar panels, and relative distances between layers
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Figure 15a displays the incident power on a single cell, as a reference node, resulting from solar, planetary, and albedo sources, with its trajectory corresponding to the temperature variation shown in Fig. 15b. It is evident that the temperature range remains within the bounds specified by the requirement (1).

Fig. 15
figure 15

a Power on a solar cell on the face 3 × 2U as a function of the simulation time. The maximum values are: 5.0290 W for the solar power, 0.6578 W for the planetary power and 0.1757 W for the albedo. b The temperature of the same cell falls within − 1.138 °C ÷  + 55.69 °C

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Table 7 shows the temperature range of the external bulk of the satellite, the docking mechanism and the glass that covers the camera: there is no need for active thermal control for these parts since every component falls within the requested temperature range.

Table 7 Temperature range of the main external components
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The temperature range of − 5 ÷  + 45 °C for the internal components is chosen based on the operational ranges described in the data sheets. In particular, the fuel tank temperature should not go above 27 °C, to avoid depressurization. To execute the measurement, a platinum resistance RTD thermometer with a resolution less than 0.5 °C has been implemented on the bulkhead. The internal temperature varies between 9.42 ÷ 13.62 °C. The analysis has demonstrated that it is necessary to cover the momentum wheel with a MLI (multilayer insulation) to keep the temperature high enough for the correct operation of the ADCS system, and to use white paint on the battery, to avoid overheating. Table 8 describes the thermal properties of the selected coatings. Figure 16 and Table 9 show the comparison between the required temperature range and the range measured via SYSTEMA.

Table 8 Properties of the materials selected for passive control [50,51,52]
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Fig. 16
figure 16

Results of the simulation. As seen from the diagram, the momentum wheel and the battery without passive control exceed, respectively, the lower and the upper limits

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Table 9 Numerical results of the simulation for the internal components
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4.8 Drag Sail

In case of docking failure, the CubeSat shall comply with the ESA Debris Mitigation Compliance Verification Guidelines and so it must come back to Earth in 25 years [9]. Possible variations on the guidelines might be considered in following and more detailed studies. In order to do that, many options have been taken into account such as using cold gas thrusters or electric thrusters to give the CubeSat the necessary DeltaV to deorbit. However, the best choice has proved to be a drag sail similar to one of the CanX-7 mission [53, 54]. It is made of 1 m2 Kapton coated both sides with aluminium; the dimensions of the storage module are 50 × 50 × 30 mm with a mass of 0.2 kg. As shown in Fig. 17 such a system guarantees a de-orbiting time of 5.5 years.

Fig. 17
figure 17

Plot of the de-orbiting time

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As it is a preliminary design, the purpose was to find a possible deorbiting method that, in future project developments, can be further explored and adapted.

4.9 Mass Budget

A mass budget was set for the study which includes all the subsystems mentioned above and the support and external structures of the CubeSat itself. This aspect is analysed in Table 10, including two margins: + 5% of the total mass and + 20% of the total mass plus the previous 5%. The margins considered took inspiration from the “Margin philosophy for science assessment studies” [18].

Table 10 Mass budget
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5 Conclusions

This paper showed the feasibility analysis of the mission starting from the definition of the system requirements to the conceiving of the CubeSat final design. Firstly, the workflow has been presented, followed by the definition of the orbit path and mission phases. This point has been particularly crucial since it has influenced many choices made for the final design, in fact one of the most challenging aspects of this work has been the definition of each subsystem characteristics, made through a lot of trade-offs, since every choice made for each of them had direct consequences on many others.

Another significant aspect has been the selection of components that could fit in a CubeSat, this has been particularly true for the imaging payload, since it has to take high quality pictures while being compact in dimensions.

The work has been concluded presenting briefly the strategy thought in the case of docking failure to deorbit the CubeSat within 25 years.

As this project is at the level of a feasibility study work, only a preliminary risk management was performed; however, the main risks have been identified, studied and discussed. The robustness of the design has been considered acceptable since we planned to procure the components as Commercial Off-The-Shelf (COTS) items. In a similar fashion, the external structure of the CubeSat is also sourced as a COTS product.

Considerable effort is needed to comply with the evolving regulations, which change frequently. For instance, the deorbiting requirement, initially set at 25 years when we planned this mission, has now been reduced to 5 years; further design iterations shall consider this new limit. The results presented in this paper will be useful for future missions developed with the goal of making in orbit servicing a reality.