Preliminary design of lunar high-resolution remote sensing micro-nano satellite

The development and utilization of lunar resources and the construction of lunar scientific research stations are important parts of China’s future lunar exploration plan. Aiming at the problems of China’s micro-nano satellites with low radiation resistance, lack of autonomous Earth-Moon transfer capability, and limited optical system volume and quality, a preliminary design scheme of a lunar remote sensing micro-nano satellite with autonomous Earth-Moon transfer capability is proposed. Using the analytical orbit average technology and transcription and collocation method to calculate the satellite’s Earth-Moon transfer orbit, the satellite can use the Hall thruster with large specific impulse and low thrust to realize the autonomous Earth-Moon transfer. The passive + active method is used to optimize the radiation resistance of the system, and the total radiation dose of some single machines can reach more than 25krad. A compact high-resolution multispectral camera is designed, and imaging simulation and verification are carried out. In the end, the satellite can achieve high-resolution imaging of the moon with a resolution of 0.2 m at an orbital height of 100 km to achieve the purpose of fine exploration of information such as lunar surface topography and geological structure.


Introduction
The moon, the earth's only natural satellite, possesses abundant unique resources and is a frontier and testing ground for humanity's journey into space [1].In recent years, lunar exploration activities have experienced a new surge due to the discovery of lunar water molecules, with major spacefaring nations worldwide proposing new lunar exploration plans.
China's lunar exploration project has been steadily advancing.The future Chinese lunar exploration plans include the Lunar Exploration Program Phase Four and the construction of an international lunar research station.Utilizing remote sensing technology for detailed surveys of the lunar surface will provide crucial scientific basis and technological support for future lunar resource development and utilization [2].
Due to their small size, lightweight, short development cycle, flexible launch options, and ease of constellation formation, micro-nano satellites have become an essential trend in aerospace development [3].Micro-nano satellites are also playing an increasingly important role in deep space exploration.

MATMA-2023
Journal of Physics: Conference Series 2691 (2024) 012043 IOP Publishing doi:10.1088/1742-6596/2691/1/012043 2 However, the current domestic and foreign lunar exploration satellite missions all rely on large-scale carrier spacecraft, which need the ability to transfer the Earth-Moon orbit autonomously [4].This is because the propulsion system is challenging to carry out long-term and high-thrust orbit transfer work due to the limitations of factors such as the volume and weight of the micro-nano satellite itself.Moreover, in the process of Earth-Moon transfer, satellites will face a strong space radiation environment, which will cause in-orbit failure of spacecraft, shorten the life of spacecraft, and even lead to mission failure [5].In addition, the limited size, weight, and power consumption of micro-nano satellites greatly restrict the improvement of the imaging quality of remote sensing cameras, and the problem of compact and lightweight optical systems needs to be solved urgently.
To sum up, the use of micro-nano satellites to conduct fine surveys of the moon is one of the development trends in the field of deep space exploration in the future.However, China's micro-nano satellites still have defects such as low radiation resistance, lack of autonomous Earth-Moon orbit transfer capabilities, and limited volume and quality of optical systems.Because of the above problems, this paper proposes a preliminary design scheme for a lunar high-resolution remote sensing micro-nano satellite with autonomous Earth-Moon transfer capability and conducts a preliminary analysis of the satellite imaging capability.

Satellite orbital design
The Earth-Moon transfer can be divided into the Earth escape segment, the Earth-Moon transfer segment, and the Moon capture segment.The satellite uses a small-thrust Hall thruster to complete the orbit transfer from GTO to the lunar polar orbit.In the orbit design process, it is necessary to consider that the small thrust needs to be continuously ignited to change orbit during the earth's ascent orbit, and it is also required to shorten the earth's flight time as much as possible to weaken the negative impact of the earth's radiation.
The orbits of the Earth escape segment, and the Moon capture segment are quickly calculated by using the analytical orbit averaging technique.The orbits of the Earth-Moon transfer segment are calculated by the transcription and collocation method.
The analytic orbital averaging technique is a fast algorithm for simulating many-revolution trajectories using low tangential acceleration and anti-tangential acceleration [6].The averaged changes of the orbital elements due to oblateness (J 2 ) perturbations are Where a is the semimajor axis, e is the eccentricity, ω is the argument of the periapsis, i is the inclination, Ω is the longitude of the ascending node, and r e is the Earth radius (r e = 1 R e = 6378.14km), is the mean motion.Let the satellite's orbital elements, running time, and quality be y=[x,t,m], then the calculation formula for the orbit information yi+k of the (i+k) circle is as follows: Where ∆y=[∆x ∆t ∆m] is the increment of the satellite's orbital elements after one revolution of the satellite.The approximate calculation formula is as follows: Where x A = [a,e,i,Ω,ω] T is r the averaged elements due to inplane thrust-acceleration perturbations and is the averaged elements due to J 2 perturbations.The transcription and collocation method transforms the low-thrust orbit optimization problem into a multi-variable and multi-constrained parameter optimization problem.This method avoids the fast integration of dynamic equations and has good convergence [7].
In the geocentric inertial system, considering the mass consumption equation at the same time, the satellite's orbital dynamics model can be expressed as: Where r=[r x ,r y ,r z ] T is the position vector of the satellite in the geocentric inertial system, v=[v x ,v y ,v z ] T is the velocity vector, u=[u x ,u y ,u z ] T is the thrust vector.
The transcription and collocation method uses the third-order Gauss-Labatto integral formula to discretize the system's differential equations and performance indicators, The specific calculation formula of the residual is as follows: The specific formula of the trajectory optimization problem is as follows: Where r 0 ,v 0 ,m 0 are the position vector, velocity vector, and initial mass of the spacecraft's initial state, r f and v f are the position vector and velocity vector of the spacecraft's terminal state, m p is the spacecraft's minimum remaining mass when the spacecraft maintains its maximum thrust from t 0 to t f .
The following assumptions are made in the orbit design process: Assume that the satellites in the Earth escape segment and the Moon capture segment are only affected by the Earth or Moon perturbation, and assume that the satellites are only affected by the Earth-Moon gravitational disturbance in the Earth-Moon transfer segment.
Finally, the moon trajectory of the satellite and the moon trajectory in the geocentric equatorial inertial system are shown in Figure 1.The total transit time is about 371.3 days, and the fuel consumption in the whole process is 24.8kg.This provides the possibility for 100-kilogram micro-nano satellites to realize autonomous earth-moon transfer.

Overall Design
The satellite has two main parts: the CubeSat and the propulsion module, with masses of 20kg and 60kg respectively.The two parts work together through the bus during the Earth-Moon transfer.After completing the Earth-Moon transfer, the CubeSat and the propulsion module are separated.After separation, the two parts realize inter-satellite communication based on the UHF/VHF band.The system composition diagram is shown in Figure 2. The CubeSat utilizes a centralized unregulated power distribution system powered by lithium battery packs and deployable solar arrays.Ground control employs an X-band spread spectrum transceiver, and X-band is used for data transmission, with GNSS information enabling autonomous positioning and operation management.Because of the harsh irradiation conditions faced by the satellite during the Earth-Moon transfer phase, a passive+active method was adopted to improve the radiation resistance of the system significantly.The passive method mainly uses anti-radiation shielding materials and reasonably increases the shell's thickness.Active methods include the method of using triple redundancy and Error Checking and Correcting (ECC) technology.
After the optimization of anti-radiation, the anti-radiation performance of the flywheel, solar sensor, AMU, which are shown in Figure 4-6, and other stand-alone machines has been greatly improved, and the total radiation dose tolerance has reached more than 25krad.This provides good anti-radiation performance for the satellite during the earth-moon transfer phase, and can greatly reduce the impact of space radiation on the satellite during the long-term transfer process.

Propulsion system design.
The Hall thruster generates thrust by dissociating the working medium under the action of an electromagnetic field and accelerating ionization to form a high-speed beam.It has a large specific impulse, long life, and mature development and is suitable as the main propulsion system for deep space probes.The Hall thruster is the main propulsion system in this mission to complete the Earth-Moon transfer from the GTO to the lunar polar orbit.It has the requirement of long-term stable small-thrust propulsion in the process of satellite earth-moon transfer.Its appearance and parameter are shown in Figure 7 and Table 1.

Compact High-Resolution Optical
System.An optical payload suitable for Micro-nano satellite deployment is designed to achieve high-resolution lunar remote sensing imaging to address the timeliness of key technology verification for lunar remote sensing and the limitations of payload-carrying platforms on Micro-nano satellites.The optical system design utilizes a coaxial two-fold mirror group with a rear-corrected structure to shorten the barrel length, reduce camera mass, and meet the design requirements of long focal length, large field of view, and wide spectral range for the optical system.High-resolution two-dimensional array imaging is achieved using time-delay integration CMOS photodetectors with small pixel sizes, offering the advantages of low power consumption, low cost, and strong anti-interference capabilities.The layout of the optical system and design specifications are shown in Figure 8 and Table 2. Through a compact optical design, the overall envelope of the optical system is smaller than φ216 mm × 256 mm while maintaining excellent imaging quality.

Imaging Simulation and Analysis
Volume compression of optical systems typically brings challenges, such as difficulty in secondary spectral correction and degradation in imaging quality.The designed optical system adopts a posterior correction mirror for chromatic aberration correction, and the imaging quality of this design is evaluated using static Modulation Transfer Function (MTF) and spot diagrams, as shown in Figure 9-10.Based on the sampling principle and the Rayleigh criterion, the system's Airy disk radius is smaller than 5 μm, and the image points can be adequately sampled and resolved by the detector within the diffraction limit.The MTF reflects the image clarity and comprehensively evaluates the image quality.The static MTF exceeds 0.216 at 118 lines per millimeter, indicating good imaging quality.
According to the imaging requirements of the lunar satellite, the lunar surface pixel resolution can be calculated based on the design parameters of the compact high-resolution multi-spectral camera: Where D pixel is the pixel size, f is the optical system's focal length, and H is the orbital altitude.At the lunar orbit's 100 km altitude, the corresponding pixel resolution is 0.2 m.
In summary, the designed Compact high-resolution multi-spectral camera has a small enough volume to meet the mission requirements, and has a good application prospect.

Conclusion
This paper proposes a preliminary design scheme for a lunar high-resolution remote sensing micro-nano satellite.Through simulation analysis, the possibility of autonomous Earth-Moon transfer of 100-kilogram-scale micro-nano satellites and high-resolution imaging of moon is preliminarily verified, which can be used as a design reference for autonomous Earth-Moon transfer micro-nano satellites.The high-radiation-resistant stand-alone and high-resolution multi-spectral camera involved can be applied to lunar micro-nano satellite missions.
The following work will further improve the satellite program, including optimizing the anti-irradiation of other subsystems and analyzing signal-to-noise ratio and modulation transfer function for imaging radiation quality based on the transmission model of the radiation characteristics of the lunar surface.

Figure 2 .
Figure 2. System composition diagram.The CubeSat adopts a standard 12U CubeSat structure consisting of ten subsystems: Structural and Mechanism Subsystem, Avionics Subsystem, Attitude Control Subsystem, Command and Data Handling Subsystem, Camera Subsystem, Navigation Subsystem, Thermal Control Subsystem, Power Subsystem, Hall-effect Thruster (HAN) Propulsion Subsystem, and Payload Test Subsystem.The CubeSat utilizes a centralized unregulated power distribution system powered by lithium battery packs and deployable solar arrays.Ground control employs an X-band spread spectrum transceiver, and X-band is used for data transmission, with GNSS information enabling autonomous positioning and operation management.

1 .
Attitude Control System.The Attitude Control Subsystem adopts the three-axis stability control system scheme of the whole star and zero momentum.The attitude measurement system includes sun sensors, star sensors, AMUs and gyroscopes, and the actuators include reaction flywheels and control moment gyroscopes.They jointly complete the attitude measurement and control tasks.The satellite control block diagram is shown in Figure3.

Table 2 .
Compact high-resolution multi-spectral camera design specifications.Layout of the optical system.