Analysis and Comparison of CubeSat Lifetime

Transcription

1 Analysis and Comparison of CubeSat Lifetime Li Qiao, Chris Rizos, Andrew G. Dempster Australian Centre for Space Engineering Research, School of Surveying and Geospatial Engineering, University of New South Wales, Sydney, NSW, 232,Australia Summary: The CubeSat satellite standard is a cheap and standardised means to gain access to space. The decay of satellite orbits is of considerable interest to CubeSat missions. This study considers a range of typical CubeSat satellites, sorted by the form factor from 1U to 6U. The tool used for the calculation of orbital lifetimes is the STK/Lifetime Tool. A number of factors are considered in the STK analyses, including atmospheric density, solar flux, orbit configuration, satellite mass, drag coefficient, and cross-velocity area. The results indicate that the CubeSat lifetimes are quite sensitive to the mass, drag area and atmospheric density model, but insensitive to solar radiation pressure. The results have implications for the design of CubeSat missions at both low and high orbit altitudes. Equation Chapter 1 Section 1 Keywords: CubeSat satellite, lifetime, orbital decay, atmospheric drag. Introduction The original CubeSat concept, now referred to as a 1U CubeSat, is a miniaturised satellite (1 1 1 cm 3 ) weighing less than 1.33 kg[1] which makes it a very affordable satellite system accessible for student projects as well as some traditional missions. Therefore, the CubeSat is of great interest to universities due to its tremendous educational benefits. Due to their affordability, the CubeSat satellites are favored by many universities for research missions in Low Earth Orbit (LEO)such as the project by California Polytechnic University and Stanford University [2] and the undergoing QB5 project[3].somewhat larger CubeSats, in 2U, 3U and 6U formats, could provide many of the functions now achieved by much larger spacecraft. An incomplete list on Wikipedia shows 1 CubeSat missions that have been sent to space[4].as a result, the issue of the space debris threat posed by CubeSats should be addressed. The inevitable decay of satellite orbits has limited the lifetime of most CubeSat missions flown to date from several days to months, due to their release altitudes as secondary payloads. As CubeSats are considered for more significant missions, it is of interest to know CubeSat orbit lifetimes at higher altitudes. This paper considers the orbit lifetime of CubeSat satellites sorted by form factor from 1U to 6U. The simulations are performed using AGI s STK lifetime tool. Types of CubeSat The significant difference between CubeSats and normal satellites is that the CubeSat structures are based on a modular frame cm 3 is the typical size of a 1U CubeSat. Other types of CubeSat satellites are available in 2U, 3U,4U and 6U in length by module integration, as shown in Figure 1. The number corresponds to the number of modules in the integrated CubeSat. Width and Depth are always ten centimetres. Other size could be custom made on request.

2 1U 1U 2U 3U 4U 5U 6U Figure 1 CubeSat satellites structural from 1U to 6U (credit to Orbit Lifetime prediction method Most of the historical CubeSat missions are on Low Earth Orbit (LEO), where the satellites have physical lifetimes determined almost entirely by their interaction with the atmosphere. We use the standard approach for calculating atmospheric drag given by the equations: Fd = 1 2 Cd(A m )ρv! (1) where Fd is the drag force; ρ is the atmospheric density; v is the orbital velocity of the satellite; A is the cross-sectional area perpendicular to the direction of motion; m is the mass; and Cd, the drag coefficient. The density of the atmosphere at LEO heights is controlled by selection of density model, satellite altitude, solar flux and particle precipitation from the magnetosphere and so varies with the current space weather conditions.. We assume a circular orbit for the remainder of the paper., Drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area usually called drag area, defined as the mean cross-sectional area of the satellite perpendicular to its direction of travel. To make an accurate lifetime estimate, a number of factors must be included in the model: orbit primarily altitude, satellite mass, cross-sectional area (normal to the velocity vector), drag coefficient, atmosphere model and solar flux. This paper presents an analysis of the magnitude of each of these factors, and attempts to estimate the uncertainty in CubeSat lifetimes. Lifetime prediction tools Numerous orbit propagation tools and atmosphere models are available for orbit lifetime estimation with the CubeSat community, such as AGI s STK software, the NASA Debris Assessment Software(DAS) and 1Earth s QProp lifetime estimation tools[5]. In this paper, only the STK 9. lifetime tool is utilised to predict the satellite lifetime. The analysis in reference [5] indicates that STK 9. provides an adequate prediction of lifetime. STK has lifetime commands that were executed for this paper through the Matlab connect feature. The lifetime module can be set up to perform calculations that predict the lifetime of

3 a satellite. User inputs include the satellite's physical characteristics as well as solar flux and planetary geomagnetic index information. In addition to the standard 1U CubeSat, there are three types of CubeSat satellites are frequently used: 2U, 3U and 6U. Less common form factors are 4U and 5U. All six types are utilised to show the lifetime variation with altitude. The various sensitivity studies use only the 1U,2U,3U and 6U form factors. Sensitivity of lifetime to design parameters In order to compare the results while varying individual parameters, the following standard set of standard parameters shown in Table 1 is always used: Table 1 CubeSat specifications used in analyses Envelope (H W L cm 3 ) and Form factor Envelope (H W L cm 3 ) Mass (kg) mass (kg) 1U U U U U U Drag coefficient 2.2 Cross sectional area W L Solar reflection coefficient 1. Area expose to sun H W Atmosphere mode NRLMSISE 2 Solar flux Orbit epoch 24 Oct 211 1::. CubeSat orbit type Sun synchronous Orbit Satellite Orbit Altitude SolFlx_Schatten.dat Figure 2 calculates CubeSat lifetimes for various form factors and altitudes. The numerical values of these lifetimes are given in Table 2.The expected result shown in Figure 2 is that as altitude increases, the lifetime also increases. The values are shown in Table 2 sorted by CubeSat form factors. When orbit altitude changes from 2km to 6km, the lifetime increases from several days to several decades. This has several implications: The lifetime of a CubeSat lower than 3km will be -1 days. A 2km CubeSat mission requires carefully design due to its abbreviated lifetime. The CubeSat satellites from 3 to 4km are a danger of collision with the International Space Station (ISS), because that the orbit of ISS is usually maintained between 335 km perigee and 4 km apogee. A CubeSat in this altitude band could last for.5 to 2 years. In contrast, the lifetimes of higher altitude satellites(> 6km) could exceed 25 years easily. CubeSat designers must comply with the requirement that the orbital decay lifetime of the CubeSat shall be less than 25 years after end of mission life [1]. Therefore a CubeSat mission for high altitude (>6km) should be considered with caution. For instance, the De-orbit device [6] could be mounted to comply with the 25- year requirement after mission termination.

4 8 Lifetime (years) vs. initial orbit altitude (km) U 2U 3U 4U 5U 6U Initial orbit altitude (km) Figure 2 CubeSat lifetime vs. initial orbit Table 2 CubeSat lifetime at different initial orbit altitude (d: days y: years) Altitude (km) 1U 2U 3U 4U 5U 6U 2 2 d 2 d 3 d 4 d 4 d 3 d 25 5 d 9 d 14 d 19 d 24 d 7 d 3 18 d 36 d 55 d 75 d 96 d 68 d d 122 d 178 d 237 d 32 d 214 d d 133 d 1.3 y 1.7 y 2.1 y 1.5 y y 2.1 y 3.1 y 4.2 y 5.7 y 3.7 y y 5.3 y 11.3 y 13.4 y 15.4 y 12.8 y y 14.4 y 23.2 y 27.5 y 37.2 y 25.9 y y 3.5 y 48.4 y 61. y 74.4 y 57.6 y Mass Though CubeSats have standardised geometry, the actual mass varies a little according to its manufacturing. For instance, although the nominal mass of CubeSat satellite is 1. kg, the actual value varies from 1. kg to maximum 2. kg, mostlyin the range of 1.33 to 1.5 kg. Similarly, the 6U CubeSat s nominal mass is 6kg, however actual masses are 8kg and may be up to 12-14kg, being limited by the launch dispenser. Figure 3 are the plots of CubeSat satellites lifetime as their mass varies. Again the standard parameter set is used. Apparently, mass affects lifetime especially in higher orbits. 1U Cube lifetime increases about 1.5 year per 1g at 6km. The increased lifetimes when CubeSat mass doubles are presented in Table 3. Take the 2U CubeSat for instance: its lifetime increases by 39 days at 3km, i.e. the lifetime increases nearly 2 days for each additional 1 grams. In the same way, a 6km 2U CubeSat will fly an additional 56 days for each additional 1 grams.

5 Orbit lifetime(year) U CubeSat lifetime (years) vs. CubeSat mass (kg) Altitude = 6km Altitude = 5km Orbit lifetime(year) U CubeSat lifetime (years) vs. CubeSat mass (kg) Altitude = 6km Altitude = 5km Orbit lifetime(day) Altitude = 4km Altitude = 3km Orbit lifetime(day) Altitude = 4km Altitude = 3km Orbit lifetime(year) U CubeSat Mass (kg) U CubeSat Mass (kg) 3U CubeSat lifetime (years) vs. CubeSat mass (kg) Altitude = 6km Altitude = 5km Orbit lifetime(year) U CubeSat lifetime (years) vs. CubeSat mass (kg) Altitude = 6km Altitude = 5km Orbit lifetime(day) Altitude = 4km Altitude = 3km U CubeSat Mass (kg) c) 3U d) 6U Figure 3 CubeSat lifetime vs. mass Orbit lifetime(day) Altitude = 4km Altitude = 3km U CubeSat Mass (kg) Drag area Table 3 CubeSat lifetime vs. mass and initial orbit altitude(d: days y: years) Form factors Mass (kg) Lifetime decrease due to edge length increase Min Max 6 km 5 km 4km 3km 1U y 2.9 y 167 d 18 d 2U y 8.1 y 287 d 39 d 3U y 7.8 y 41 d 61 d 6U y 6.5 y 365 d 55 d As previously mentioned, 1U CubeSat satellite nominal size is 1 cm 1 cm 1cm. Assuming the CubeSat flies along its height direction, the drag area is approximated by its frontal area. Figure 4 shows the decreased lifetime when the CubeSat W and D increase by 2 cm at different orbit altitudes. For instance, Figure 4 a) plots the 1U CubeSat lifetime when the W D is 1 1 cm 2,11 11 cm 2, and cm 2. Table 4 presents the decreased lifetime of CubeSats at certain altitudes with increasing cross-velocity area. For instance, at 6km a 1U CubeSat lifetime decreases by 2.5 years when its W and D increase by 2 cm. A 3U decreases by 15.2 years when its edge length increases by 2 cm. Thus, the lifetime of a CubeSat is quite sensitive to its drag area. And as mentioned before, this will depend on how its attitude is controlled (or is uncontrolled).

6 U CubeSat lifetime (years) vs. drag area (m 2 ) Altitude = 6km Altitude = 5km U CubeSat lifetime (years) vs. drag area (m 2 ) Altitude = 6km Altitude = 5km U CubeSat drag area (m 2 ) Altitude = 4km Altitude = 3km 3U CubeSat lifetime (years) vs. drag area (m 2 ) U CubeSat drag area (m 2 ) 6U CubeSat lifetime (years) vs. drag area (m 2 ) Altitude = 4km Altitude = 3km Altitude = 6km Altitude = 5km Altitude = 6km Altitude = 5km U CubeSat drag area (m 2 ) Altitude = 4km Altitude = 3km c) 3U d) 6U Figure 4 CubeSat lifetime vs. drag area U CubeSat drag area (m 2 ) Altitude = 4km Altitude = 3km Table 4 CubeSat lifetime vs. Drag area (y: year d: day) Form factors W D (cm 2 ) Lifetime decrease due to edge length increase Min Max 6 km 5 km 4km 3km 1U y -.7 y -49 d -6 d 2U y -.7 y -16 d -11 d 3U y -5.6 y -12 d -17 d 6U y -2.1 y -146 d -19 d It is important to realize that the cross-sectional area will be determined both by the CubeSat s design, and by how its attitude is being maintained. For example, if the CubeSat has one face maintained Earth-facing, another face will be perpendicular to the velocity vector. Drag Coefficient Drag coefficient Cd is generally assumed to be equal to 2, and is 2.2 for a typical spacecraft. For satellite in Cube sharp, Cd varies from 2. to 2.2[6]. Figure 5 displays the lifetime change with drag coefficient.

7 2 1U CubeSat lifetime (years) vs. drag coefficient 4 2U CubeSat lifetime (years) vs. drag coefficient Altitude = 6km Altitude = 5km Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km U CubeSat drag coefficient U CubeSat drag coefficient 3U CubeSat lifetime (years) vs. drag coefficient U CubeSat lifetime (years) vs. drag coefficient Altitude = 4km Altitude = 3km Altitude = 6km Altitude = 5km Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km U CubeSat drag coefficient c) 3U d) 6U Figure 5 CubeSat lifetime vs. drag coefficient Altitude = 4km Altitude = 3km U CubeSat drag coefficient As expected, lifetime is longer with lower drag coefficient. The changed lifetime values at different altitude are shown in Table 5. For instance, when Cd changes from 2. to 2.2, the 6U lifetime reduces for 3.7 years and 7 days at an altitude of 6 km and 3 km, respectively. Table 5 CubeSat Lifetime change when Cd increases from 2 to 2.2(d: days y: years) Form Lifetime change due to edge length increase factors 6 km 5 km 4km 3km 1U -1.3 y -.2 y -15 d -2d 2U -5.6 y -1. y -28 d -4 d 3U -1.9 y -.8 y d -6 d 6U -3.7 y -.6 y -73 d -7d Sun area and solar radiation reflection coefficient Solar radiation pressure has a perturbing effect on a satellite s orbit. This effect is most noticeable on satellites in high Earth Orbit satellites with large cross-sectional area. But CubeSats are small and normally fly in Low Earth Orbit, so the effect of solar radiation pressure is negligible in LEO. Cr is the coefficient of reflectivity which indicates the absorptive and reflective properties of the material and the susceptibility to incoming solar radiation. For CubeSats, the Cr value used is between.8-1.2, where 1 is the mean value. Figure 6 and Figure 7Error! Reference source not found. shows the lifetime varies with sun

8 area and solar radiation pressure coefficient, respectively. Here we have used the mass values MMMM, drag coefficient DDD, etc., etc. The figures show that the solar radiation pressure for CubeSat can be ignored in the lifetime prediction. 2 1U CubeSat lifetime (years) vs. sun area(m 2 ) 4 2U CubeSat lifetime (years) vs. sun area(m 2 ) Altitude = 6km Altitude = 5km Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km Altitude = 4km Altitude = 3km U CubeSat sun area (m 2 ) U CubeSat sun area (m 2 ) 3U CubeSat lifetime (years) vs. sun area(m 2 ) 6 6U CubeSat lifetime (years) vs. sun area(m 2 ) Altitude = 6km Altitude = 5km Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km 4 2 Altitude = 4km Altitude = 3km U CubeSat sun area (m 2 ) U CubeSat sun area (m 2 ) c) 3U d) 6U Figure 6 CubeSat lifetime vs. sun area 2 1U CubeSat lifetime (years) vs. solar radiation pressure coefficient 4 2U CubeSat lifetime (years) vs. solar radiation pressure coefficient Altitude = 6km Altitude = 5km Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km Altitude = 4km Altitude = 3km U CubeSat Cr (m 2 ) U CubeSat Cr (m 2 )

9 5 3U CubeSat lifetime (years) vs. solar radiation pressure coefficient 6 6U CubeSat lifetime (years) vs. solar radiation pressure coefficient Altitude = 6km Altitude = 5km Altitude = 6km Altitude = 5km U CubeSat Cr (m 2 ) Altitude = 4km Altitude = 3km c) 3U d) 6U Figure 7 CubeSat lifetime vs. solar radiation pressure coefficient 4 2 6U CubeSat Cr (m 2 ) Altitude = 4km Altitude = 3km Atmosphere density model The atmospheric density errors are the main source of unreliability in orbit lifetime predictions. The simplest way to model the atmospheric density is an exponentially decreasing density with altitude, but it is not accurate enough for a precise prediction. It is because the atmospheric density is very complex and exhibits spatial and temporal variations. For our simulation with STK software, six models were used of the ten atmospheric models available in STK : Harris Priester, Jacchia 7, Jacchia 71, MSIS 86, MSISE 9 and NRLMSISE 2. Figure 8 displays the lifetime change with atmosphere density model where the flux file is setup to use the schatten.data. Table 6 shows the maximum differences. It is quite obvious that the orbit lifetimes varies much with the atmosphere density model selection. It could be seen that the difference is up to 2 years for 6U CubeSat at 6km. Apparently, the question how to choose a correct model for CubeSat mission lifetime estimation raises up as long as the orbit lifetime is discussed. Among all the six models, Harris Priester model predicts the longest lifetime. The models belong to Jacchia (Model 2 and 3 in Figure 8) predict shorter lifetime than those belong to MSIS family (Model 4-6). Several references have analysis the these atmosphere model basis on their characteristics and properties [7][8]. MSISM 2 model is recommended as it is one of the last update models U CubeSat lifetime (years) vs. Atmosphere Density Altitude = 6km Altitude = 5km U CubeSat lifetime (years) vs. Atmosphere Density Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km 5 6 Density model for 1U lifetime caculation 1:Harris Priester 2:Jacchia7 3:Jacchia71 4:MSIS86 5:MSIS9 6:MSIS2 5 6 Density model for 2U lifetime caculation 1:Harris Priester 2:Jacchia7 3:Jacchia71 4:MSIS86 5:MSIS9 6:MSIS Altitude = 4km Altitude = 3km

10 U CubeSat lifetime (years) vs. Atmosphere Density Altitude = 6km Altitude = 5km U CubeSat lifetime (years) vs. Atmosphere Density Altitude = 6km Altitude = 5km Density model for 3U lifetime caculation 1:Harris Priester 2:Jacchia7 3:Jacchia71 4:MSIS86 5:MSIS9 6:MSIS2 Solar flux c) 3U Altitude = 4km Altitude = 3km 5 6 Density model for 6U lifetime caculation 1:Harris Priester 2:Jacchia7 3:Jacchia71 4:MSIS86 5:MSIS9 6:MSIS2 d) 6U Figure 8 CubeSat lifetime vs. atmosphere density model Table 6 CubeSat Lifetime change with atmosphere density model(d: days y: years) Form Lifetime change due to drag area increase factors 6 km 5 km 4km 3km 1U 9.4 y 5.5 y 15 d 2 d 2U 11.4 y 5.8 y 136 d 17 d 3U 19.2 y 4 y 219 d 23 d 6U 21.9 y 3.5 y 292 d 27 d Solar flux presents the solar and geomagnetic activity[9]. The simulations are performed to using the solar flux file models provide by STK, including SolFlx_Schatten.dat, SolFlx911_Schatten.dat, stkfluxgeomag.fxm, and stkfluxgeomag.5yr.fxm which are updated on September 211. These files contain predictions of solar radiation flux and geomagnetic index values produced by K.H.Schatten in ASCII format[1].during the simulation, the lifetime calculator was setup to use the MSIS2 atmospheric density model. Figure 9 displays the CubeSat lifetime changes with solar flux file. Table 7 shows the maximum differences. These numbers reflect the uncertainty caused by the solar flux. For instance, he 6U CubeSat lifetimes are 57.6 years,12.8 years,1.5 years and 68 days at 6, 5,4,3 km respectively(shown in Figure 8). Associated with the values listed in the last row, the uncertainty due to solar flux values is one the order of 5-25%. 1 5 Altitude = 4km Altitude = 3km

11 U CubeSat lifetime (years) vs. Solar flux file used for caculation Altitude = 6km Altitude = 5km U CubeSat lifetime (years) vs. Solar flux file used for caculation Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km Solar Flux file for lifetime caculation 1:SolFlx Schatten.dat 2:SolFlx911 Schatten.dat 3:stkFluxGeoMag.fxm stkfluxgeomag.5yr.fxm Solar Flux file for lifetime caculation 1:SolFlx Schatten.dat 2:SolFlx911 Schatten.dat 3:stkFluxGeoMag.fxm stkfluxgeomag.5yr.fxm 3U CubeSat lifetime (years) vs. Solar flux file used for caculation Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km 6U CubeSat lifetime (years) vs. Solar flux file used for caculation Altitude = 6km Altitude = 5km Altitude = 4km Altitude = 3km Solar Flux file for lifetime caculation 1:SolFlx Schatten.dat 2:SolFlx911 Schatten.dat 3:stkFluxGeoMag.fxm stkfluxgeomag.5yr.fxm c) 3U d) 6U Figure 9 CubeSat lifetime vs. solar flux Table 7 CubeSat Lifetime change with solar flux(d: days y: years) Form Lifetime change (uncertainty) due to solar flux factors 6 km 5 km 4km 3km 1U 2 y.3 y 9 d 1 d 2U 1.7 y.1dy 1 d 3d 3U 7.2 y 3.3 y 3 y 6U 7.3 y 3.2 y 36 d 4 d Conclusion Solar Flux file for lifetime caculation 1:SolFlx Schatten.dat 2:SolFlx911 Schatten.dat 3:stkFluxGeoMag.fxm stkfluxgeomag.5yr.fxm The orbit lifetime is of interest to CubeSat mission designers., However, its accurate prediction is challenging as there is much variability in the relevant parameters. In this paper, the STK9. lifetime tool was utilised to explore the CubeSat lifetimes. The simulation results indicate that: on the one hand, the orbit lifetimes are mainly determined by the primary orbit altitude, and have large uncertainties associated with the, atmosphere density model and solar flux prediction. One the other hand, though the CubeSat satellites have standardised design, its lifetimes have noteworthy differences with slightly change in mass and size. Also, the specific approach to attitude control will have a major effect on the lifetime. The results also demonstrate that lower than 34 km CubeSat missions are encouraged as their typical mission orbit lifetimes are on the order of several months. Thus they are unlikely Altitude = 4km Altitude = 3km

12 to contribute to the growing orbital debris problem. High attitude CubeSat satellites will become future space debris after their mission ends, threatening to other spacecraft, unless deorbit devices are included. As The only thing certain is uncertainty, the CubeSat mission designer should keep the uncertainties with a sustainable range to ensure the mission performs properly. Acknowledgments This research project is funded by the Australian Space Research Program on "SAR Formation Flying". The authors acknowledge the support of the Australian Centre for Space Engineering Research. A special thanks to the first author s colleagues Gordon Roesler for his support for the work described in this paper. References 1. CubeSat Design Specification Rev.12,.The CubeSat Program, California State Polytechnic University. Retrieved Oct 16,21, pp AMSAT Cubesat Information. assessed 4 Dec QB 5 project. assessed 4 Dec. 212, 4. WIKIPEIDA List of CubeSat 5. Oltrogge, D.L.,Leveque,K., An Evaluation of CubeSat Orbital Decay, Proceedings of the 25th Annual AIAA/USU Conference on Small Satellites, Logan,UT, USA, Aug 8-11, Reynerson, C., Aerodynamic Disturbance Force and Torque Estimation for Spacecraft and Simple Shapes Using Finite Plate Elements Part I: Drag Coefficient,. Advances in Spacecraft Technologies, Dr Jason Hall (Ed.), ISBN: , InTech, 211. pp ISO Standard 27852, Space Systems Determining. International Organization for Standardization. Geneva, Switzerland,29 8. Picone, J.M., Hedin, A.E., Drob, D.P., and Aikin,A.C., "NRL-MSISE- Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues", Journal of Geophysical Research, Vol. 17,No. A14, 23, pp Nassiz, B.J., Berry, K. and Schatten, K., Orbit Decay Prediction Sensitivity to Solar Flux Variations, Proceedings of the AIAA/AAS Astrodynamics Specialists Conference, Paper 7-264, Mackinac Island, MI,USA, August Analytical Graphics, Inc., Lifetime Tool, accessed 4 December 212