Accepted Manuscript Temperature restrictions for materials used in aerospace industry for the near-Sun orbits Elena Ancona, Roman Ya. Kezerashvili PII: S0094-5765(16)31308-X DOI: 10.1016/j.actaastro.2017.09.002 Reference: AA 6453 To appear in: Acta Astronautica Received Date: 18 December 2016 Revised Date: 20 June 2017 Accepted Date: 3 September 2017 Please cite this article as: E. Ancona, R.Y. Kezerashvili, Temperature restrictions for materials used in aerospace industry for the near-Sun orbits, Acta Astronautica (2017), doi: 10.1016/ j.actaastro.2017.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT Temperature restrictions for materials used in aerospace industry for the near-Sun orbits I Elena Anconaa,b , Roman Ya. Kezerashvilic,d,∗ a Telespazio RI PT VEGA Deutschland GmbH, Darmstadt, Germany b Politecnico di Torino, Torino, Italy c New York City College of Technology, The City University of New York, Brooklyn, USA d The Graduate School and University Center, The City University of New York, New York, USA Abstract M AN U SC For near-Sun missions, the spacecraft approaches very close to the Sun and space environmental effects become relevant. Strong restrictions on how much close it can get derive from the maximum temperature that the used materials can stand, in order not to compromise the spacecraft’s activity and functionalities. In other words, the minimum perihelion distance of a given mission can be determined based on the materials’ temperature restrictions. The temperature of an object in space depends on its optical properties: reflectivity, absorptivity, transmissivity, and emissivity. Usually, it is considered as an approximation that the optical properties of materials are constant. However, emissivity depends on temperature. The consideration of the temperature dependence of emissivity and conductivity of materials used in the aerospace industry leads to the conclusion that the temperature dependence on the heliocentric distance is different from the case of constant optical properties [1]. Particularly, taking into account that emissivity is directly proportional to the temperature, the temperature of an object increases as r−2/5 when the heliocentric distance r decreases. This means that the same temperature will actually be reached at a different distance and, eventually, the spacecraft will be allowed to approach closer to the Sun without compromising its activities. We focused on metals used for aerospace structures (Al, Ti), however our analysis can be extended to all kinds of composite materials, once their optical properties - in particular emissivity - are defined. TE D Keywords: materials for aerospace, temperature restrictions, near-Sun orbits 1. Introduction 10 15 EP AC C 5 Materials in space are nowadays a key topic of research 20 for every aerospace industry. In fact, their characteristics and performances are extremely relevant for every feature of the mission, including the cost: the main objective is to obtain very light materials with great mechanical, thermal and optical properties. Aluminum has been for long 25 time a valid compromise for its weight and good characteristics, however the actual trend is to shift to carbon fiber and composite structures, and possibly in the future to combinations of plastics and various hybrid materials such as metal-matrix composites, that will greatly reduce 30 the weight of a spacecraft and also its launch costs. Indeed, carbon fiber has already replaced many spacecraft components, except for bulkheads that are still made from titanium, aluminum or other conventional metals and alloys because of the tremendous thermal and mechanical 35 I This paper was presented during the 67th IAC in Guadalajara. address: Physics Department, New York City College of Technology, The City University of New York, Brooklyn, USA. Tel.: 1 718 260 5276; fax: 1 718 260 5012. Email addresses: [email protected] (Elena Ancona), [email protected] (Roman Ya. Kezerashvili) ∗ Correspondence Preprint submitted to Acta Astronautica 40 demands. All materials have a well defined range of temperature in which their behavior is optimal. Out of these bounds, their properties’ degradation leads to failing performances. Temperature is one of the most considerable drivers, especially for near-Sun missions, with electromagnetic radiation and solar wind. When approaching the Sun, the increasing temperature could become unbearable, depending on the specific material characteristics. Moreover, the temperature reached by the spacecraft depends not only on the outer environment, but also on the spacecraft itself. In particular, the spacecraft’s temperature depends on electro-optical properties of its materials. However, the latter ones are function of temperature (see for example Refs. [2, 3, 4]). It is clear, then, that a better knowledge of the materials’ electrical and optical properties dependence on temperature could be the key to design properly a near-Sun mission. For example, to study this particular region, a Solar Probe mission has been proposed, that flies into the Sun atmosphere or corona [5, 6]. Approaching as close as 3 solar radii above the surface of the Sun, the Solar Probe will employ a combination of insitu measurements and imaging to achieve the mission’s scientific goals. The primary focus of a Solar Probe would be to address outstanding questions regarding the dynamJune 20, 2017 ACCEPTED MANUSCRIPT 60 65 70 2LSU N (1)110 P = 4πcr2 where LSU N = 3.842 × 1026 W is the Solar luminosity and c is the speed of light. However, any kind of device meant for a mission approaching so close to the Sun, would require extreme attention for temperature restrictions of its materials. Let us mention that, consideration of optical 115 degradation of materials due to proton and electron radiation for a near-Sun mission is very important, however we do not address this issue in the present study. This paper is organized in the following way: in Section 2 a brief overview of the most commonly used materials 120 in space applications is given, while Section 3 provides the key features of temperature dependence of a spacecraft material on heliocentric distance. Our analysis and results for metals are reported in Section 4, whereas Section 5 suggests plausible future developments of the study. Conclusions follow in Section 6. 85 90 EP AC C 80 RI PT 3. Temperature dependence on heliocentric distance It might be convenient to remark the difference between environmental temperature in space and the temperature of an object, such as a spacecraft, in space. 3.1. Environmental temperature in space Matter in space is extremely concentrated into celestial bodies. The space between them could be considered as a near-vacuum, where particles may be many miles apart. Hence, under outer space conditions, almost no energy is transferred “directly” because of the vast distances involved. As a result, radiation is effectively the only heatexchanging mechanism in most of the space environment. In fact, the average temperature of interplanetary space is 2.7 K, due to the cosmic microwave background. 3.2. Spacecraft temperature dependence on heliocentric distance An object in space radiates heat and receives heat radiated from other bodies. The result of this energy balance 2. Materials in space is that if the considered body radiates more heat than it receives it will cool down; on the contrary, if the incoming One of the principal design driver for a spacecraft is heat is more than that radiated, it will warm up. As the mass: the main challenge is to minimize it, and conse130 intensity of received radiation decreases with the square quently launch costs, without compromising reliability and of the distance from the energy source, a spacecraft apfunctionality. Moreover, a spacecraft must accommodate proaching the Sun will be exposed to higher level of electhe payload and its subsystems, satisfying the mounting requirements, and then support itself and its payload through tromagnetic radiation. Distance from stars and radiation exposure are the prime all phases of the mission, included the launch. In partic135 temperature determinants for an object in space. In fact, ular, not only good stiffness and strength properties are if one side of a spacecraft is exposed to direct sunlight required, but also oscillation and resonance frequencies of and radiation, while the other side is shadowed and facing structures must be taken into account. Hence, the design out into deep space, the spacecraft would suffer an extreme of spacecraft structures needs an extremely careful selectemperature differential which, if not sapiently contrasted, tion of materials based upon their strength, stiffness, dam140 could be dangerous and critical for the system survival. age tolerance, thermal and electrical properties, as well as It is clear then that the temperature of a spacecraft decorrosion resistance and shielding capabilities. For this pends on its optical properties: reflectivity, absorptivity, reason, the space sector has traditionally been a promoter transmissivity and emissivity. for the development and the application of advanced engineering materials. Our study has been conducted for the two most vastly 125 75 SC 55 used metals in aerospace industry: aluminum and titanium. In fact, considering their strength and density, it is clear why aluminum and titanium are the preferred materials for lightweight aerospace alloys. Titanium alloys are used where lighter aluminum alloys no longer meet strength, corrosion resistance and elevated temperature requirements [11], as aluminum features a melting temperature of 660 ◦ C, whereas titanium of 1668 ◦ C. Aluminum has a low density, good specific strength and it is easily workable. For its range of applicability it is also cheap and widely available. However, its weak spot is the low melting temperature. Titanium is more expensive but guarantees better performance in hostile environments due to its great corrosion resistance. Moreover, it can bear temperatures higher than 1000 ◦ C. M AN U 50 TE D 45 ics of the outer solar atmosphere: the solar corona, the formation and origin of the solar wind and the mechanisms 95 for storing and transporting energetic charged particles, as well as how the solar wind is accelerated, and also measurements of solar parameters. Solar sails, that takes advantage of the Sun’s electromagnetic radiation, have long been considered for a diverse range of mission applications:100 from a Solar Probe to interstellar travel [7, 8, 9, 10]. The dynamic efficiency of a solar sail as a propulsion device increases with its approach to the Sun. In particular, a solar sail can generate a high cruise speed if it is deployed as close to the Sun as possible, so that the force105 due to the solar radiation pressure is maximized. In fact, according to Maxwell’s electromagnetic theory, the radiation pressure P exerted on an idealized perfectly reflecting flat surface normal to the radiation at a distance r from the Sun is given by 2 SC RI PT ACCEPTED MANUSCRIPT 145 In fact, the solar electromagnetic radiation can be reflected, 170 absorbed or transmitted. Therefore, one can write: 160 EP where spectral hemispherical reflectivity ρ (λ, T ), absorptivity α (λ, T ) and transmissivity τ (λ, T ) are the radiative 175 or optical properties of the material that depend on wavelength and temperature [12]. The contribution of transmissivity can be neglected, as experimental data confirm it is a very small fraction (almost 2%) of the incoming solar energy flux. Indeed, once that energy has been absorbed, it can also be emitted from the surface, as a secondary process. From the Stefan-Boltzmann’s law, the rate of energy emitted from a surface at a certain temperature is 180 proportional to the fourth power of the temperature. In order to estimate the temperature of a body’s surface its effective temperature is commonly used. The effective temperature of a generic object is defined as the temperature of a black body that would emit the same 185 total amount of electromagnetic radiation [13]: AC C 155 (2) TE D ρ (λ, T ) + α (λ, T ) + τ (λ, T ) = 1, 150 Figure 2: Temperature dependence on the heliocentric distance for different values of emissivity. The graph shows the actual temperature of a generic body with defined albedo a = 0.5, for different values of emissivity. The solid curve represents a body with low emissivity ε = 0.1, whereas the dashed curve a body with high emissivity ε = 0.9. The actual temperature of a body with generic emissivity 0.1 < ε < 0.9 would be between these limits. M AN U Figure 1: Temperature dependence on the heliocentric distance for different values of reflectivity. The graph shows the effective temperature of a body with different values of reflectivity (albedo). It is the temperature of a black body (ε = 1) that would emit the same total amount of electromagnetic radiation. If the body has lower emissivity, its actual temperature will be higher of Tef f . The solid curve represents a body with low reflectivity a = 0.1, whereas the dashed curve a body with high reflectivity a = 0.9. The effective temperature of a body with generic albedo would be between these limits. Tact = Aabs L (1 − a) Arad 4πσεr2 1/4 , (5) where Aabs and Arad are the portion of the total area involved into absorption and radiation, respectively. Eq. (5) allows to evaluate the surface temperature of celestial bodies. The ratio Aabs /Arad is equal to 1/4 in the case of a sphere (such as a planet), since absorption is for a cross-sectional circular area and radiation is over the entire area of the sphere. The ratio is 1/2 in the case of a flat surface (such as a solar sail) since the object absorbs sunlight only on the face directed towards the Sun but radiates from the anti-Sun face as well. Note that the net emissivity of the planet may be lower due to surface or atmospheric properties, such as the greenhouse effect. When the planet’s net emissivity in the relevant wavelength band is less than unity (less than that of a black body), the ac- 1/4 L (1 − a) , (3) 16πσr2 where L is the star’s luminosity, a is the albedo, σ = 5.67 · 10−8 W m−2 K −4 is the Stefan-Boltzmann constant and r 190 is the distance of the object from the star, all in SI units. The luminosity of a star depends on its radius RS and 1 The albedo changes in the range 0 - 1 depending on the surface surface temperature TS : material, e.g. a = 0.06 for the Moon, which main surface component Tef f = 165 For what concerns the albedo, it is a reflection coefficient, defined as the ratio of radiation reflected from the surface to the incident radiation, so a = 0 for a perfectly black surface and a = 1 for a perfectly white surface1 . Fig. 1 shows the effective temperature dependence on heliocentric distance for different values of albedo. Eq. (3) is useful when the real emissivity of the specific body is unknown. However, it can be modified to account for the actual emissivity of a body ε, leading to more accurate results: L = 4πσRS2 TS4 . is basalt, a = 0.16 for Mars (iron oxide), a = 0.38 for Earth, and a = 0.70 for Jupiter (gas). (4) 3 ACCEPTED MANUSCRIPT where ϑ is the solar sail pitch angle, RE = 1AU is the Sun-Earth distance and φE = 1346W/m2 is the Solar irradiance at RE . 4. Temperature dependence on heliocentric distance for metals 230 215 220 TE D EP 210 Let us focus our attention on metals, largely used in the aerospace industry. In Section 3 a method for evaluating the surface temperature of a body has been provided: Eq. (5) can be applied to any material, once its constant emissivity and reflectivity are known. It requires as input the emissiv235 ity and reflectivity of the material, and gives as result its surface temperature. However recent studies show that reflectivity and emissivity also depend on temperature [15]. 4.1. Optical parameters dependence on temperature In Eqs. (3), (5) and (6) the optical coefficients have been considered constant and not variable with time or temperature itself. Although reflectivity dependence on temperature can be neglected, the same does not apply240 for emissivity, which is directly proportional to the temperature, as suggested by Parker and Abbott [18], because electrical conductivity is inversely proportional to T . The expression they found for the total hemispherical emissivity for metals is the following: AC C 205 Figure p 3: Total hemispherical emissivity of various metals as function of T /χ (T ), where χ is the material’s conductivity [16]. where χ (T ) is the electrical conductivity in Ω−1 m−1 , which is defined as the inverse of resistivity ρe (T ). As in Fig. 3 it has been shown with experimental results [16] that a very good approximation can be obtained considering only the first term in Eq. (8): s T . (9) ε (T ) = 7.66 χ (T ) M AN U 200 RI PT 1/4 L (1 − a) , (6) Tact = 273 εr2 where L = L/LSU N is the luminosity of a generic star in multiples of the Sun’s power and r is the distance between the body and the star in AU. As a result, the temperature of an object increases as r−1/2 when the heliocentric distance decreases, if all the other parameters are constant. For example, for the case of a solar sail, this formula can225 be written as [14]: 1/4 2 [1 − ρ − τ ] · φE · cosϑ · RE r−1/2 . (7) T = 2·ε·σ SC 195 tual temperature of the body will be higher than the effective temperature: Tact > Tef f . In other words, Tef f is the lower limit for the temperature of a body with a given reflectivity ratio, at a distance r from a star of luminosity L. The actual temperature of a body with a mean value of reflectivity coefficient (a = 0.5) is shown in Fig. 2, for two different values of emissivity. Eq. (5) is sometimes written in a more functional form2 : s T T ε (T ) = 7.66 + 10 + 8.99 ln χ (T ) χ (T ) 3/2 T T × − 17.5 , χ (T ) χ (T ) (8) The electrical resistivity of most materials changes with temperature. Usually a linear approximation is used: ρe (T ) = ρe0 [1 + αt (T − T0 )] ' ρe0 T, T0 (10) where αt ' 1/273 K −1 is called the temperature coefficient of resistivity, T0 is a fixed reference temperature (commonly room temperature) and ρe0 is the resistivity at temperature T0 . Values for electrical conductivity, resistivity and temperature coefficient of various materials can be found in literature. As χ (T ) is almost inversely proportional to the temperature, this means that ε (T ) ∝ T : s p ρe0 ε (T ) = 7.66 T · ρe (T ) = 7.66 T . (11) T0 Hence, by introducing emissivity dependence on temperature in Eq. (5), the temperature of the spacecraft varies as r−2/5 . If one considers the solar sail, Eq. (7) then becomes: 1/5 [1 − ρ − τ ] · φ · cosϑ · R2 E E s # r−2/5 . T = " ρe0 2 · 7.66 ·σ T0 (12) 4.2. Results for aluminum and titanium In this study the constant optical coefficient were taken from [16]. Experimental data for aluminum are ρ = 0.88 2 http://spacemath.gsfc.nasa.gov. 4 RI PT ACCEPTED MANUSCRIPT 250 and ε = 0.03, whereas ρ = 0.22 and ε = 0.19 for titanium. For aluminum the coefficient in (9) is 7.52K −1/2 Ω−1/2 m−1/2 , instead for titanium the same given in Eq. (9) was used. Considering a reference temperature of T0 = 293K, the re-270 sistivity for aluminum and titanium are ρe0 = 2.82·10−8 Ω· m and ρe0 = 4.2 · 10−7 Ω · m, respectively. Table 1: Temperature dependence of an object on the heliocentric distance for aluminum and titanium considering emissivity constant 275 or function of temperature itself. 255 260 265 TE D T [K] Ti T ∝ r−1/2 T ∝ r−2/5 ε = const ε (T ) 1485.7 1261.3 1050.6 955.9 857.8 812.8 742.9 724.4 664.4 662.6 606.6 616.0 561.6 579.1 525.3 549.0 495.2 523.8 469.8 502.1 EP T [K] Al T ∝ r−1/2 T ∝ r−2/5 ε = const ε (T ) 1476.1 1140.6 1043.8 864.4 852.2 735.0 738.1 655.1 660.1 599.2 602.6 557.0 557.9 523.7 521.9 496.5 492.0 473.6 466.8 454.1 AC C r [AU] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 of optical parameters for aluminum and titanium, influencing the multiplying factor. However in both cases it is clear that, considering the temperature dependence of emissivity (solid curve), the object’s temperature increases more slowly than in the case of constant emissivity (dashed curve), as the body approaches the Sun [1]. This should be taken into account for the design of any mission aiming to reach such distances. For example, the ESA’s Solar Orbiter thermal design is discussed in Ref. [17]. The Solar Orbiter mission is part of ESA’s Science Program. Its closest approach to the Sun is set to 0.23 AU, where materials would be experiencing a flux of 28000W/m2 (twice the Sun flux of BepiColombo going to Mercury). Thus, a Sun shield is required to minimize the absorbed energy. As we discussed, the temperature of the shield depends on the thermo-optical properties of its materials. In Ref. [17] a trade-off is conducted, to evaluate the best solution for this specific mission. Among metals, aluminum and titanium are considered, being materials with good resistance to high temperatures. The maximum operational temperature is 800 K for aluminum and 1470 K for titanium. Note that the difference between their operational temperature is 670 degrees. With the common approach that considers constant optical properties, one finds the reached temperatures at 0.23 AU to be 973 K for aluminum and 979 K for titanium. Results of our calculations, indeed, show that the reached temperature for aluminum and titanium would be 817 K and 903 K, respectively. Therefore, the delta in the temperature prediction is 156 degrees for aluminum and 76 degrees for titanium. If one considers the given operational temperature limits then, the spacecraft is allowed to approach closer to the Sun: 0.24 AU (instead of 0.34 AU) for aluminum and 0.07 AU (instead of 0.11 AU) for titanium. However, let us mention that also the ratio absorbed/emitted heat flux influences the temperature. For metals this ratio is typically high (α/ε varying between 0 and 5). The cited study on Solar Orbiter [17] shows M AN U 245 SC Figure 4: Dependence of material’s temperature on the heliocentric distance for aluminum (left) and titanium (right), both for constant and variable emissivity. Maximum operational temperature for aluminum is around 843 K, instead for titanium 1473 K [17]. 280 285 290 Dependence of temperature on the heliocentric distance for a case of constant emissivity and, conversely, when emissivity of the metal depends on temperature is shown in Fig. 4, and listed in Table 1. Let us notice that the two curves in Figure 4 for titanium cross each other, while for 295 aluminum it seems they don’t. The comparison of Eqs. (7) and (12) shows that not only the power of r is different, but also the multiplicative factor. If one will set equal to unity the factor multiplying the power function rn - where n is any real number -, it is clear that all power 300 functions will cross each other at r = 1. However, the crossing of the curves for aluminum occurs at r > 1, out of our figure field of view, while for titanium it occurs at r < 1. Such situation is due to the different values 5 ACCEPTED MANUSCRIPT 310 that only titanium wouldn’t reach its limit operative temperature. Therefore, a MLI (Multi-layer Insulation) with a front layer in Alumina-Boria-Silica (ABS) and titanium metallic foils was selected for the final design. A valid alternative to this would be a Carbon-Carbon based shield,360 also used for NASA’s Solar Probe, that reaches 1300◦ C [19]. Carbon-Carbon composites are obtained by composing carbon-fibers with other materials, such as graphite, which have a very high heat tolerance (up to 2000◦ C). 365 5. Future development 325 330 335 SC M AN U 320 Even though aluminum and titanium are the conventional materials for flight structures, graphite-fiber/polymerReferences matrix composite materials are the most probable candidates for the future of aerospace industry. Carbon-fiber370 [1] R.Ya. Kezerashvili, Space exploration with a solar sail coated by materials that undergo thermal desorption, Acta Astronautica composite materials are easier to shape and lighter than 117 (2015) 231–237. metals, with much higher strength to density ratio [20]. [2] J. C. François, J. Casset, G. Chassaing, P. Gravier, M. Sigrist, Significant weight savings (25 to 50 percent) could be Optical properties of ZrN as a function of temperature, Journal of Applied Physics 58 (1985) 3841. achieved through the use of polymer-matrix composites.375 [3] L. F. Jiang, W. Z. Shen, Q. X. Guo, Temperature dependence However, a great engineering effort is required to establish of the optical properties of AlInN, J. Appl. Phys. 106 (2009) confidence in their use. In fact, carbon-fiber’s performance 013515. and resistance to high temperatures depends on the com[4] D. Marla, U. V. Bhandarkar, S. S. Joshi, Models for predicting temperature dependence of material properties of aluminum, J. posite structure and baking technology. Standard epoxy380 Phys. D: Appl. Phys. 47 (2014) 105306. carbon-fiber composites that underwent proper baking fea[5] J. E. Randolph, Nasa solar probe mission and system concepts, ◦ ture resistance up to 70-100 C. If the material is required Advances in Space Research 17 (1996) 3–12. [6] W. Feldman, B. Goldstein, B. Tsurutani, Scientific objectives to stand higher temperature, phenol resins are used. These of a solar probe mission, Advances in Space Research 17 (1996) composites feature momentary resistance up to 500◦ C.385 41–47. Nevertheless, the production process is extremely delicate [7] E. F. Mallove, G. L. Matloff, The Starflight Handbook: A Pioand costly [21]. neer’s Guide to Interstellar Travel, 1st Edition, Wiley, 1989. [8] G. L. Matloff, Deep-Space Probes. To the outer solar system Our analysis could be easily extended to these materials, and beyond, 2nd Edition, Proxis Publishing, Chischester, UK, once their optical properties are known. Nevertheless, due390 2001. to the unicity of each composite material, experimental [9] Y. Guo, R. Farquhar, Current mission design of the solar probe values are required. mission, Acta Astronautica 55 (2004) 211–219. TE D 315 6. Conclusions 350 355 Within the standard approach the reflectivity and emissivity of materials used in aerospace industry are conserved400 as constant values. As a result the temperature of the material increases when the spacecraft approaches to the sun as T ∼ r−1/2 , where r is the heliocentric distance. In our approach we consider the temperature dependence of the405 electro-optical parameters of materials that have implicit dependence on the temperature through the temperature dependence of the electrical conductivity of metals. It is shown that the temperature dependence of the emissivity410 and conductivity leads to the dependence of temperature for the materials used in aerospace industry approximately as T ∼ r−2/5 with the heliocentric distance. The proposed study compares the temperature dependence on heliocen-415 tric distance for metals (aluminum and titanium in particular) when their optical properties are considered constant or function of temperature. For a near-Sun mission it is of crucial importance to understand as much as possible420 the behavior of the spacecraft materials, as the greatest AC C 345 EP 395 340 constraint will be the maximum temperature at which it can be fully functional and operative. In our study the temperature reached at 0.1 AU with variable emissivity is lower than when one assumes that the emissivity is constant, both for Al and Ti. In other words, the spacecraft could approach closer to the Sun than it was assumed before based on the consideration that emissivity of materials used in aerospace industry does not depend on temperature. However, note that the titanium graph shows an intersection between the two curves. This indicates that there is no common behavior and the study must be carried out with a complete set of the chosen material’s electro-optical parameters. RI PT 305 6 [10] A. Lyngvi, P. Falkner, A. Peacock, The interstellar heliopause probe technology reference study, Advances in Space Research 35 (2005) 2073–2077. [11] M. Peters, C. Leyens, Materials Science and Engineering, 1st Edition, Vol. III - Aerospace and Space Materials, EOLSS Publishers Co. Ltd., 2009. [12] Y. A. Çengel, A. J. Ghajar, Heat and Mass Transfer - Fundamentals and Applications, 5th Edition, McGraw-Hill Education, 2015. [13] A. E. Roy, D. Clarke, Astronomy: Principles and practice, 4th Edition, Taylor and Francis, 2003. [14] C. 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ACCEPTED MANUSCRIPT RI PT SC M AN U TE D EP AC C 425 [21] Dexcraft.com, Aluminium vs carbon fiber comparison of materials (2015). URL http://www.dexcraft.com/ articles/carbon-fiber-composites/ aluminium-vs-carbon-fiber-comparison-of-materials/ 7 ACCEPTED MANUSCRIPT RI PT Highlights • Temperature restrictions for materials in aerospace industry for near-Sun missions. • Consideration of the temperature dependence of emissivity. • The temperature dependence on the heliocentric distance goes as r • Different perihelion distances affordable: spacecraft can approach closer the Sun. • Focus on Al and Ti but analysis can be extended to other materials. . AC C EP TE D M AN U SC -2/5
