Total solar irradiance fluctuation effects on sailcraft-Mars rendezvous

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<ul><li><p>ffec</p><p>Solar sailing</p><p>secon</p><p>re ex</p><p>y op</p><p>ects.</p><p>type.</p><p>quantw-ecceacecraianceerformc Earththe a</p><p>sailcraft trajectory computations.</p><p>(1) Strange enough, for three-four decades of solar-</p><p>ured] forHissta-</p><p>tions on mountains of U.S., Chile, and Arabia, and by</p><p>prolonged measurement campaign carried out by Abbot</p><p>Contents lists available at ScienceDirect</p><p>journal homepage: www.else</p><p>Acta Astro</p><p>$ Paper presented at the sixth edition of the IAA Symposium: Realistic</p><p>Near-Term Advanced Scientic Space Missions, Aosta, Italy, 69 July 2009.</p><p>Acta Astronautica 68 (2011) 6446500094-5765/$ - see front matter &amp; 2010 Elsevier Ltd. All rights reserved.</p><p>doi:10.1016/j.actaastro.2010.01.010and his team can be found in [6].(2) The rst cavity radiometer, named HF after Hickey</p><p>Frieden, was switched on aboard the U.S. satelliteNIMBUS-7 on November 16, 1978. This satellite (the last</p><p>E-mail address: giovanni.vulpetti@fastwebnet.it1 IAA Member of Section 2.2 Retired, formerly at GalileianPlus s.r.l., Rome, Italy, Telespazio</p><p>S.p.A., Rome, Italy.means of new instrumentsnevertheless indicated toomuch high solar variations. An interesting synopsis of thisitems regarding the investigation of the so-named solarconstant before the space era, (2) to move on the spaceera, and (3) to dene the purpose of this paper precisely inthe context of a number of problems regarding realistic</p><p>(Italy) in the 19th century, C.G. Abbot (USA) measthe solar irradiance and its potential variability [5decades in the rst-half of the 20th century.measurementsthough performed from observationments of TSI coming from space satellites. It turned outthat large trajectory deviations can happen. In this paper,the author enlarges the case of the sailcraft-Marsrendezvous by an optimized multi-arc sail control. Beforethat, very briey, it is useful: (1) to report some historical</p><p>Several historical concepts, ideas and facts (from China,Europe, and United States) about the Sun, and the searchfor the solar objects affecting the Suns electro-magneticemissions are reported in [4]. During the industrial era,mainly after the works of S.P. Langley (USA) and A. SecchiNon-linear programming</p><p>1. Introduction</p><p>The current paper follows thepreliminary, results regarding locentric orbits of solar-photon sail spundergoing variable total solar irrada 1-year circular orbit for high-pmissions, and a single thrusting-arvous mission were considered withitative, thoughntricity helio-ft (or sailcraft)(TSI) [1]. There,ance warningMars rendez-ctual measure-</p><p>photon sailing studies, the solar radiation pressure on thesail has been supposed a constant, and virtually given bythe analyst. Before the astronautical era, there was nouniversally accepted evidence that the solar constantmight exhibit a time-variable behavior. Ground measure-ments, resulting in a time series sufciently precise andaccurate to reveal real variations of this quantity, were notpractically possible before articial satellites (e.g. [2,3]).Lightness vectorTotal solar irradiance uctuation esailcraft-Mars rendezvous$</p><p>Giovanni Vulpetti 1,2</p><p>Via Casal De Pazzi 20, 00156 Rome, Italy</p><p>a r t i c l e i n f o</p><p>Article history:</p><p>Received 28 October 2009</p><p>Received in revised form</p><p>4 January 2010</p><p>Accepted 12 January 2010Available online 6 February 2010</p><p>Keywords:</p><p>Total solar irradiance</p><p>a b s t r a c t</p><p>This paper is the</p><p>solar irradiance a</p><p>sailcraft trajector</p><p>studying such eff</p><p>in this trajectoryts on</p><p>d one of a research line whereupon the variations of the total</p><p>plicitly included in a large high-precision computer code for</p><p>timization. Sailcraft-Mars rendezvous has been chosen for</p><p>It turns out that irradiance-uctuation perturbations are large</p><p>&amp; 2010 Elsevier Ltd. All rights reserved.</p><p>vier.com/locate/actaastro</p><p>nautica</p></li><li><p>plasma features and its interaction with celestial bodies,phothistooverfor i</p><p>(3sourinterof thSSI),neglfollo</p><p>(ii)</p><p>with. As a point of fact, during a typical solar cycle,</p><p>well-known to be particularly sensitive to small accelera-tion changes.</p><p>2. Solar-sail thrust acceleration</p><p>G. Vulpetti / Acta Astronautica 68 (2011) 644650 645SSI undergoes band-dependent uctuations, e.g. [10].Very briey, the visible region variability amounts toabout 0.1%, even less is for the near/medium infraredbands, and of the order of 1%, or less, in the far-infrared region. Much more high is the variability inthe UV, EUV, and XUV regions, and such uctuationsgenerally increase as the wavelength decreases. Thus,uctuations in the SSI bands add up resulting in TSIvariations. As a result, however, the thrust accelera-tion undergoes alterations ascribable to the SSIchanges.</p><p>Point (i) can be considered part of the general determina-tion of the bidirectional scattering distribution function ofa material surface, in this case that one of the sail. Such afunction may be restricted to reection or transmission.Point (iii) is the target of the authors current researchline; it implies signicant difculties, as it will be clearerfrom Sections 3 to 4. In this paper, we will analyze theeffect of point (ii) on a rendezvous trajectory, which is(iii)trajectory computation. Such issue regards theuctuations of the whole irradiance, namely, theTSI. This framework assumes that the thermo-opticalfunctions of the sail materials are sufciently atover the TSI wavelength range of interest in solarsailing.The actual issue is the most complicated to be dealtAccording to [9], few percent of thrust may be lostbecause some sail materials may be transparent tovery short solar wavelengths, especially XUVphotons. This issue regards the wavelength-depen-dent interaction of light with materials, indepen-dently of the related irradiance time behavior.Though TSI uctuations are of the order of a fewwatts per square meters, nevertheless the resultscarried out in [1] show that the accumulation of thetotal thrust acceleration could produce signicanttrajectory deviations with respect to the TSI-constant(i)on irradiance, etc.), the Sun is notably variable. Earlyrical analyses by means of satellite data collectedmonths or years from various missions can be found,nstance, in [7,8], respectively.) As the solar radiation pressure is the primaryce of thrust for a solar-photon sailcraft (via theaction with a material surface), might the variabilitye TSI (through that of the Spectral Solar Irradiance, oraffect the sailcraft thrust acceleration in a non-</p><p>igible way? To begin with, let us consider whatws:one of the NIMBUS series) was followed by many othersatellites endowed with advanced instruments for obser-ving the Sun. One of the most impressive results in solarphysics has been the discovery that the Sun is a variablestar. Let us be more precise: from the astrophysicalviewpoint, the Sun is a main-sequence star, and its radiantpower is considered constant. From the viewpoint of thesolar system evolution (planetary climates, interplanetaryIt has been shown in the past (e.g. in [11]) that asailcraft with total areal density (or sailcraft sail loading)of 2.2 g/m2 could escape from the EarthMoon system allby itself in about 2 months. Such sailcraft could slowdown for an orbit insertion about another inner planet.Actually, sailcraft as heavy as 10g=m2 in areal densitymay deal with the planetocentric branches withoutanother propulsion system. For instance, starting from alow Earth orbit of 4:5 earth radii, escaping times wouldbe 200 days [12].</p><p>Here, we focus our attention on a case that could havea signicant relevance for the future of non-rocket in-space propulsion: a heliocentric multi-arc sailcraft-Marsrendezvous. We use the Heliocentric Inertial Frame ofreference (HIF) dened by counterclockwise rotating thespatial axes of the International Celestial ReferenceSystem (ICRS) about its X-axis by the ecliptics obliquityat J2000. In addition, the (classical) sailcraft-centered(Cartesian) orbital frame (SOF) is important. Its x-axis isalong the radial direction rR=R, whereas its z-axis isparallel to the orbital angular momentum hH=H, whereH R V, as usually, and H denotes the length of H.(Plainly, R and V denote the sailcrafts vector position andvelocity in HIF, respectively.) The y-axis, given by h r,completes the positive basis.</p><p>Let us recall the basic form of the thrust accelerationequation of sailcraft motion. This equation consistsof four main blocks (not all separable completely) [13]:(a) actual solar pressure and solar gravitational accelera-tion, (b) sailcraft sail loading s, (c) sails thermo-opticalquantities, (d) sail axis orientation. Set-(a) cannot becontrolled, whereas sets(cd) can produce thrust throt-tling in the open interval (0,2). In this paper, we report thenon-relativistic lightness vector L (Eqs. (1) and (2)) for apoint-like Sun and ideal space environment: n and udenote the sails unit vector (in the shadow hemisphere)and the local sunlight direction, respectively. Here, idealmeans no optical degradation. Ls generalization can befound in [13] as well; nevertheless, we will not use itsextended formulation in order to highlight the effectscoming from the TSI uctuations. Here, the equations ofinterest are related to L lr; lt; lnT 3 for a sailcraft ofmass m and nominal sail area A:</p><p>ASOF</p><p>GMR2</p><p> L 1</p><p>2</p><p>scs</p><p> nx2 rspecnxwf rdiff kan</p><p>ardiff u 1</p><p>a 1rspecrdiff t</p><p>k wf ef TwbebT=ef TebT 2</p><p>3 The Ls components have been called the radial, transversal, andthe normal (lightness) numbers, respectively. They have full physical</p><p>meaning in as much as energy, energy rate, and angular momentum rate</p><p>depend on them. All sailcraft trajectories can be characterized via L.</p></li><li><p>sct 2I1AUt=cgSun1AU</p><p>gravitational acceleration at 1AU, I1AU is the reference TSI,</p><p>satellites. There appears a signicant variability undervery active research, e.g. solar physics, Earth climatology,and (before long) solar-photon in-space propulsion. Atleast two practical questions immediately arise: (1) whatabout TSI/SSI reconstruction, especially considerably backin the past centuries and millennia, (2) what about TSI/SSIprediction? There are some good models that reconstructTSI during the solar cycles and back in time (on average).In contrast, prediction still presents many uncertainties.Qualitatively speaking, TSI variabilitythat is stronglyrelated to the magnetic activity on the solar surfacemaybe thought of consisting of three parts: (a) secularvariations, (b) cyclic variations, and (c) stochasticuctuations. Feature (a) does not concern solar sailing(time scales are very long, and general trends5 areimportant for climatology). Feature (b) may be ofinterest for long operational orbits about the Sun,</p><p>0 2000 4000 6000 8000 10000</p><p>Days (Epoch Jan 0, 1980)</p><p>el M I</p><p>M I II O</p><p>5 Since the Maunder minimum, the cycle-averaged TSI has shown an</p><p>overall increase of 1:30:20:4 W=m2 or 0.029% and per century, with a max</p><p>error range of 0.013% and per century [14].</p><p>G. Vulpetti / Acta Astronautica 68 (2011) 644650646and c denotes the speed of light in vacuum.Eq. (1) highlights terms regarding the sailcraft tech-</p><p>nology, sail thermo-optical properties, and sail orientation(resolved in SOF); rspec ; rdiff ; and a denote the specularreectance, the diffuse reectance, and the absorptance ofthe sail, respectively, over the TSI spectrum. Adding thetransmittance t, the rst equation of (2) holds. e is theemittance of either sail side, and T is the sail temperature(assumed uniform) throughout the surface. In general, amulti-layer sail has the front-side and the backsideemittances different; together with the generally non-Lambertian character of the two sides, this causes anadditional acceleration usually modeled along signk n,with k given by the second of (2), provided a40.</p><p>Near-term multi-layer sail technology entails no over-all transmittance of the sail. In contrast, concepts of futuremonolayer sails do not exclude some transmittance t40in ultra-light materials; even though this implies thrustloss, however, an overall strong gain could result fromvery low s.</p><p>The quantity sc , known as the critical density, shouldlose almost its usual meaning because I1AU appears to bevariable. Nevertheless, a reference value, say, based on theTSI averaged over the solar cycles 2123 can still retain itsmeaning. L is dened in the sailcrafts orbital frame (SOF)referred to the Sun. Were I1AU time invariant, then anyconstant-in-SOF attitude n would entail the thrust vectorconstant in SOF, but not in HIF. This general advantageallows optimizing sailcraft trajectories via Non-LinearProgramming (NLP) by using the same frame wheresunlight is sensed naturally. With variable TSI,n constant does not entail L constant.</p><p>3. Total solar irradiance in a nutshell</p><p>With regard to accurate and systematic measurementsof TSI, spacecraft have been enlarging the knowledge ofthe Sun enormously.4 Modern photosphere models take ave-element typology into account: the Quiet Sun, sun-spot umbrae and penumbrae, faculae, and the photo-spheric network. Besides network, sunspots and faculaeare regions of high magnetic eld. In the sunspots darkercore or umbra, the magnetic eld is higher than in</p><p>4 On NIMBUS-7, the HF radiometer replaced at radiometers</p><p>working onboard former satellites.I1AUt TSI</p><p>sm=Ae; Ae ZAA 3</p><p>sref c 2 Iref 1AU=cgSun1AU 1:5367g=m2</p><p>Iref 1AU 1365:9W=m2 4In these relationships, Ae represents the equivalent atarea that exhibits the same max radiation-pressure force</p><p>as the actual sail. In addition, gSun1AU denotes the solarref penumbra. Faculae appear considerably brighter thansunspots, indicating higher temperatures of their magne-tized plasma ows. Faculae are observed mainly at thelimb of solar-disk images (in visible light). Over them,images mainly in the ionized Ca or H-a light reveal largebright chromospherical regions, the plages. Simplifyingconsiderably, during a typical sunspot cycle, faculae andsunspots are usually close to each other; in periods of highmagnetic activity, the area covered by faculae risesconsiderably. In addition, sunspots mean life is brieferthan faculas, and sunspots evolve into faculae: as a result,when the number of sunspots increases, TSI increases.Equally much important (and dominant in certainresearches/applications) is SSI, which tells us that theSun is not like a black body. Fig. 1 shows the extendedcomposite of TSI consisting of daily means. This timeseries is the result of the measurements, over the threesolar cycles 2123, and the in-progress cycle-24, fromvarious radiometers onboard some solar-physics</p><p>Year 75 77 79 81 83 85 87 89 91 93 95 97 99 01 03 05 07 09</p><p>1362</p><p>1364</p><p>1366</p><p>1368</p><p>Sol</p><p>ar Ir</p><p>radi</p><p>ance</p><p> (Wm</p><p>-2)</p><p>Min20/21 Min21/22 Min22/23 Min23/24</p><p>Mod H</p><p>FA</p><p>CR</p><p>I</p><p>HF</p><p>AC</p><p>RI</p><p>HF</p><p>AC</p><p>RIM</p><p>VIR</p><p>G</p><p>0.1%</p><p>Fig. 1. The extended PMOD Composite of the TSI (October-2009 update).Gray lines represent daily means (from C. Frohlich, PMODWorld</p><p>Radiation Center, Switzerland).</p></li><li><p>tude proles. Table 1 reports the values of the 10</p><p>G. Vulpetti / Acta Astronautica 68 (2011) 644650 647another celestial body, or Lagrange points. Feature (c)regards short-term changes and mission analyst shouldhave interest in; if f...</p></li></ul>