ANALYSIS OF INTERSTELLAR SPACECRAFT CYCLING BETWEEN THE SUN AND THE NEAR STARS

R.W. JBIS, Moi Vol. 58, and pp.33-341, W.L. Ba 005 ANALYSIS OF INTERSTELLAR SACECRAFT CYCLING BETWEEN THE SUN AND THE NEAR STARS R.W. MOIR 1 AND W.L. BARR 1. 607 E. Vallecitos Road, Livemoe, CA 94550, USA. Email: RMoi@acbell.net. deceased. This pape exploes what cyclic tajectoies ae possible within the limits of known laws of physics and pactical populsions systems fo a spacecaft o wold ship that could tavel between the Sun and the nea stas peiodically. Because of the long duations, the spacecaft is assumed to be massive to house many people fo many geneations. The spacecaft is initially acceleated up to speed at geat expense but fom then on only minimal populsion is assumed to be available fo couse coections. The spacecaft, as it neas a sta, follows a hypebolic tajectoy. The spacecaft etuns by using gavity to swing aound each of thee o moe stas, one of which is the Sun. The minimum distance of closest appoach found duing the flyby was 3 Sun adii, whee the heat flux of 7 MW/m was shielded fom the spacecaft by a adiation-cooled shield made of a poous woven cabon fibe whose peak tempeatue was about 500 K. A thin sheet of gaphite by contast would have a tempeatue of 800 K and high evapoation mass loss ate. The coasting speed was found to be 115 km/s o 0.0004c. The minimum peiod found fo this class of tajectoy was about 41,000 yeas fo a tip aound thee stas with a 16 light-yea closed path and about 57,000 yeas fo fou stas with a light-yea path length. If an ode of magnitude moe heat flux could be handled somehow, then the spacecaft could just skim the suface of the Sun (00 km/s o 0.0007c) giving a minimum cycle time of 4,000 yeas fo thee stas and 33,000 yeas fo fous stas. Keywods: Cycling intestella spacecaft, cyclic intestella obits, minimum tavel time intestella obits, wold ship cyclic tajectoy α = inteio half-angle of hypebola, (see fig.1) a = semi-majo axis (see fig. 1) AU = distance fom eath to Sun=1.50 x 10 11 m=500 light-sec A = absobtivity c = speed of light= 3.00 x 10 8 m/s = deflection angle (see fig. 1) ε = eccenticity (see fig. 1) E = emissivity E cohesive = enegy to heatup and evapoate (MJ/kg) G = 6.67 x 10-11 m 3 kg -1 s - λ ϕ H = = sola flux ( W / m ) 4π h = (non) impact distance (see fig. 1) J = evapoation ate (kg m - s -1 ) k = constant of motion = x total enegy pe unit mass L = angula momentum pe unit mass 1 Light-yea = 9.5 x 10 15 m = 6.3 x 10 4 AU Notation List λ Θ = 3.9 x 10 6 W = total sola adiation M Θ =.00 x 10 30 kg = mass of the Sun M = 6.0 x 10 4 kg = mass of the Eath µ GM Θ = 1.33 x 10 0 m 3 /s σ = Stefan-Boltzmann constant = 5.67 x 10-8 Wm - K -4 p = semi-latus ectum (see fig. 1) q = total sola flux duing time spent in high heat flux Φ= pola angle dφ Φ= dt φ = 180 -α (see fig. 1) R Θ = 6.96 x 10 8 m = 4.64 x 10-3 AU = adius of the Sun p = distance of closest appoach on a flyby at peigee = adius, m t H = time spent in high heat flux v = speed duing coast peiod between stas v p = speed at peigee 1. INTRODUCTION This pape exploes what cyclic tajectoies ae possible fo tavel between the Sun and the nea stas. The spacecaft is assumed to be vey massive in ode to house a lage numbe of people fo many geneations. Owing to the long duation of such a spacecaft flight it will have to be a fully functional and self-contained wold and theefoe has been called a wold ship [1]. The spacecaft is initially acceleated up to speed at geat expense but fom then on only minimal populsion is assumed to be available fo couse coections because of its lage mass. The spacecaft, as it neas a sta, follows a hypebolic tajectoy as shown in fig. 1. The spacecaft etuns by using gavity to swing aound each of thee o moe stas in 33

Analysis of Intestella Spacecaft Cycling Between the Sun and the Nea Stas Fig. 1. Hypebolic tajectoy aound a sta. Fig.. Hypebolic tajectoies aound thee stas. the cicuit, one of which is the Sun as shown in fig.. If thee ae thee stas in the cicuit, a deflection of 10 on aveage fo each passage is equied and 90 fo a fou-sta case. To get a deflection this lage equies a close encounte flyby. Duing the flyby of a few hous the heat flux is lage and the spacecaft must be shielded to pevent oveheating. To get shote cycle time equies highe speeds that in tun equie a close encounte in the flyby with a highe heat flux to get the same deflection. So thee is a tade-off between cycle time and heat shielding, which is the subject of this pape. The concept of cycling space ships between planets similaly has the goal of minimizing populsion equiements [].. TRAJECTORIES NEAR THE SUN This section analyzes the tajectoy of a spaceship as it passes nea the Sun. In paticula, it focuses on unbound tajectoies that ae deflected by the Sun s gavity, but then etun to oute space. A teatment by Szebehely [3] using standad notation common in celestial mechanics texts is used. Total enegy pe unit of mass, (1/)k, is a constant of the motion because the gavitational foce is deivable fom a potential. The angula momentum pe unit mass, L, is also a constant of the motion because the foce is diected towad the cente and exets no toque on the spaceship. In pola coodinates, these two consevation equations ae: ( φ ) µ k = + and L = φ (.1) Theefoe: L d d d φ φ = and = = = φ ' whee ' d dt dφ dt dφ Eliminating t gives: (.) Substituting u=1/ gives: µ u k u ' + u = with solution L L µ kl u ( φ) = 1+ 1+ cosφ L µ (.4) Whee µ GM Θ = the gavitational constant times mass of the sta (Sun). With =1/u, this becomes: p kl = whee ε = 1 +, 1+ ε cosφ µ µ p = a( ε 1, ) a = k (.5) Hee, a = µ/k is the semi-majo axis (See Fig. 1) and the distance of closest appoach is p = a(ε - 1). These equations define a hypebola when ε > 1, and of an ellipse when ε < 1. Theefoe, positive total enegy, k > 0, esults in a hypebolic tajectoy with k = v = µ/a and when φ φ = cos -1 (-1/ ε). A elated paamete is the (non)impact paamete, h = aε sin φ (See Fig. 1). The paamete, h, is impotant because it should be measuable and contollable by couse coection populsion fom within the spacecaft, and h and v detemine φ. The angle swept out by the spaceship as it passes a sta is the deflection angle shown in fig. 1. = 180 -α. At peigee (the distance of closest appoach), p φ = 0, = 0, and = = = a ( ε 1) (.6) 1+ ε ε = 1 + / a (.7) Also at peigee, using the consevation of enegy p L ' 4 L µ + = k (.3) µ µ v = φ = k + = v + (.8) 333

R.W. Moi and W.L. Ba It is at peigee, the point of closest appoach, that the heat load might be a poblem. The heat flux at distance fom the cente of the Sun is H = λ Θ /(4 π ), and the time spent in this high heat flux is appoximately t H π / v. Theefoe, the total heat load pe unit of aea, q, is q = H t H λ Θ /(4 v ) = λ Θ /(4 h v ), since v = h v = L, the angula momentum about the Sun pe unit of mass. To illustate the calculations equied, an example is given. Choose v = 0.0003 x c = 1.0 x 10 5 m/s and = 3 x R Θ =.09 x 10 9 m. Calculate k = v = 1.0 x 10 10 m /s, a = µ/k = 1.33 x 10 10 m, v = v + m/ = 1.37 x 10 11 = (3.73 x 10 5 m/s), and ε = 1 + /a = 1.16. This value of ε gives f = cos -1 (-1/ε) = cos -1 (-0.866) = 150. That is, the full inteio angle of the hypebola is x 30 = 60. The deflection angle is 10, equiing thee sta encountes to complete a oundtip. The heat flux at distance fom the cente of the Sun is H = λ Θ /(4 π ) = 7.4 MW/m fo =3 Sun adii. The time spent in this high heat flux is appoximately t H π /v = 4.8 h, which esults in about 1.3 x 10 11 J/m incident on the ship. The esults ae given in Table 1, case No. 1, whee the units ae: velocity (km/s), distance (10 10 m), angle ( ), Heat flux (MW/m ), time (h), and Total Heat (10 10 J/m ). These heat fluxes, H, can be compaed to some pactical cases. Fist, the maximum on eath is 1.39 x 10 3 W/m. Second, wate-cooled coppe heat dumps fo high powe ion beams can toleate 5 x 10 6 W/m in steady state. And, thid, adiatively cooled tungsten wies immesed in an ion beam will ise to a tempeatue of about 000 C when the beam deposits about 1 x 10 6 W/m on thei pojected sufaces. Cases and 3 in Table 1 esult in heat fluxes that ae too high to be toleated even fo some of the athe shot times, t H. The ability to shield against heating while in nea passage with a sta is discussed in Section 5, whee Case 4 is shown to be pactical. The Case 4 tajectoy is shown to scale in figs. 1 and. The time in yeas fo the spaceship to tavel 1 light-yea is t = c/v, whee c = 300,000 is the speed of light in these units o a few thousand times ou speed of 115 km/s. It would take twelve thousand yeas fo the spacecaft to tavel to even the neaest stas, the Alpha Centaui tiplet, which ae 4.3 lightyeas away. In section.1, we teat examples of cycling aound fou stas, one being the Sun; in section., thee stas and in section.3, the geneal case of the deflection angle fo stas of vaious mass and luminosity type..1 An Obit Aound Fou Stas A spaceship with speed of a few 10-4 times c must pass close to a Sun-like sta in ode to be deflected by even as much as 10 (a=30 ). Such a close encounte with a sta would cause sevee heat poblems, and any tiangula obit aound any of the nea stas would equie at least one deflection of about 10. Fo that eason we looked fo 3 neaby stas that, along with the Sun, fom a small nea-egula quadilateal as shown in Fig. 3. All of the 1 stas that lie within about 10 light-yeas fom the Sun lie within ±7.7 of a plane (RA=17.7 ) that includes the Sun. This supising fact allows us to ignoe the small displacements out of the plane, and to plot them on that plane and look fo the smallest quadilateal that contains no intenal angle as small as 60 (α = 30 ) as shown in Table and fig. 3. The smallest angle is the Sun s at 34. The 4 stas - ou Sun, α Centaui A, Siius A, and Wolf 359 define the smallest good obit. The total path length is 1.7 light-yeas, which means that the peiod of the obit would be 57,000 yeas fo a spaceship taveling at 115 km/s (0.00038 times the speed of light) and passing the Sun at about 3 Sun adii at closest appoach (case 4, Table 1). In section 5, a pactical heat shield is discussed fo case 4, Table 1 at 3 Sun adii duing the 5 hous of passage close to the Sun. If the spaceship just skimmed the Sun s suface [case, Table 1] (clealy a limiting case of exteme heat shielding), the speed would be 198 km/s (0.00066c) and the oundtip time would be 33,000 yeas. In eality, the elative motion of the stas needs to be accounted fo, including the speed incement to ou spacecaft on each passage. Howeve, in ode to aive at an appoximation to the oundtip time in all cases, the elative motion between stas is ignoed fo the pesent wok. Couse coections ae made to adjust the distance of closest appoach, p by measuing h, and the angle α, appopiate to each pai of stas as shown in fig... An Obit Aound Thee Stas Using 3 stas as shown in fig., one being the Sun, the othe two being white dwafs we get a shote path length. Fo Sun- oxima-banad s Sta we have a path length of 15.6 light yeas and a speed of 113 km/s giving p =3 Sun adii, the cycle time is 41,000 yeas. The path including the Sun, oxima and Alpha Centaui is pecluded as it equies close to 180 deflection angle on the sola flyby. If we conside thee white dwafs not including passage by the Sun, fo example, Banad s Sta-oxima-Siius B, we have a path length of 15.7 light yeas. The small angle at oxima of alpha = 35.5 gives v = 16 km/s with p = 0.035 R Θ and a cycle time of 9,000 yeas. The adii of these white dwafs ae small, and the enegy given off is small enough that the adiation shield discussed late is less demanding than to pass 3 adii fom the Sun..3 Deflection Angle fo Vaious Stas The equations have been solved fom the point of view of a navigato who wants to plot a couse. He can pass close to a low luminosity sta eithe just skimming the suface if the heat flux TABLE 1: Hypebolic Tajectoies. No. v h/r Θ /R Θ v ε a H t H q 1 100 11 3 373 10 1.16 1.3 7.4 4.8 13 198 3.3 1 649 11 1.1 0.34 64 0.94 3 140 7.6 459 11 1.1 0.68 16.6 15 4 115 9.8 3 375 11 1.1 1.01 7 4.9 13 334

Analysis of Intestella Spacecaft Cycling Between the Sun and the Nea Stas TABLE : Location of the Closest Stas. Sta Dist.(ly) RA( ) Dec.( ) Class AbMag x (ly) y (ly) Sun 0 0 0 G 4.8 0 0 oxima 4. 1.75-6.7 M 15.5 1.93-3.73 α Centaui A 4.4.0-60.8 G 4.3.15-3.84 α Centaui B K 5.7 Banad s Sta 5.9 7.0 +4.7 M 13. 5.88 +0.48 Wolf 359 7.8 16.5 +7.0 M 16.6 7.74 +0.95 BD+36 147 8.3 16.5 +36.0 M 10.5 6.71 +4.88 Siius A 8.6 10.1-16.7 A 1.5 8.4 -.47 Siius B DA 11.3 Luyten 76-8 A 8.7.5-18.0 M 15.4 8.7 -.69 Luyten 76-8 B M 15.8 Ross 154 9.7 8.3-3.8 M 13.0 8.88-3.91 Ross 48 10.3 35.6 +44. M 14.8 7.38 +7.18 Fig. 3 Tajectoy aound fou stas with a ound-tip peiod of 57,000 yeas. is less than 7 MW/m o out to a adius such that the heating is about 7 MW/m that can be handled by the heat shield, as will be discussed in Section 5. Using the mass, luminosity and adius of the nea stas one solves fo the deflection angle vesus v [4]. Remembe the aveage deflection angle needed fo a oundtip fo thee stas is 10 and fo fou stas is 90. The deflection angle is deived fom Eq..5 and.6: = 180 + cos o 1 1 p v + 1 mg (.9) Notice the tajectoies ae self-simila as long as the atio p /m is the same, whee m is the mass of the sta. The esults ae plotted in fig. 4 fo the closest appoach, set by skimming the suface o maximum heat load of 7 MW/m, whicheve is lage. The atio of R p /m is given in units of Sun adius and Sun mass. These examples ae low luminosity white dwafs except fo the Sun. Siius-B being simultaneously low luminosity and small adius esults in the lagest deflection. If low adiation (<7MW/m at peigee) neuton stas o black holes wee available, lage deflections could be obtained. 3. HOW MUCH DOES IT COST TO ACCELERATE MASS TO A SEED V AND HOW LONG DOES IT TAKE? How much does it cost to acceleate mass to a speed of 115 km/s o 3.8x10-4 times the speed of light, which is the assumed speed in calculations used elsewhee? A spaceship whee people live fo thousands of yeas has to be a fully functional wold, a wold ship. The mass must be much moe than a ton pe peson, the mass of an odinay ca. Let s suppose the mass is 10 tons pe peson. To get the spaceship up to speed, use of a mass beam [5] is assumed. Othe populsion methods such as nuclea-pulsed populsion ae possible. Small masses ae acceleated towad the spacecaft fom space-based beam pojectos with thei independent powe station. These then seek the cente of a lase beamed both fom the 335

R.W. Moi and W.L. Ba The cost, assuming a cost of electicity typical of bus ba cost of 0.05 $/kwh and an efficiency of electicity to acceleation is 1/3, is given next: Fig. 4 Deflection angle vesus speed, v. taget spacecaft and fom the mass beam pojecto athe than spead out [6]. The masses ae vapoized and/o ionized as they appoach the spaceship and made to bounce off a eflecto (a physical o magnetic sail ). The beam velocity is gauged so that the eflected mass is left with negligible kinetic enegy in the sola fame of efeence the kinetic enegy of the beam having been efficiently tansmitted to the spacecaft. In othe wods the jet efficiency is assumed ideal at 100%. Suppose powe-limited electic populsion is used and the expellant mass is extenally supplied. The mass beam pojecto, its powe supply and souce of mass would be space based. dv dm F = M ( v V) dt = dt (3.1) whee M is the fixed mass of the ship and V is the spaceship speed and v is the vaiable exhaust speed. We will assume the ideal case of elastic ebound whee v=v. A lesse value will incease the equied beam powe and equie heat dissipation on the spacecaft. v = V dm m = = mass flow ate (3.) dt 1 ( ) = powe in the flowing mass = m V (3.3) dv. F = M ( v V) m V, o MVdV dt dt = = V = (3.4) Integating, assuming = constant. 1 E = MV = t (3.5) Using Table 1 case 4 example of v =115 km/s 1 E/ M = MV / M = t/ M = 0.5 (1.15 10 ) 9 = 6.6 10 J / kg 5 (3.6) 9 1 6.6 10 J / kg 0.05$/ kwh Cost / M = = 70$/ kg 1/3 1000 W 3600 s/ h kw (3.7) Owing to the ideal assumptions on elastic ebound and othe assumptions, the actual cost will be consideably highe. Fo compaison, the cost pe unit mass into low eath obit today in the shuttle is about $0,000/kg o almost 100 times moe. If each peson needs 10 tons, then the cost would be.7 10 6 $/ peson and $7 billion fo the 10,000 population. This is about the cost of the Apollo moon poject fo populsion alone. Fo compaison, Wold Wa II cost the US about $4.3 tillion. Clealy, thee will be incentives to economize on mass pe peson and efficient acceleation ticks such as using the gavity slingshot effect commonly used by NASA even today whee an incement of velocity up to that of the object of the flyby is picked up. The time to acceleate is: 1 MV t = (3.8) The powe supply is assumed to be space based but some couse coection powe on boad is needed as well as fo unning the society (lighting, heating, agicultue, communications, etc). Suppose the powe souce on boad supplies powe at 1 kw/kg (including all the mass of the ship and its expellant), which might be an uppe limit of technology, then the time to acceleate is 1 MV 9 6.6 10 J / kg 7.0 10 0.6 t = = = s = yeas 1, 000 W / kg 0.333 (3.9) If each peson needs 10 tons of mass, then each peson s po-ated powe would be 10 MW pe peson. Fo a spaceship of 10,000 people, the total powe would be 100 GW fo the 10 tons pe peson case. This powe is vey lage and can be deceased by polonging the acceleation peiod fom the 0.6 yeas to 6 yeas, fo example, which would lowe the powe to a moe pactical 1 GW fo the 10-ton case. This would be a pactical 10 W/kg o 100 kw pe peson. What expellant mass is needed to popel the ship? Fo constant, the ate that mass must be supplied is M m = = V 4t (3.10) This expellant mass is supplied to the ocket at the time it is needed at speed V. (Note that m > as t > 0.) Integate to find the total expellant mass: dm = M dt,om= M ln t 4t 4 t (3.11) 0 336

Analysis of Intestella Spacecaft Cycling Between the Sun and the Nea Stas This expession shows it takes a lot of expellant mass to get the spaceship stated but m deceases apidly as V inceases, although emains constant. The time to acceleate to the intemediate speed of 7 km/s, which is x 10-5 c, is 56 h at the lowe powe of 1 GW. Fo compaisons, the appoximate speed of a low eath obit is 7 km/s (x10-5 c) and speed of the eath aound the Sun is 30 km/s (10-4 c) and 4 km/s to escape the Sun s gavity fom eath s position. Using 56 h fo t 0, the expellant mass needed to acceleate to 115 km/s (3.8x 10-4 c) in 6 y is M/4xLn(100) =1.15 M. Again, this shows that it will be impotant to economize on expellant mass, especially in the ealy stages of acceleation. We must add a small amount to the above estimates of powe cost and expellant mass needed to escape the Sun s gavity. 4. COURSE CORRECTIONS The next question is, what is the amount of couse coection pactical with onboad powe? Assume that the coectional thust is at ight angles to the diection of tavel so that no speed change occus. Also assume that the expellant used is small compaed to the ship s mass. mt << M dv F = M = vjetm (4.1) dt Whee dv is the esultant pependicula velocity, and v jet is expellant mass speed elative to the ship. M V = vjetmt (4.) 1 mv jet = η (4.3) Whee now is the powe consumed to poduce the steeing jet. 1 jet η v jet MV v jet MV V V vjetmt mv t t = = = V MV 1 1 8 7 (4.4) V 10 W 0.333 100y 3.15 10 s/ y = = 0.16 V 9 1 6.6 10 J / kg 10, 000 kg / peson 10, 000 people 1 (4.5) When v jet =V and efficiency is 33%. Fo 10 tons/peson, 10,000 people, and 100 MW powe fo 100 yeas, this coesponds to a deflection of 9 fo a 100-yea bun couse coection. The couse coections should be much smalle than this. The mass expended in this assumed 9 coection is: 8 7 η 0.33 10 W 100 y 3.15 10 s/ y mt = t= v 5 jet (1.15 10 m/ s) 7 = 1.6 10 kg = 16, 000 tons (4.6) mt M 3 16 10 = = 1.6 10 4 4 10 10 4 The mass used fo steeing is much smalle than M. V Fo 50 MW powe, = 0.01and V mt M. = 10 = 1 10 0 4 5 which might be adequate fo couse coections and uses negligible mass as expellant. A coection that bings the ship back to the sta fom which it just came would equie V = V Rathe than 100 MW fo 1000 yeas, we would need (/0.16=13) 13 times this much ocket powe o duation. The expellant mass would still be small. The point to be made hee is the impacticality of speeding up then slowing down fo the flyby with such a massive space ship in ode to educe significantly the cycle time. 5. RADIATION SHIELDING FROM THE SUN DURING FLYBY The spacecaft will need shielding fom the Sun s (o sta s) electomagnetic adiation duing the close encounte flyby. One way to do this is put up an umbella-like thin sheet between the Sun and the spacecaft. The sola flux will intecept the shield, which in tun adiates fom both sides. Then the spacecaft can be located some distance away in the shadow. If this eduction is not enough, anothe shield can be imposed to successively educe the heating to any desied value, and is only limited by the weight of the shields. The limiting technology then is fo the fist shield to suvive. We do not discuss shielding fom stella paticle emissions duing flae events, which could coincide with stella flybys. A NASA poject called Sola obe planned to use a gaphite shield fo flyby at fou Sun adii [7]. The heat shield is discussed in seveal epots with emphasis on tempeatue limits set by adiation and evapoation [8, 9]. The total sola flux is 3.9x10 6 W and the Sun s adius o is 6.96x10 8 m. The sola flux is then 64.4 MW/m at the suface and falling as ( o /). The input powe fom the incident sola flux must be balanced by adiation fom the thin disk of a shield assuming total absoption. The adiation fomula is: 4 =Ε σ T (5.1) A The emissivity E is a popety of mateials, σ is the Stefan- Boltzmann constant (5.67x10-8 Wm - K -4 ) and T is tempeatue of the suface in Kelvin. The tempeatue of the suface of the shield is then: 337

R.W. Moi and W.L. Ba Fig. 6 Emissivity vesus tempeatue. Fig. 5 Umbella-like shadow shield fom sola adiation (not to scale). The uppe vesion shows a schematic of the idea and the lowe one shows a pespective view. 1 T o = Εσ A 1/4 (5.) whee the facto of comes fom adiation fom both font and back. The emissivity is given fom Kohl (p.165 and 74 p.158) [10] and plotted in fig. 6. The esults show why gaphite is the best of the candidate shield mateials. Radiation powe using the data above and Eq. 5.1 is plotted in fig. 7. The aows show the maximum pactical tempeatue whee loss of stength occus; the cuves end at the melting tempeatue. The esults of Eq. 5. ae plotted in fig. 8. Thee is a decided advantage in using gaphite because of its high emissivity. The distance of closest appoach fo gaphite would be 3 Sun adii and a little ove 4 fo tungsten. The tempeatue of cabon fibes is limited by evapoation fom the solid (sublimation). The theoetical evapoation ate is given by the expession J = 17.14 ( T / M) 0.5 (5.3) Fig. 7 Calculated adiated powe. A B/ T = e (5.4) whee is the vapo pessue in ascals, T in Kelvin, M is mass pe mole, which fo cabon is 0.01 kg and J is in kg/m s. A easonable fit to the data fo vapo pessue fom Kohl [10] fo electogaphite is A=37.5 and B=99,500. The sublimation ate fom Ref [7,9,11,8] fo the Sola obe was taken as 0.0015 mg/m s at 04 K and 0.0046 mg/m s at 4 K. They note that sublimation ates wee measues. about an ode of magnitude lowe than fo gaphite pesumably due to suface enegy effects of fibes. The suface mateial loss ate is J/ρ in units of m/s. The density of gaphite is about 1400 kg/m 3. We plot in fig. 9 the theoetical loss ate based on measued vapo pessue fom gaphite in units of micometes/h. Also shown ae two measued loss ate data points and the theoetical cuve adjusted to pass though the measued points (dashed cuve). 338

Analysis of Intestella Spacecaft Cycling Between the Sun and the Nea Stas Fig. 8 Calculated tempeatue of the shield nomal to the Sun vesus distance fom the Sun. Based on use of fibes of tens of micons thickness and a few hous exposue time, the tempeatue is limited to about 600 K. A somewhat highe heat flux is toleable if the shield is made of fabic, which is the most likely constuction mateial anyway. A thin poous weave would expose single fibes to the incident flux popotional to its diamete, but it adiates fom its peimete, o 3.14 times its diamete, compaed to a disk of twice its diamete fo both sides. Thus a facto of up to π/ can be put into Eq. 5.. Adjacent fibes will shield each othe somewhat, so this coection would have to be educed. The same tempeatue will be eached at a educed adius by a facto of (π/) 0.5, which is 1.5. At the same adius, the tempeatue would be educed by 1%. Use of fibes can make a flat suface of 800 K become 500 K. The shield could be tilted to spead the heat load ove moe aea. Fo example, tilting 60 fom that shown in fig. 6 would educe /A in Eq. 5. by a facto of giving a tempeatue eduction of 19%. A pactical fabic might be woven fom fibes of 10-µm diamete. If the weave wee equivalent to a single laye side by side touching, then the mass would be: π D Lρ 4 π π = D ρ = 10 µ m 3400 kg/ m = 0.067 kg/ m DL 4 4 3 A 100-m adius shield would then have a mass of 840 kg. (5.5) If a cabon fibe shield of 100 m adius wee adiating at 500 K appopiate to thee Sun adii o about 3 MW/m fom each side, then the adiant flux on the spacecaft would be π100 3 7500 MW = = A (5.6) 4π x x whee x is the distance fom the shield to the spacecaft and x o is a typical distance taken hee to be 100 m. Fig. 9 Evapoative loss ate of the cabon fibe shield vesus tempeatue. x o = 0.75 MW / m A x (5.7) Fo example, at 500 m, the flux athe than being 7 MW/m fom the Sun would be only 0.03 MW/m o a facto of 100 eduction. A second shield could futhe educe this heat load. The Sola obe [7] planned to fly by the Sun at 4 Sun adii. The pesent wok is consistent with the Sola obe wok. A somewhat highe tempeatue owing to 3 Sun adii apogee is allowed because a 100 times highe evapoation ate is allowed duing the flyby. 5.1 Ablative Shield The flux at thee sola adii (Case 4 of Table 1) peaks at 7 MW/ m and the total enegy is 1.3x10 11 J/m duing the flyby. This can be handled using a two-sided adiation shield made of cabon fibes. Fo highe heat fluxes, conside an ablative shield simila to that used to shield e-enty vehicles. The cohesive enegy of cabon is about 100 MJ/kg to heat up to about 3000 K fom nea zeo and then to evapoate. Fo a 100 m adius shield the amount of mateial evapoated duing a flyby of the Sun would be: 11 1.3 10 J / m π 100 m 6 100 10 J / kg 7 = 4.1 10 kg (5.8) The assumed spacecaft s mass is 10 8 kg (10,000 people x 10 tons pe peson) so this loss on each pass would be 40% of the ship mass. This is too much but could be cut down by designing a smalle adius ship. Fo example, a adius as small as 10 m might be a limiting case that would esult in an ablated mass on each flyby to 0.4% of the ship s mass. Fo compaison ou ealie adiative shield of mass 840 kg was only 10-6 of the ship mass. The ablative shield is possible but much moe massive than the adiative shield and theefoe consideed impactical. A moe in depth analysis of ablation (evapoative) cooling can be seen fom a powe balance. The input powe to the shield is the sola flux that is balanced by adiation cooling and evapoative cooling. See fig. 10 fo the elative stength of each cooling pocess. 339

R.W. Moi and W.L. Ba to include atificial habitats of the sot featued in the Athu C. Clake novel Rendezvous with Rama [13] and discussed as wold ships by Matin [1] it would be moe undestandable. This second possibility examined was cyclic obits to the nea stas. Howeve, as aleady discussed, the shotest cycle time found was 41,000 yeas with a ealistic heat shield, and this only educes the cycle time to 4,000 yeas if the Sun s suface is just skimmed with some futuistic heat shield duing the flyby. So the pesent analysis is off by about an ode of magnitude fom explaining the 3,600-yea peiod poposed by Sitchin. 7. DISCUSSION AND CONCLUSIONS Fig. 10 Radiation and ablation cooling vesus tempeatue. H = sola flux 4 H A= Ε σt + Ε cohesive J (5.9) A = absotivity 1 Ε= 0.9 = emissivity 8 1 4 σ = 5.67 10 J m s K Ε cohesive = enegy to heatup and evapoate 100 MJ / kg 1 J = evapoate ate kg m s (5.10) The facto of two in Eq. 5.9 accounts fo two-sided adiation and evapoation. 6. DISCUSSION OF SITCHIN S HYOTHESIS This study stated with speculation as to whethe peiodic visitations to the sola system as poposed by Sitchin [1], could be the esult of cycling intestella ships. In his book The 1 th lanet, Sitchin [1] poposed that the eath had been visited by extateestial life on a cyclic basis evey 3,600 yeas. The cycle was the esult of the obit of thei planet. The pesent analysis was initiated patly to see how this might be possible. The fist possibility examined was elliptic obits like comets and planets. A peiod of this duation means the tunaound point is 30 AU (one AU is the distance fom the eath to the Sun) fom the Sun o six times futhe than the distance to luto. This is difficult to undestand with ou cuent undestanding of sola system evolution. If we extend Sitchin s idea Cyclic tajectoies wee found that would etun a lage spaceship to the sola system peiodically with minimal populsion fo couse coections only. The cycle time was 41,000 yeas fo a couse including thee stas and 57,000 yeas fo fou stas. The cycle time was detemined by faily had equiements: distance of closest appoach, which was about 3 Sun adii on the flyby, set by adiation cooling and the need to have a cumulative deflect of 360, which was on aveage 90 fo each of 4 flybys of the neaest fou stas in the cicuit o 10 fo thee stas. The maximum deflection equied was the Sun encounte of 11. The assumption of distance of closest appoach to the sta on flyby (about thee Sun adii) is based on one design of shielding using adiation cooling at 7 MW/m. A bette shield design would allow close appoach. The smallest distance of closest appoach skimming the suface of the Sun would shoten the oundtip to 4,000 yeas fo thee stas and 33,000 yeas fo the fou sta case. This closest appoach distance would esult in a heat flux of 60 MW/m, making fo a difficult shielding poblem. Howeve, owing to a shote exposue time the enegy to be absobed is only twice that at 3 Sun adii. The cycle times might be pohibitively long fom the human viewpoint. Howeve, space-faing civilizations evolving on planets cicling widely-sepaated membes of multiple-sta systems o living in galactic egions of highe stella density might well apply the techniques descibed in this pape. 8. ACKNOWLEDGEMENTS We want to acknowledge Edwad Cheng fo his inteest and suggesting this topic and Geald Nodley fo a numbe of useful suggestions and discussions. The many useful suggestions by the efeees and edito of JBIS ae appeciated. W. L Ba, a long time fiend and colleague in the fusion eseach pogam at Lawence Livemoe National Laboatoy contibuted many calculations of obit mechanics. He passed away Apil 4, 004. REFERENCES 1. A.R. Matin, Wold ships Concept, cause, cost, constuction and colonization, JBIS, 37, pp.43-53, 1984.. Buzz Aldin, Dennis Bynes, Ron Jones, and Hubet Davis, Evolutionay space tanspotation plan fo Mas cycling concepts, AIAA Space 001 Confeence and Exploation, Albuqueque, NM. Aug 8-30, 001. 3. Victo G. Szebehely, Adventues in Celestial Mechanics, U. of Texas ess, 1989. 4. E. F. Mallove and G. L. Matloff, The Staflight Handbook, John Wiley & Sons, Inc., New Yok, 1989. 5. C. E. Singe, Intestella populsion using a pellet steam fo momentum tansfe, JBIS, 33, pp.107-115, 1980. 6. G.D. Nodley, Momentum Tansfe aticle Homing Algoithm pesented at NASA/JL/MSFC/AIAA Annual Tenth Advanced Space opulsion Wokshop, Huntsville, AL, Apil 5-8, 1999, also cited on p.98 and 100 of G. L. Matloff, "Deep-Space obes", Spinge axis ublishing, Chicheste, UK, 00. 7. G. Gloeckle, Chaiman, Sola obe Science Definition Team, Sola obe: Fist Mission to the Neaest Sta Repot of the NASA Science Definition Team fo the Sola obe Mission 1999. 8. J.E. Randolph, W. Imbiale, R.N. Miyake, E.A. ieson, R.B. Diling, 340

Analysis of Intestella Spacecaft Cycling Between the Sun and the Nea Stas J., The sola pobe heatshield development, unpublished epot about 1999. 9. J. Randolph, J. Ayon, R. Diling, W. Imbiale, R. Miyake, D. Le Queau, G. Olalde, E. ieson, S. Rawal, B. Rivoie, J. F. Robet, C. Royee, R. Taylo,. Valentine, W. Vaughn, The sola pobe shield/antenna mateials chaacteization, Cabon, 37, pp.1731-1739, 1999. 10. W.H. Kohl, Handbook of Mateials and Techniques fo Vacuum Devices, Reinhold ublishing Copoation, New Yok, 1967. 11..G. Valentine,.W. Teste, R.O. Haington, J., Mass Loss Testing of Cabon-Cabon at High Tempeatues, GA-C515, 1997. 1. Z. Sitchin, The 1 th lanet, Avon Books, Hape Collins ublishes, New Yok, 1976. 13. A.C. Clake, Rendezvous with Rama, Bantam Books, New Yok, 1973. (Received 13 Septembe 004; 10 Januay 005; 18 Mach 005; 8 July 005) * * * 341