OOn the maximum sufficient range of interstellar vessels
Daniel Cartin ∗ Naval Academy Preparatory School, 197 Elliot Street, Newport, Rhode Island 02841 (Dated: October 8, 2018)This paper considers the likely maximum range of space vessels providing the basis of a matureinterstellar transportation network. Using the principle of sufficiency, it is argued that this range willbe less than three parsecs for the average interstellar vessel. This maximum range provides accessfrom the Solar System to a large majority of nearby stellar systems, with total travel distanceswithin the network not excessively greater than actual physical distance. ∗ [email protected] a r X i v : . [ phy s i c s . pop - ph ] A p r The last few decades have seen design studies – such as Project Daedalus [6], its successor, Icarus [7], and theLongshot effort [8] – aimed to create realistic plans for future vehicles able to travel to other solar systems. Thesedesigns are meant to be the first step in developing engineering methods for the transportation needs of an interstellarcivilization. Because of the great gulf between our current knowledge and the daunting nature of this task, muchof this effort has focused on developing the appropriate technology for travel between the stars within a reasonableamount of time with a large probability of success. However, it is interesting to consider further into the future, whenengineering expertise is developed to make interstellar travel relatively commonplace. Specifically, the question iswhat are the likely characteristics of the products of a mature interstellar travel technology. In this work, it is arguedthat the maximum travel distance capability (before resupply at a port of call) of a typical interstellar vehicle willbe on the order of three parsecs (pc). Although technological development may continue to progress, increasing themaximum possible travel distance, the factors of cost and sufficiency will conspire to limit the need for craft withlonger ranges.Many assume that as interstellar travel becomes more frequent, the range of such spacecraft will increase hand-in-hand with improving technologies and designs. An example of this is the idea of the “incessant obsolescencepostulate” [2] or the ”incentive trap” [3], a suggestion that the earliest starships launched towards another star willactually arrive later than subsequent missions due to improvements in speed and other characteristics. To some extentthis is in line with the development of transportation technologies on the Earth’s surface – for example, the increasingrange of aircraft over the last century. However, this avoids the question of sufficiency, as opposed to ability. Tocontinue the example of aircraft, it is certainly in the realm of possibility to design airplanes with global ranges, butthis is not done for several reasons. First, these craft would have a vastly increased resource cost over current designs.In addition, it has been deemed better to operate aircraft with shorter ranges, to match a transportation system thatcaters to passengers with a wide range of destinations. This type of design can minimize the various costs in thecomplete transportation system (see, e.g. [9]).Specifically for interstellar spacecraft, there are other considerations to factor into the effective safe travel distanceof a vessel. One is the need for self-repairing systems; since these craft will be isolated for years, if not decades,any damage must be repaired within the vessel, rather than relying on outside help. It is likely that there is aroughly fixed chance of equipment failure happening for a given amount of time. Thus, extending the travel rangeof a vehicle without an accompanying change in cruise speed results in the increasing probability of either a singlecritical fault or multiple such incidents resulting in collapse of vehicle effectiveness and mission failure. Another issueis the amount of shielding required to protect sensitive passengers and control equipment – as the cruise velocity ofa vessel increases (and thus the range), so does the amount of radiation and collision protection required in place.Technological advances may result in active, rather than passive, means to shield the craft (e.g. magnetic fields vicelarge amounts of ”dumb” material in front of vital areas), but this returns again to the worry about critical failures ofactive shielding mechanisms. Finally, there is the simple matter of resource and effort costs. Although longer rangevessels may be possible, if there is insufficient need for them or ship cargos are directed to multiple destinations, thesame resources can be devoted to constructing a greater number of shorter range craft to facilitate the transportationnetwork.Thus, in this work we consider how the properties of an interstellar transportation network vary with the maximumphysical distance D max of its links between stellar systems. First, the total number of star systems reachable fromthe Solar System changes is examined, setting the lower limit for D max . After this is done, a comparison is madebetween the travel distance within the transportation network – where the maximum distance between systems isfixed – compared to the actual physical distance between the departure and destination systems, for trips startingat the Solar System. In particular, how the ratio of these two distances, geodesic distance inside the transportationnetwork to physical distance, changes as the spacecraft range D max is increased. The requirement that the averagevalue of this ratio is not “too large” will set the largest sufficient value for D max . Note the emphasis on maximumrange, rather than on an upper time in travel time. Presumably such times will decrease as technology advances, butthe range of travel distance is predicated solely on the already existing physical distances between nearby stars.Before presenting the results, the method of deciding on the maximum travel range is briefly discussed. This paperdepends crucially on the principle of sufficiency for the transportation network – namely, what is the largest travel rangeneeded to connect most of the star systems in the Solar neighborhood, without requiring vessels to execute journeysof distances much greater than the actual physical distance. A more rigorous analysis – using linear optimization,for example, to minimize the total resource cost of the transportation network – would require an engineering modelto describe the additional resources needed to improve spacecraft range capabilities by a specific amount. If thismodel is acceptable, an optimization procedure could design the most efficient network, given transportation supplyand demand at each stellar system. This would include the possibility of several interstellar vehicle designs, suitedto particular duties with the network. However, the issue is that these supply and demand factors depend cruciallyon D max . Suppose transportation needs within the travel network are based roughly on random walks within thenetwork. As a result, equilibrium supply and demand at a particular star system would depend on the number of Maximum travel distance (pc) Largest component size Solar component size Mean component size2.0 75 5 2.76712.2 153 5 4.05292.4 399 399 5.99132.6 476 476 8.61252.8 562 562 13.25TABLE I. Variation in the sizes of the connected components in the interstellar transport network as a function of the maximumtravel distance. The total sample size is N = 689, consisting of all stellar systems within 15 pc of the Sun (including our ownSolar System). Note that over 80% of all such systems are reachable from the Solar System when D max = 2 . N = 257 stellar systems reachable from the Solar System when D max = 2 . connections this system makes with its neighbors [4]. However, this degree increases with the travel range D max .Even if there was a reasonable engineering model of cost versus capability, finding the optimal D max would be anon-linear optimization problem. Thus, we consider only an averaged range capability over all interstellar vessels thatis sufficient to connect most star systems in the Solar neighborhood as a first approximation of this more optimaltransportation network.Moving on to the simpler situation described here, the term “star system” as used here includes all large-mass objects– not just stars (in the sense of masses shining due to nuclear fusion), but also white and brown dwarfs. The suppositionhere is that a civilization capable of building reliable interstellar craft will pass through an interplanetary phase first,due to the enormous energy requirements for interstellar (compared to interplanetary) colonization, developing thecapability to colonize a variety of environments, such as asteroids, comets, and other non-Earth-like locations. [1].Thus, there would be no a priori bias towards certain types of stars, with spectral types close to the Sun’s; insteadsuch a civilization would be capable of developing resources and living structures across a wide range of habitats.Singular white and brown dwarfs may be important solely due to their role in the interstellar transportation network,serving as repair or replenishment stations for vehicles en route to other destinations. In addition, some stars withsufficient distance between them are counted as separate stellar systems, e.g. Proxima Centauri is treated as distinctfrom the α Centauri A/B system. Finally, for the purposes of this paper, only stellar systems within 15 pc of theSun are considered, giving a total sample size of 689 systems, including the Solar System; the overall picture does notchange appreciably for differing samples.The first question is what is the minimum travel distance D max needed for an interstellar vehicle. Obviously, D max > . D max > . α Centauri system,Barnard’s Star, and Ross 154. Thus, the minimum sufficient D max is about 2.3 pc, which allows for a connectedtransportation network of five systems. This is seen in Table I, listing the size of all stellar systems connected to theSun (“Solar component”) by vessels with a given D max , compared to the largest transportation network possible forall the stars within 15 pc of the Sun. The interesting fact, however, is that this D max of 2.3 pc is rather large forthe local stellar neighborhood. For example, with interstellar vehicles with a range D max = 2 . D max = 2 . FIG. 1. Histogram of the ratio of travel distance to physical distance from the Solar System for an interstellar vessel with amaximum travel range of 2.3 pc ( N = 257 systems). Note that going from the Solar System to almost all other stellar systemsrequires twice the travel distance that a direct path would take. travel range. Thus, at D max = 2 . D max of spacecraft reduces this ratio of travel to physical distance. If we comparethe distance ratio for the same N = 257 star systems reachable when D max = 2 . D max is 2.6 pc and 2.9 pc, respectively, as seen in Table II. Therefore, by the timethe maximum vessel range is 2.9 pc, the travel distance to the average stellar system from the Solar System within thetransportation network is on average 31% greater than a straight line journey. In addition, this route typically includesone or more ports of call along the way, allowing for both resupply and repair of the vessel, and facilitating connectionswith other vessels traveling to multiple destinations. Even when all star systems accessible with D max = 2 . [1] Frank Drake, ”A comparative analysis of space colonization enterprises, The Search for Extraterrestrial Life: Recent Devel-opments , pp. 443-447, ed. by M. D. Papagiannis (1985).[2] Paul Glister,
Centauri Dreams: Imaging and Planning Interstellar Exploration , New York: Copernicus Books. [3] Andrew Kennedy, ”Interstellar Travel: The Wait Calculation and the Incentive Trap,”