21 - Interstellar Spaceflight THE PHYSICS OF SPACE TRAVEL (AS WE UNDERSTAND IT) For a spacecraft accelerating at a rate a, the velocity v reached and distance x traveled in a given interval of time t is: at v(t) = ( ) 1+ at 2 c c = speed of light c2 ì ü x(t) = ï í 1+ c a ï î ( ) at 2 - 1ï ý ï þ Accelerating at 1g = 9.8 m/s2: Crew Duration (yr) Earth Duration (yr) Range (pc) 1 1 0.02 10 24 3 - nearest stars 20 270 42 40 36,000 5,400 - center of Galaxy Cost of Interstellar Travel Note: 3 Limitations to high-speed travel 1. Imagination - not a problem today 2. Technology - constantly improving 3. Laws of Nature - may provide ultimate limits Unless there is a MAJOR revolution in technology - rockets are all we have. Rocket engines most efficient when v~vexhaust. Going faster makes them less efficient. Rockets must accelerate payload and all the fuel they carry! For a final velocity Vf, a ratio of initial mass (payload plus fuel) to final mass (ditto) M, and exhaust velocity W, then: Vf 1 - M -2W /c = c 1 + M -2W /c For Vf < 0.1c, then M = “e” = 2.7182….. For a round trip, where 4 legs of the trip each require a factor of M: M RT = M 4 Suppose we took a round trip to a star 5 pc away: Via Chemical Rocket Via Nuclear Rocket Vf / c ~ 10-5 Vf / c ~ 10-1 MRT = 55 (=e4) MRT = 55 t = 3 million years t = 300 years Co$t Example: Controlled Nuclear Fusion (can’t do this yet!) 1000 ton payload 55,000 tons fuel in the form of H, dissociated from 440,000 tons of H2O ice mined from one of Saturns’ moons Dissociating 440,000 tons of ice requires 1016 Joules (Watt- sec) = 3x109 kW-hours = 3000 GW-h ~ 0.1% total annual energy consumption in the US But it won’t go very fast. Vf 1 - M -2 = c 1 + M -2 Matter/Antimatter Rockets x(dist.) = c2 2a( M + M -1 - 2 ) W=c T (earth) = 2c a ( M - M -1) c t(crew) = ln(M ) a Illustration - flat-out acceleration (No stopping, drifting, or return). Vf/c = 0.1 Vf/c = 0.98 Vf/c = 0.1 Vf/c = 0.98 a = 0.01 g a = 0.01 g a=1g a=1g M = 1.1 M = 9.95 M = 1.1 M = 9.95 Tcrew = 9.7 y Tcrew = 230 y Tcrew = 0.1 y Tcrew = 2.3 y tearth = 39 y tearth = 2000 y tearth = 0.4 y tearth = 20 y x=0.44 l.y. x=390 l.y. x=0.0044 l.y. x=3.9 l.y. The fuel supply needed to reach Vf / c=0.98 for a round-trip (MRT=M4=9,800) 10-ton payload requires 100,000 tons matter-antimatter mc2 = E = 1025 Joules About 1 million times the annual energy consumption in the US Project Orion - detonate nuclear bombs to provide thrust (motion picture “Deep Impact”) Solar Sailing Solar wind only reaches 0.003c, need to use sunlight Planetary Society - Cosmos 1 June 21, 2005, launched on Volna rocket from Russian sub. Failed to reach orbit Suppose we start at 1 AU 2x v¥ = from the Sun (i.e. Earth's R1AU orbit), a sail area A and a payload (plus sail mass) M. ALSun x= M 2p c 10-ton payload, sail 1000 km x 1000 km in size. v∞ is then only 0.04 c. It would take roughly 3/0.04 = 75 years to get anywhere, i.e. 3 ly away (ignoring deceleration & stopping) Oops! The SAIL ALSO has mass! A 1000 km x 1000 km. A gold leaf sail 1 atom thick (a real sail would have to be much thicker) would have a mass of 170 tons (it effectively becomes the payload), and so the top speed is 0.009 c. Now it takes over 300 years to get anywhere! Science fiction story - sails from star to star in a day or two (1/300th of a year), This is impossible by a factor of 300 x 300 = 90,000 times! Such trips are, therefore, unrealistic fantasy. Yet other "Possibilities" for Interstellar Flight Ships pushed by X-ray lasers A rear reflector plays the same role to a powerful planet-based light source as the solar sail did to sunlight. Interstellar Ramjets This uses interstellar gas as fuel. You no longer need to carry it with you. Avoid low-density regions? How do you get the fuel into the engine? FTL (Faster-Than-Light) Warp drives, etc. Contrary to all known physics. Sorry. Exploration by Proxy - Robotic Von Neumann Machines/Probes - self-replicating: 1. Travel to a destination 2. Mine resources 3. Make copies of itself 4. Send copies out to new destination 5. Spread though the Galaxy an exponentially growing fleet of machines that consume raw resources Is this really a good idea? MY opinion (for what it’s worth) 1. Unless there is a major revolution in our understanding of the laws of nature, space travel is likely to be confined to the solar system, unless someone wants to launch "generation ships" that only their distant descendents will see arrive somewhere. 2. IF interstellar travel were to become, but still limited to relatively slow travel, all trips will be 1-way. For M="e", M1way = M2 = 7.4, while MRT = M4 = 55. Also, why return? Everyone you know back on Earth will be dead. You will be an anachronism (how would your great-great-great-great grandparents fit into today's society?), or worse, a specimen in a zoo. HAZARD of interstellar flight A 1-mm grain (mass of 0.012 grams) hit by a spacecraft traveling 0.1 c - energy (E=1/2 mv2) of 5.4x109 J. Same energy as a 1-ton object hitting at Mach 9.5 (7,000 mi/hr)!! Unless there is a way to screen out all interstellar dust, the spacecraft will be easily destroyed. What seems most likely today? (Example: Planetary Report - March 2012) Solar sail with: small payload - no humans! micro-robotics and/or pre-programmed DNA launch close to the Sun area/mass ratios of 1000 m2/kg (currently we only have ~10 m2/kg Will take half-century to reach 10,000 AU (nearest stars in over 1,300 years.....) Past "Attempts" at Physical Contact The Pioneer 10 spacecraft - plaque The Voyager 1 and 2 spacecraft - gold record (and stylus for "playing") with images and sounds of Planet Earth. For more Scenes of Earth Voyager Trajectories Neither of these are targeted at any specific star. Their trajectories were constrained by their science missions to the jovian planets. Will the Pioneers & Voyagers ever “GET ANYWHERE”? To come within 1 AU of a star & accidentally be found: “Mean Free Path” (how far to go in order to hit something) x=1/(n) n = number of systems per pc3 = "target area" to be hit. (For a circle, the target area is times the radius (here 1 AU) squared, which we will express in pc2 to get the units we need.) n = 2.5x10-3 stars / ly 3 = 0.1star / pc 3 2 s = p (1AU )2 =pæ 1 ö pc÷ = p ´ 2.4 ´ 10 -11 pc 2 ç è 206, 265 ø 1 1 x= = = 1.3x1011 pc ( )( s n 0.1pc -3 7.5x10 -11 pc 2 ) MWG is less than 105 pc across (and less than 103 pc thick) Changes of “hitting” are less than 10-6 or 0.0001%. Using Neptune’s orbit as target - goes up to a whopping 0.1%.
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