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:. c = speed of light. Accelerating at 1g = 9.8 m/s 2 :.
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For a spacecraft accelerating at a rate a, the velocity v reached and distance x traveled in a given interval of time t is:
c = speed of light
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
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:
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:
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
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.
W = c
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 = 1 g a = 1 g
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
About 1 million times the annual energy consumption in the US
Project Orion - detonate nuclear bombs to provide thrust (motion picture “Deep Impact”)
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 from the Sun (i.e. Earth\'s orbit), a sail area A and a payload (plus sail mass) M.
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.
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.
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?
Warp drives, etc. Contrary to all known physics. Sorry.
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.
(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.....)
The Pioneer 10 spacecraft - plaque
The Voyager 1 and 2 spacecraft - gold record (and stylus for "playing") with images and sounds of Planet Earth.
Neither of these are targeted at any specific star. Their trajectories were constrained by their science missions to the jovian planets.
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%.