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:
1+ at 2
c c = speed of light
c2 ì ü
í 1+ c
at 2 - 1ï
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
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
2a( M + M -1 - 2 )
W=c T (earth) =
M - M -1)
t(crew) = ln(M )
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 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
from the Sun (i.e. Earth's R1AU
orbit), a sail area A and a
payload (plus sail mass) M. ALSun
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.
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
Warp drives, etc. Contrary to all known
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
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
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
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)
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
s = p (1AU )2 =pæ 1 ö
pc÷ = p ´ 2.4 ´ 10 -11 pc 2
è 206, 265 ø
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%.