C-ship: Our Sturdy Craft
Here's the Lorentz, one of the fleet of C-ships we'll
dispatch on missions to explore space and time. The Lorentz
is has just pushed off from space dock, and is preparing for
departure.
GIF
JPEG
Powerplant and Engines
Our C-ship is powered by the annihilation of matter and antimatter,
and can accelerate at a sustained rate of 100 metres per second per
second--a little more than 10 Earth's gravities--to velocities
arbitrarily close to the speed of light. Most C-ship missions are
unmanned: probes or lifeseeds. Manned missions generally accelerate
no faster than 1.2 gravities due to the frailness of their cargo. The
C-ship violates no known principle of physics, but producing the
antimatter consumed by a C-ship's drive in a single second would cost,
using current technology, many orders of magnitude more than all the
economies of Earth combined. But by the time our descendents are able
to make use of all the resources of the Solar System, including the
entire energy output of the Sun, they'll be able to build C-ships,
albeit with a maximum speed set by the energy available to power them.
Streamlining
C-ships are streamlined not for style, but by necessity. Space is not
a vacuum but rather a diffuse gas of relict photons left over from the
Big Bang--the cosmic background radiation with a temperature at the
current epoch of about 2.7 degrees above absolute zero. When we
travel at velocities approaching the speed of light, this radiation
creates a drag on our ship
which we must minimise through radical streamlining. Interplanetary
ships may look like flying junkyards, but our interstellar and
intergalactic craft must be rapier-like to pierce the tenuous
birth-cry of the universe.
Shield
Our ship is icy-white in colour for the very excellent reason that its
exterior is made of water ice, one of the most abundant substances in
the universe. When we travel at extreme velocities, dust particles
impact our ship with the energy of a nuclear bomb, and even hydrogen
atoms erode her hull. Before embarking on a mission, we re-make
the surface of the ship with ice harvested from the abundant comets
surrounding the star we're departing. During the mission,
self-reproducing robots built
with molecular-scale engineering repair
damage to the ice shield around our ship. The ice protects us against
impacts with interstellar and intergalactic gas and tiny dust
particles. If we hit something of tangible size, like a rock, it'll
be a really bad day; astronomers on distant planets will catalogue
yet another enigmatic gamma ray burst.
Performance
The performance of the Lorentz is governed by the
relativistic rocket equations for constant acceleration:
where a is the rate of acceleration of the ship, t
is the time, measured by the ship's clock, the acceleration has
been underway, and c is the speed of light in vacuum. Then
d is the distance travelled, v is the velocity
attained, and Tr is the elapsed time at the location where
the ship began its acceleration.
Mission Profiles
Let's apply these equations (including their solutions for ship's
time, t, expressed in an
equation package developed for
use with Wolfram Research's
Mathematica and derived using that tool), to show how the
captain of a C-ship is truly a master of space and time.
Here's a table that shows how long it takes, in time measured on board
the Lorentz, to travel to various places, near and far. In
each journey, we'll accelerate at a constant 100 metres per second per
second
until the halfway point, turn around, and decelerate at the same rate,
coming to a stop relative to our destination. For each voyage, I'll
show the maximum speed at the halfway point as a fraction of the
speed of light, and the elapsed time, measured at the starting point,
when the ship arrives at its destination.
Destination Distance Ship's time Max v/c Earth time
Moon 384401 km 1.09 hour 0.0065 1.09 hour
Mars (mean opp) 0.52 AU 1.1 days 0.0159 1.1 days
Jupiter 5 AU 2 days 0.0288 2 days
Pluto 39 AU 5.6 days 0.0804 5.6 days
Now we depart the Solar System for the gulf between the stars
Alpha Centauri 4.36 ly 268 days 0.999128 4.56 years
Sirius 8.64 ly 314 days 0.999769 8.84 years
Polaris 783 ly 1.71 years 0.999999997 783.4 years
...and onward to the heart of the galaxy...
Nucleus, Milky Way 32616 ly 2.43 years 0.9999999999830 32637 years
and into the realm beyond. The velocities start to take so
many digits to write I have write them on the next line!
Andromeda galaxy 2,180,000 ly 3.22 years 0.999999999999996 2,181,447 years
Virgo cluster 42,000,000 ly 3.78 years V 42,027,876 years
0.99999999999999999
Quasar 3C273 2,500,000,000 ly 4.56 years V 2,501,659,318 years
0.999999999999999999997
Universe edge 17,000,000,000 ly 4.93 years V 17,011,283,360 years
0.99999999999999999999994
In other words, on board our C-ship, we can go anywhere in the
universe in five years ship's time, though millions or billions of
years may have passed at our port of departure. As absurdly close to
the speed of light as the last few velocities may seem, and however
unimaginable the energy it may take to attain them, they're nowhere
close to the speed record for material objects in the universe. On
October 15, 1991, a cosmic ray proton collided with the Earth's
atmosphere, releasing an energy of 3×1020 electron
volts—as much energy as a brick falling on your toe. To pack
such energy, this
Oh-My-God particle
had to be travelling at 0.9999999999999999999999951 times the speed of
light, so much faster than even the maximum velocity on our 17
billion light-year journey to the edge of the universe that the
particle would make the trip in only 19 days, compared to the
4.9 years it took our ship.
Sensors
Our ship is equipped with a full complement of powerful sensors,
covering the electromagnetic spectrum from very low frequency radio
waves through gamma ray and cosmic ray energies. Its powerful
on-board computer presents sensor input on the main viewer with or
without compensation for the effects of relativistic flight.
by John Walker