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Fig 1. Fireball XL5 ran for a single 1962—63 series, produced by husband and wife team Gerry and Sylvia Anderson and was set one hundred years later. It is every schoolboy's dream. To
travel space. According to the
Anderson’s vision, in 2062 we will be policing the solar system. 50 plus years on from their vision and where are we? When I was six
years old my teacher asked the class if we would go to the moon.
After careful consideration I added my hand to the 25% of those
of the other children who wanted to go.
I was surprised at the large number who opted not too, as the
popularity of space travel programs was as popular then as now.
Of course, at that time it was just to our neighbouring satellite
and planets that featured in the radio and television programs.
Then in 1969 a man set foot on the moon and space was finally
open to humanity. Only it
wasn’t. Where
then are the lunar bases, the settlements on mars, the mining colonies
on the asteroids and the scientific bases on the Jovian moons?
All of which were supposed to have been well established by the
year 2000. Incidentally, of
us 25% of the class who were willing to go to the moon, I am almost
certainly the only one that subsequently applied to go into space;
unfortunately, unsuccessfully. So
where exactly did we go wrong? Conventional Rockets' Travel Times. Earth to The Moon.
Fig 2. The Light Side of the
Moon. From
"Range zero" to LM lunar landing*.:
Apollo 11: 4 days 6 hours 45 minutes Apollo
12: 4 days 14 hours 32 minutes Moon
to Earth travel time (from LM ascent stage ignition to splashdown*): Apollo
11: 2 days 22 hours 56 minutes Apollo:
The Definitive Sourcebook. Richard Orloff & David Harland. Springer-Praxis, 2006. Earth to Mars
Fig 3. Mariner 7 made the journey to Mars in a record time of only 131 days. Earth to Jupiter
Fig 4.
Galileo, launched on 19th January 2006, flew past
Jupiter after 13 months. Note
this was a fly past and attaining orbit would have required a
significantly additional amount of time for deceleration.
Earth to Pluto
Fig 5.
New Horizons, launched on 19th January 2006, took 9½
years and represents the shortest travel time to Pluto to date. So
why does it take so long to get to other celestial bodies?
Because, conventional spacecraft use an inertial drive, spending
almost the entire journey drifting in free fall.
The craft is pointed at the target, the engines fired up for a
very short time and then switched off for almost the entire journey.
Of course, the craft is not pointed directly at the target.
Rather it is pointed in a direction that will result in it
arriving in the neighbourhood of the target at some time in the future
when the target’s orbit takes it there. There are also many intervening bodies to be taken into
account. This can be
advantageous. If there is a
large celestial body in the right position at the right time the craft
can get a boost from a slingshot manoeuvre.
In
this manoeuvre the craft passes close to a planet or other celestial
body behind it in its orbit. The
craft then ‘steals’ some of the planet’s velocity by slowing it
down. This will not cause
planets or moons to hurl out of their orbits as, even though the craft
can gain a lot of speed the planet loses very little; in direct
proportion to the ratio of their masses in accordance with law of
conservation of momentum. The
asteroid belt is a problem in that it contains billions of rocks any one
of which could cause irreparable damage to a craft passing through it.
Fortunately, it is a belt and it can be avoided very simply by
angling the craft so that it passes safely outside the relatively narrow
orbital plane of the belt. The
gravitational attraction of the belt curves the craft back towards its
target and again this can be used to advantage by again stealing some of
the orbital energy from some of the bodies within the belt.
Once
in a while the crafts rockets have to be fired up briefly to make fine
corrections to its course. The times to reach the planets in our solar system above
frequently involved using this manoeuvre, sometimes several times.
Still the vast majority of the journey is accomplished drifting
and this is a very slow process.
The
answer is simple, fuel! The problem presented by rocket fuel is a Red Queen’s race.
The more fuel the ship carries the more fuel it needs to carry
that fuel which in turn requires more fuel and so on!
Most of a craft’s fuel is used up in attaining escape velocity.
The remaining fuel is used to aim them in the right direction
where they are then left to drift at relatively low velocities towards
their destination and, on the rare occasions when they have a human
crew, to bring them back. .
The
problem of fuel and escaping the earth’s gravitational well will be
discussed later. First,
we consider the problems posed by using the inertial, drift, drive.
Most
of our exploration of space has been undertaken with unmanned craft.
Provided we have the patience to wait while the ship drifts to
its destination, unmanned probes are fine.
Unless, that is, something goes wrong with it and it crashes
rather than lands. Conversely,
if we want to go anywhere in space travel time is crucial.
We have to breath and in the vacuum of space this means we have
to take a viable atmosphere along with us.
We also need water and food.
To a degree we can recycle these essentials but no system is
perfect and some replenishing of these resources is required.
In addition, the longer the journey, the greater the chances of a
critical failure and natural disaster.
Assuming
we can somehow overcome these difficulties, there is the problem of
gravity. We have evolved
for hundreds of millions of years at the bottom of earth’s 1g
gravitational well. Consequently,
we are eminently adapted to living there and taking us out of it results
in various problems such as the wasting away of muscles and bones.
Without constant exercise, like that provided by fighting the
downward drag of gravity on the mass of our bodies, muscles rapidly
waste away. Without stress
on our bones our bodies begin dissolving the calcium from them.
Worse, it takes far longer to rebuilt muscle and bone mass than
it does to lose them in the weightless environment of a drifting ship in
space. Hibernation
is one possibility for alleviating this.
Provided we are willing to undergo the necessary genetic
manipulation to allow us to slow down our metabolism like other mammals,
such as the bear, or even stop it completely as some frogs able to do,
allowing them to be completely frozen.
This latter has distinct advantages when you are surrounded by
the almost absolute zero temperature of space.
This still means we will be away from earth for years, even to
visit our neighbour Mars. There
is an alternative. Imagine
if it were possible to drive a spacecraft at constant acceleration.
There are no feasible engines that can do this at the moment but
methods have been proposed. One means is to scoop up charged ions in the surrounding
space and drive them backwards, in turn propelling the craft forwards.
Other possibilities will be considered later.
Putting
aside the practicalities of such a means of propulsion, let us consider
what the effects would be on travel times.
Let choose a convenient acceleration.
We evolved on the surface earth where we are subject to its
gravitational field of 1g. As
we have seen, even short exposure to zero and low g forces results dire
health consequences. Conversely,
at higher g forces we risk a host of problems such as burst blood
vessels from the increased pressures we would subject them too.
. We
could, of course, simulate gravity.
There are two known ways of achieving this. The first is what is essentially the anti-gravitational
force, resulting from rotation. In
the movie ‘2001 a space Odyssey’ a large, thin, torus, section of
the spacecraft rotates about the central body creating an artificial
gravity in which the astronauts can maintain the health of their bodies
during the long drift journey outwards towards Jupiter. A
much more useful approach would be continuously accelerating the craft
at 1g for the first half of its journey then decelerating it at, the
same rate, for the second half; in order that the craft comes to rest at
its destination. The result
of this strategy on stellar and inter-stellar travel times is quite
surprising as the table below shows. Destination Closest distance
to earth (ly=light-year) Minimum craft
time to destination. Earth time. Light travel time Maximum velocity
(m/s) c = 3 x 108
Mercury
9.17 x 107 km 2.24 days 2.24 days 5.1 mins 9.5 x 105 Venus
4.14 x 107 km 1.5 days 1.5 days 2.3 mins 6.4 x 105 Mars
7.83 x 107 km 2.07 days 2.07 days 4.4 mins 8.8 x 105 Jupiter 6.29 x 108 km 5.86 days 5.86 days 35 mins 2.5 x 106 Saturn 1.28 x 109 km 8.36 days 8.36 days 71 mins 3.5 x 106 Uranus 2.73 x 109 km 12.2 days 12.2 days 2.5 hours 5.2 x 106 Neptune 4.35 x 109 km 15.43 days 15.43 days 4 hours 6.5 x 106 Pluto 5.77 x 109 km 17.75 days 17.75 days 5.3 hours 7.5 x 106 Moon 3.84 x 105 km 3.48 hr 3.48 hr 1.3 secs 6.1 x 104 Asteroids 2.99 x 108 km 4.04 days 4.04 days 16.6 mins 1.7 x 106 Sun 1.50 x 108 2.86 days 2.86 days 8 mins 1.2 x 106 Proxima
Centuri 4.24 ly 2 years 5.24 years 4.24 years <c Andromeda 2 x 106 ly 2 years 2 x 106 years 2 x 106 years <c 1 ly 2 years 2 year 1 year <c 10 ly 2 years 11 year 10 years <c 100 ly 2 years 101 year 100 years <c 1000 ly 2 years 1001 year 1000 years <c Matching
relative speed with the destination requires only a small adjustment to
these times. For
velocities less than the speed of light the Newtonian approximation for
the equations of motion are extremely accurate.
This works adequately for travel within the solar system as
demonstrated in the figures above.
The
inner planets are too hot to handle.
The moon desolate, though a very viable launching base as it has
only 1/6th the surface gravity of that of the earth to
overcome. Mars is the
planet most like our own in the system and consequently the most viable
one on which to establish colonies and perhaps even of terraforming.
Here
then is an analysis of travel to Mars using a continuous force drive at
1g.
Fig 6.
Journey to Mars Because
the acceleration is constant, the craft can reach terrific velocities in
the middle of its journey; as shown in figure 2 below.
Fig 7.
Velocities to Mars. Most of the distance is covered in the
middle the journey because of the terrific velocities reached during
this part of the journey. To
Mars, as in this example, at a constant 1G acceleration for the first
half of the journey the craft reaches over 3 million kilometres per
hour. For
interstellar distances over one light-year the speeds become
relativistic and the picture is a little different.
In fact, this has a profound effect of travel times. After accelerating for 354 days at 1g a craft would be
travelling at close to the speed of light.
At this point, time on board the craft would be running very
slowly relative to the rest of the universe.
From the perspective of the passengers the distances shrink
correspondingly. Consequently,
to those aboard the craft the remaining distance to the halfway point is
small and reached very quickly. At
which point the craft begins decelerating, which it continues to do for
approximately another year. Thanks
to the effects of relativistic time dilation, the total journey requires
approximately only some two years in total and this remains true for all
journeys within the entire universe.
This is one of those strange coincidences, accelerating at one-g
for one-year achieves close to one-c.
Don’t read too much into this.
After all, we take it for granted that we live on a planet whose
moon has the same apparent diameter as our sun providing us with
spectacular eclipses. Now
the ability to travel anywhere in the universe in two years seems too
good to be true. There is a catch. While
the time dilation effect results in only two years passing for the
occupants of the craft, the journey takes very much longer as far as the
rest of the universe is concerned.
As we have seen to attain speeds close to that of light requires
almost exactly one year, by which time the craft will have travelled
approximately half a light-year. It
will take a further half a light-year to decelerate and for the rest of
the distance the spacecraft is travelling at approximately the speed of
light while very little time passes for those on board.
But, as far as the rest of the universe in concerned, it takes 1
year for the first half light-year, 1 year for the last half light-year
and one year per light year for the rest.
Fig
8. Proxima Centuri, our
nearest neighbouring stellar system. For
Sol’s nearest neighbouring star, Proximal Centuri, this would require
a total time of two years for accelerating and decelerating and a
further three and a quarter years to travel the remaining 3.24 light
years at almost the speed of light.
So on earth a total of five and a quarter years would have
passed.
Fig 9.
Andromeda, our nearest neighbouring galaxy.
If you can’t go now, it is due to collide with our Milky Way in
a mere four billion years time. As
this two years that have passed aboard the spacecraft is almost the same
however far it travels a craft could also reach the next galaxy
Andromeda in only a little more time than one to Proxima Centuri. Now on earth though, a lot more time would have passed, of
the order of two million years. G-Force
propulsion then, offers a means of travelling to and from destinations
within our solar system and even as far as our nearest neighbouring star
systems. For all practical
purposes, beyond a few light years the earth-relative travel times make
the journeys one way unless we wish to travel back to a very changed
world. While
1g is the optimum acceleration as far as we human beings are concerned
attaining it may not be feasible in the foreseeable future. It may be possible though to achieve lower accelerations.
Fortunately, the travel time is inversely proportional to the square
root of the force. So
reducing the force to 1/4 g would only double the time.
Conversely, there is little to be gained by increasing the
acceleration particularly since the human body could not tolerate a
sufficiently high g to significantly reduce journey times.
For example, to halve the time would require quadrupling the
acceleration and 4g is not a force the human body can survive for more
than a short time without serious damage.
The
most important factor in reducing journey times is having a sustained
acceleration. For example,
at only 1% of g the journey time is increase only tenfold. Even at this low acceleration the journey time to Mars would
still be less than three weeks. Fuel.
As
we have seen this Red Queen’s race is what limits us. What is needed is a vastly powerful energy source that has
little mass. There is such
a source, antimatter. When
antimatter and matter meet they annihilate each other releasing all the
energy stored in that combined mass, according to what must be the most
famous equation in science E=mc2.
If somewhat over published due to it being simple, readily
understandable and the basis of nuclear power, the conversion factor of
the speed of light squared means that a small amount of mass can
liberate a tremendous amount of energy.
For example, 20gms of antimatter would be sufficient to power a 1
metric ton spacecraft at 1g to mars and back with enough left over for
the more mundane essentials of sustaining life during the four day round
trip. Conventional
rocket fuel is hydrogen and oxygen.
To produce the same amount of energy as the released by one gram
on matter annihilating one gram of antimatter we would need to burn
624,000 metric tonnes of hydrogen in five million metric tonnes of
oxygen. This before taking into account the amount of extra fuel you
would need to take along all the extra fuel needed. Those are the pros.
There are cons.
1 Obtaining antimatter.
2 Keeping
it safe.
3 Using it efficiently. Antimatter
is created in high-energy collisions.
The sort that regularly occurs in high-speed colliders.
Unfortunately, even in the super-collider at CERN it is produced
in quantities of only a few sub-atomic particles. Yet
there is another place where high-energy collisions occur regularly and
without any financial cost. The
earth is continuously bombarded with high-energy particles from space,
predominantly for the sun. Indeed,
were it not for the deep atmosphere surrounding the earth, we would be
very quickly fried by the high-energy radiation pouring down upon us.
When these collide with the upper atmosphere antiparticles are
generated. Unfortunately,
these are very rapidly annihilated by their matter counterparts, just as
are those ones in man made colliders.
Still due to their very high velocities a tiny fraction make is
as far as the earth’s surface. The
reason these do not last long is that they are mainly in the form of
anti-electrons, positrons, and very occasionally anti-protons and our
universe is full of electrons and protons just waiting to annihilate and
be annihilated by them. Contrary
to fiction, your anti-matter counterpart would not have to meet you in
order to blow up the entire planet.
Any matter will do as everything is predominantly made up of
electrons and protons. Collecting
antimatter before it is destroyed is obviously a problem.
Doing so on any large scale, even a few grams, is extremely
difficult. Once
you have it you then have the problem of storing it. What do you store it in when anything material will, almost
instantly, destroy it and itself be destroyed?
One
possibility is electromagnetic fields.
Individual particles of both positrons and anti-protons can be
captured and held in electromagnetic fields away from any pesky normal
matter. Larger amounts of
matter, even in the form of atoms comprised of both anti-protons and
positrons, could be stored this way as long there was a sufficient
imbalance in the numbers so that the anti-matter retained a sufficiently
strong charge for it to be prevented from impinging on the walls by
magnetic fields. The
danger of a breakdown of containment cannot be over stressed.
In a typical nuclear explosion only a small amount of matter is
actually converted to energy. The annihilation of approximately 23gm of antimatter with the
same amount of matter results in an explosion of one megaton.
Finally,
if we have managed to obtain and contain a sufficient amount of
antimatter to actually power our spacecraft we would not want to waste
it. Ejecting mass energy in
the direction opposite from that in which we want to go produces
propulsive force. When
matter and antimatter annihilate each other the result is a pair of
high-energy photons. The
use of reflectors would result in almost all of this energy being
liberated in the direction we wish.
Providing for a very efficient propulsion system.
There
remains the problem of all that wasted energy getting us up out of the
gravitational well that is the earth.
We could use our precious antimatter but there is another
intriguing possibility. The
technology for which is actively being developed. Anti-gravity
is a dream that would certainly solve the problem. Take a bucket with a strong handle. Put some water in it and rapidly swing it in a vertical
circle. If you did this
swiftly enough, and your bucket held, the water would have stayed in the
bottom of the bucket and not soaked you.
This is the best we can do at the moment for something
approximating anti-gravity. This
is the reason that objects in orbiting spacecraft and stations are in
zero gravity. The
higher the orbiting object the slower it has to orbit to remain in
orbit. There is a specific
distance at which an object orbits at exactly the same rate as the earth
below rotates. Objects
orbiting at this height at the equator remain directly over the same
spot on earth. At other points they appear to drift north and south once a
day. These are termed
geostationary orbits. Naturally,
this is a preferential orbit for satellites of all kind.
For the earth this is some 35.8km above its surface.
If
you could swing your bucket at this height as the equator it would
remain there with the water suspended upside down without effort. Swing the bucket a little higher and it would actually pull
upwards as it would now be moving faster than it needs to in order to
maintain this height. An
object orbiting at this height would mover slower.
The excess speed of tethering it to the earth and dragging it
along at the orbital speed provides the upward force.
This is the principle behind the space elevator.
.
Fig 10.
The Space Elevator: The
elevator’s ‘shaft’ stretches from the earth’s surface at the
equator to a point directly above at the height of geostationary orbit
(dotted line.) The elevator
moves up and down this shaft carrying payloads into space at a tiny
fraction of the cost of rocket travel.
In this case a cable stretches from the equator to above the
height of geostationary orbits. A
counter weight attached to the space end holds the cable taut. A second
weight lifts the elevator up the shaft.
To
construct a space elevator a shaft has to reach from a point on the
equator to a point just above geostationary orbit.
This shaft does not have to be rigid, as a counterweight outside
the geostationary orbit will hold it up, as it would be travelling
faster than is necessary for it to maintain orbit and consequently will
exert a net upward force on the shaft.
It does not even have to be a shaft; a cable serves just as well
as it is just a guide and tether for the elevator.
A
cable attached to a second mass runs to the elevator on the earth below.
The second mass is detatched from this shaft and this draws the elevator
up the tether with its precious cargo.
While energy is required to winch this weight back down in order
to lower the elevator this is a tiny fraction of that required in
launching a rocket and can be applied gradually.
This
is not free energy; there is no such thing.
As the weight moves outwards the earth actually slow a tiny
amount. Fortunately, the
earth speeds back up again upon winching the weight back in.
Back. |
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| Dr. Whom? |
Proprietary content; Please acknowledge the source of any material quoted or cited. |
