**Arthur C. Clarke**

**Interplanetary Flight**

**An Introduction to Astronautics**

First published by Temple Press, 1950.

First American edition by Harper & Brothers, 1951.

Second impression [slightly revised], 1951.

Third Impression, 1952.

**Preface**

This book is intended as a survey of the
possibilities and problems of interplanetary flight, as far as they can be
foreseen at the present day. Although the science of “astronautics” still
belongs to the future, many of its basic conceptions will remain unaltered by
the passage of time, and most of the fundamental techniques already exist in
embryo. It is, for example, possible to calculate by quite simple methods the
velocities and durations required for interplanetary journeys, irrespective of
the physical means that may be used to accomplish them.

The attempt has been made throughout this book to
keep the treatment quantitative, and to give exact values and magnitudes rather
than vague generalities. Nevertheless, almost all mathematics has been
relegated to the Appendix, and it is believed that the argument can be followed
without undue difficulty even by readers with little mathematical or scientific
training.

[…]

The approach throughout has been from the
astronomical rather than the engineering point of view. The author makes no
apologies for this, as there are now several excellent books on rocket
technology, but none, at least in English, which develop the theory of
astronautics in any detail.

[…]

**Chapter 2**

**The Earth’s Gravitational Field**

*Escape Velocity*

Man is still essentially a two-dimensional creature:
all his journeys in the vertical direction have so far been of negligible
extent. It is, therefore, perhaps not surprising that very curious ideas
persist about gravity – one of the commonest being that it ceases, more or less
abruptly, at a definite distance from the Earth. The frequently-encountered
phrase “beyond Earth’s gravity” is a good example of this survival from
pre-Newtonian thinking.

Strictly speaking, no point in the Universe is
“beyond Earth’s gravity”, which decreases as the inverse square of the distance
and so becomes zero only at infinity. At the greatest heights yet attained by
rocket, its value is still nearly 90% of that at sea-level, and one must go to
an altitude of 2620 km (1630 miles) before it is even halved.

Over astronomical distances, however, the decrease is
extremely rapid, as an inspection of Figure 1 will show. The point beyond
which, for practical purposes, the Earth’s gravitation field may be neglected,
depends entirely on the particular case being considered. As will be seen
later, a body travelling at a very high speed quite close to the Earth will be
far less affected by its field than a slow-moving body at a great distance.
Thus the Earth is incapable of capturing a meteor skimming just outside the
atmosphere at 50 km/sec, while it holds the Moon (moving at 1 km/sec) firmly
chained in its orbit a thousand times farther away.

Since the work done in lifting a body of unit mass
vertically against the Earth’s field is the product of distance times force, it
follows that, for equal distances, this work decreases with height according to
the inverse square law or the “

*g*” curve of Figure 1. At ten radii from the Earth’s centre, moving a body through a given vertical distance requires only a hundredth of the energy needed to perform the same feat at sea-level. The*total*energy,*E*, required to lift unit mass from the Earth’s surface to “infinity” (or to a point where for all practical purposes gravity can be neglected) is clearly proportional to the area beneath the “*g*” curve in Figure 1. An integration (see Appendix) gives the surprisingly simple result: –
where

*g*is the value of gravity at the Earth’s surface (981 cm/sec^{2}or 32.2 ft/sec^{2}) and*R*is its radius (6360 kms or 3960 miles).
This equation makes possible a striking mental
picture of the work involved in lifting or projecting a body completely away
from the Earth. The energy expended in climbing a mile is something which can
be visualized as not outside the range of normal experience, though only an
Alpine guide would consider it a part of the day’s work. […] But as Equation
II.2 shows, the escape from Earth is equivalent to a climb of one radius, or
almost four thousand miles, under a gravity equal to its sea-level value.

This peculiarly simple law, which we will often
invoke, holds for all planets and gravitating bodies. To take a case which, as
will be seen later, is not as academic as it sounds, the escape from the Sun
(whose radius and surface gravity are 109 and 28 times that of the Earth) is
equivalent to a vertical climb of almost 109X28X4000 miles, or approximately
12,000,000 miles (say 20,000,000 kms) against one terrestrial gravity. In the
same way, the work required to leave any other body in the Solar System may be
easily calculated.

Our position here on the Earth’s surface may best be
visualized by an analogy which will play an important part in later
discussions. Since the escape from our planet is equivalent to a vertical
ascent of four thousand miles against one gravity, we may picture ourselves as
being at the bottom of a valley or crater four thousand miles deep, out of
which we must climb if we are ever to leave Earth. The walls of this imaginary
crater are at first very steep, but as Earth’s gravity weakens they become
slowly less vertical and the ascent correspondingly easier. At very great
distances (a hundred thousand miles or more) the slope becomes more and more
nearly horizontal until at last we have, for all practical purposes, reached
the level plain and can move in any direction with no appreciable expenditure
of energy.

This imaginary “gravitational pit” has been
accurately drawn in Figure 2, which shows the amount of work needed to reach
“infinity” from any point within about 300,000 miles (500,000 kms) of the
Earth. The figure must of course be regarded as three-dimensional, like the
stem of an inverted wine-glass: its section is actually the rectangular
hyperbola defined by Equation II.3.

In the same way, all other celestial bodies have
their exactly similar gravitation pits. That of the Sun, as we have already
seen, is 12,000,000 miles or 20,000,000 kms deep. The Moon’s, on the other
hand, is only 170 miles (280 kms) deep, and is represented to scale by the
small dimple far up the slope of the Earth’s field in Figure 2. If we imagine
this diagram as showing the profiles of two adjacent valleys, it will be seen
that the problem of escape from the Moon is enormously simpler than that of
leaving the Earth.

There are, in principle, two main ways by which a
body can be transferred from the Earth’s surface to infinity. It can be moved
at a slow and more or less uniform speed, by the continuous application of some
force; but this method, as will be seen later, is excessively wasteful of
energy. Alternatively, it can receive the necessary kinetic energy in one
instalment, as it were, by being given a velocity sufficient for it to “coast”
up the slope of the gravitational crater under its own momentum before coming
to rest. The velocity needed to do this is known as the escape or parabolic
velocity: it is equal to √(2

*gR*) (Equation II.4) and its numerical value at the Earth’s surface is 11.2 km/sec (7 miles/sec or 25,000 m.p.h.). This is also the velocity which a body would acquire during a fall to the Earth’s surface from a very great distance: it follows therefore that a spaceship leaving the Earth must not only reach this speed on the outward journey but must also neutralize it on the return, if it is to make a safe landing.
Escape velocity, though usually quoted for the
Earth’s surface, naturally decreases with distance as a body starting at a
considerable altitude would need less initial speed to reach infinity.[1]
The rate of decrease is rather slow and is also shown on Figure 1 (the curve
being given by Equation II.5).

This curve gives the same sort of information as
Figure 2, but in a more useful and immediately understandable form. It shows at
a glance the vertical projection velocity needed, at any point, to send a body
right away from the Earth – and, conversely, the velocity a body initially at
rest would acquire in falling to that point from a great distance.

[…]

A planet’s escape velocity is one of its most
important characteristics, and not only from the view-point of astronautics. It
determines whether that planet can retain an atmosphere, for if the gas
molecules have average speeds comparable with the escape velocity, the
atmosphere will quickly leak away into space – as has happened in the case of
the Moon and is happening for Mars. A table giving this value for the more
important bodies in the Solar System will be found in Chapter 10.

*Circular Velocity*

Closely related to escape velocity is the conception
of orbital or circular velocity, which is the speed at which a body would
continue to circle the Earth indefinitely like a second Moon, its outward
centrifugal force equalling the inward pull of gravity (just as one may whirl a
stone at the end of a piece of string). The necessary speed to maintain a
stable orbit at any distance from the Earth is easily calculated (Equation
II.8) and near the Earth’s surface is about 7.9 km/s (18,000 m.p.h.) This is
less than the corresponding escape velocity in the ratio 1:√2, a proportion which holds universally at
all points. It is, therefore, much easier for a body to become a close
satellite of Earth than to escape completely, a point which as we shall see
later is of great importance. The conception of a rocket or other structure
circling round the Earth forever with no expenditure of energy seems peculiarly
difficult for the layman to understand – his usual reaction being: “Why doesn’t
it fall down?” Perhaps if, like Jupiter, our planet had a dozen or so natural
satellites at varying distances, the idea of a few artificial ones would be
more readily accepted.

Circular velocity, like escape velocity, decreases
slowly with distance according to an inverse square root law, and the values of
both for points out to the Moon’s orbit are shown in Figure 1.

[…]

*Other Orbits*

We have now considered the two simplest cases of
movement possible for a body projected beyond the Earth’s atmosphere at a point
where the only force acting is that of gravity. It now remains to consider the
more general case, where the motion is neither radial nor circular.

To fix ideas, imagine a point just beyond the
atmosphere and consider what happens when a body is given various horizontal
speeds. At 7.9 km/sec (5 miles/sec) it will, as we have seen, travel round the
Earth forever in a circular orbit. A lesser speed will make it impossible to
maintain this orbit and it will eventually fall to Earth – though it may travel
half-way round the planet before doing so.

If the original speed is in

*excess*of the orbital velocity, then the body will move outwards. It will recede from the Earth along an elliptical path, gradually losing speed until at the point farthest from the Earth (“apogee”) its motion will again be tangential and it will be travelling at its lowest speed. Thereafter, unable to maintain itself at this distance, it will fall back with increasing velocity to its original point of projection (“perigee”) and will continue to retrace its path indefinitely.
[…]

As the initial velocity is increased, the ellipse
becomes more and more elongated and the furthest point moves steadily towards
infinity. (Figure 4.) When escape velocity is reached, the ellipse changes into
a parabola and the body never returns. (This is the reason why escape velocity
is often called parabolic velocity.) For speeds greater than this value, the
body moves away from Earth along a hyperbola, which at very great speeds indeed
(over 100 km/sec) would become almost a straight line.

[…]

**Chapter 3**

**The Rocket**

*Fundamentals*

The rocket motor is unique among prime movers in two
respects – its independence of any external medium, and its ability to generate
colossal thrusts and powers. Both of these characteristics are required for
space-flight, the former for obvious reasons, the second because very large
masses fuel are necessary for interplanetary missions.

No detailed discussion of the purely engineering
aspects of the rocket will be given in this book, as several excellent works on
the subject are now available. (See Bibliography.) But it may be as well to
spend some little time considering why the rocket, unlike all other forms of
propulsion, can operate in space, which for all practical purposes is a perfect
vacuum.

All forms of locomotion depend of reaction. Surface
vehicles, through the friction of their wheels, try to thrust the Earth away
from them and, to an immeasurably small extent, succeed; but such is the
disparity of masses that the effect on the Earth is unnoticeable. Aeroplanes
and ships operate by giving momentum to a mass of air or water, thus acquiring
equal momentum in the opposite direction. This is most clearly seen in the case
of the jet aircraft, the rocket’s closest relative. The jet collects a large
quantity of air, which it heats and expels at a very great velocity, thereby
obtaining a thrust which is proportional to the product of the jet’s mass and
its increase in speed. If it could carry its own oxygen supply, instead of obtaining
it from air, a jet aircraft could then operate as a self-contained unit capable
of functioning in a vacuum – and would, indeed, then be a type of rocket.

It cannot be too strongly emphasised that neither the
rocket nor the jet obtains thrust by “pushing on the air behind”, as a great
many people believe. All the “push” occurs

*inside*the combustion chambers and exhaust nozzles, and the subsequent adventures of the burnt gases once they have left the system can have no effect on it whatsoever. It is sometimes helpful to think of the rocket’s still burning and expanding gases as thrusting against the already burnt gas further down the nozzle, so producing a recoil in exactly the same way as the charge in a gun, driving the bullet forwards, forces the gun backwards with equal momentum. The rocket may indeed be regarded as a sort of continuously operating gun firing out a stream of gas instead of solid material.
The velocity which a rocket can attain, after burning
all its fuel, is clearly dependent on the speed with which the gases leave the
nozzle (the exhaust or jet velocity) and the amount of fuel ejected. These
quantities are connected by the simple relation (see Appendix), the most
important in the whole of rocketry: –

From these equations, it follows that although the
rocket’s speed increases in direct proportion to the exhaust speed, it does so
only slowly with increase in mass-ratio. This result is best shown graphically,
as in Figure 5.

These curves show that, for a given value of exhaust
velocity

*c*, impossibly high values of mass-ratio*R*would be needed if the rocket is to attain a final speed much greater than*c*. For*R*=*e*=2.718…, the rocket’s final speed would equal its jet speed. This value presents no engineering difficulties: it would mean, for example, building a rocket of empty mass 1 ton, carrying 1.72 tons of fuel. V.2 did considerably better than this, having a mass-ratio of over 3 with its normal one ton warhead, and almost 4 if carrying only light meteorological instruments. But to*double*the final speed, with the same exhaust velocity, would mean*squaring*the mass-ratio, i.e. increasing it from 2.72 to 7.4 (*e*^{2}). This would be a considerable technical feat, though perhaps not an impossible one. A rocket capable of travelling three times as fast as its exhaust would need a mass ratio of 20 (*e*^{3}), which may be regarded as quite impracticable, since it would require that 95% of the machine’s total mass be fuel and only the remaining 5% be devoted to payload, structure, motors, etc. It appears, therefore, that no simple rocket can be built to travel more than 2 or 3 times as fast as its exhaust. When, as in the next chapter, the inevitable losses to air-resistance and gravitational retardation are considered, it will be seen that the value 2 is more likely to be the upper limit.
The attainment of high exhaust speeds is therefore
the first concern of the rocket engineer, and is a problem involving chemistry,
thermodynamics, metallurgy, and a great deal of still somewhat empirical
mathematics. The

*absolute maximum*of exhaust velocity available from any given fuel is easily calculated by assuming that the motor converts all the propellant’s energy of combustion into kinetic energy at 100% efficiency. The figure obtained in this way, however, has very little relation with reality. In practice, owing to the inevitable losses in any heat engine, no more than about 70% of this theoretical or ideal velocity can ever be achieved: with current designs, the figure is about 55%.
The best-known rocket fuel (that used in V.2) is the
alcohol-liquid oxygen combination with an ideal exhaust velocity of about 4.2
km/sec (14,000 f.p.s.). The value realized so far in practice is only some 2.25
km/sec (7,500 f.p.s.).

Considerably more powerful fuels exist, with ideal
exhaust velocities up to 6.5 km/sec (21,000 f.p.s.). These involve “combustion”,
not with oxygen, but with still more reactive element fluorine. When such
propellants are fully developed (which will require many years of research and
considerable improvements in metallurgy to permit motor operation at high
temperatures) it is possible that exhaust speeds of around 4.5 km/sec (15,000
f.p.s.) may be obtained. It can be shown[2]
that,

*irrespective of the energy contained in any possible propellant*, this figure is near the absolute limit which may be achieved with chemical rockets, since much higher values would require impossible temperatures and pressures in the motor.
[…]

A table giving some of the more important propellants
known at present or likely to be used in the near future is given overleaf,
together with their exhaust velocities in km/sec. These values can only be
somewhat approximate as they would vary from motor to motor or in the same
motor from sea-level to vacuum.

Since we have seen that it is not practicable to
build a rocket capable of travelling more than about twice as fast as its
exhaust, it would therefore seem that – even when chemical propellants and
motors have been developed to the ultimate – we cannot hope to build rockets capable
of attaining speeds of over 9 km/sec (20,000 m.p.h.) This would be sufficient
to achieve circular velocity, but insufficient for an escape from the Earth. In
later chapters, however, we will see that there are various ways of avoiding
this difficulty, notably by the principle of “step construction”.

[…]

**Chapter 4**

**The Problem of Escape by Rocket**

*Velocity Requirements*

The ground covered in the last two chapters now
enables us to discuss, in a quantitative manner, the problem of escape from
Earth by rocket. We have seen that if a body can attain a speed of more than
11.2 km/sec (or less if it is already at a great height) then it will travel
away from the Earth indefinitely with no further expenditure of power. And we
have seen how to calculate the final velocity reached by a rocket after
combustion of its fuel.

Equation III.2, on which our previous calculations
were based, was however derived for the theoretical case of a rocket acted upon
by no forces except its own exhaust. A machine rising in the Earth’s atmosphere
will experience two retarding forces which may be considerable – air
resistance, and the downward pull of gravity. The corrected equation for the
rocket’s final velocity after a vertical ascent (at the moment of fuel cut-off)
must therefore be written

where

*t*is the time of flight and*V*is the total velocity loss due to air-drag. The acceleration of gravity,_{D}*g*, is of course assumed to be constant during the period of powered ascent: this is nearly true in most cases that are likely to occur, for a rocket would burn most of its fuel while still relatively near the Earth.
It is quite impossible to give a general formula for
the air-resistance loss: it depends on the shape and size of the rocket, the
acceleration characteristics of its path, and the height of take-off. Since a
high-velocity rocket spends only a short part of its powered trajectory in the
relatively dense lower atmosphere, it does not reach considerable speeds until
the air is already very rarefied, and towards the end of the burning period
air-drag is quite negligible.

[…]

Considerably more important, it will be noticed, is
the gravitation loss term,

*gt*. Since this depends directly on the time of operation of the motors, it can be reduced only by short burning times*and hence high accelerations*. The maximum acceleration which a large rocket can employ is, however, limited by the thrust of its motors. At take-off, when it was fully loaded, V.2 had an acceleration of only 1*g*and the value for “Viking” is about the same. (The leisurely ascent of a giant rocket invariably surprises those who are only acquainted with the common or back-garden variety, with their accelerations of 50*g*or more.) When the propellant is nearly exhausted, liquid-fuel rockets may reach accelerations of about 10*g*unless the motor thrust is reduced. For manned rockets, such “throttling back” might be desirable, though as mentioned in Chapter 9 a properly protected man can tolerate higher linear accelerations than it would be practical to stress a large machine to withstand.
In order to reach escape velocity, therefore, thrust
periods of several minutes would be required – and each minute of vertical
ascent means a loss to gravity of 0.6 km/sec or 1,300 m.p.h. This would be a
very serious matter, but fortunately substantial savings can be effected by
using non-vertical departure curves – “synergic curves”, as will be explained
later.

Since any rocket escaping from the Earth’s neighbourhood
must reach 11.2 km/sec, we can substitute this constant value in Equation
III.2.a. and see how the mass-ratio

*R*varies with the assumed exhaust velocity*c*. The equation – ignoring “gravitation loss” for the moment – then becomes
Neglecting gravitational loss assumes that the
rocket’s acceleration is infinite (t=0) and this limiting case is shown by the
curve n=∞ in Figure 7. It will be seen that with the best
present-day fuels (

*c*less than 2.5 km/sec) a mass-ratio of about 100 would be required – about ten times the limit that is practicable even with a very small payload.
When exhaust velocities of around 4.5 km/sec are
available, which should be the case when high-energy fluorine-based fuels can
be handled, the mass-ratio necessarily would be reduced to rather more than 10.
This is still too high a value, thus confirming the conclusion already reached in
the last chapter that it is impossible to build a single-stage,
chemically-propelled rocket to escape from the Earth, even with no payload.

When one allows for the gravitational loss caused by
the rocket’s finite acceleration, the picture is even blacker. Assuming that
the rocket maintains a constant acceleration of

*ng*(where*n*is not likely to exceed values of 5 to 10) it is easy to show (see Appendix) that the required mass-ratio for escape is given by the increased value
This function has been plotted in Figure 7 for
various values of

*n*, and the enormous losses incurred when*n*is low will be readily seen. The*reductio ad absurdum*case occurs when*n*=0, and the rocket has merely enough thrust to hang motionless in the air above its launching site until the fuel is exhausted!
Figure 7 will repay careful study, since it shows at
one and the same time the paramount importance of high exhaust velocities and
high accelerations. If a 10 km/sec fuel were available, the problem of building
a single-stage rocket to reach escape velocity would be relatively easy. For a
rocket accelerating at 5

*g*, the mass-ratio required would be less than 4, whereas with present propellants the figure would be about 200.
The above discussion is quite valid as far as it goes
and has been used by many to prove that space-flight must remain impossible. There
are, however, few cases in scientific history of “negative predictions” surviving
the passage of time. When,

*taking all factors into account*, anything can be proved to be impossible, that usually means that it will be done in some different manner and employing a new and unforeseen technique. Demonstrations of the impossibility of heavier-than-air flight (a popular recreation among conservative scientists at the end of the last century) overlooked the petrol engine: those who believed that atomic power would never be released did not imagine the self-sustaining chain reaction and the ubiquitous neutron.
Much of technological progress consists of pincer
movements around insoluble problems which eventually become left so far behind
that their very existence is forgotten. In the case of astronautics, two
solutions were put forward to overcome the difficulties discussed above. The
first accepted the need for very high mass-ratios and proposed a method of
construction – the step-rocket – which made them engineering possibilities. The
second was much more daring: it proposed that the escape from Earth should not
take place in one stage, but in two or more, the rocket actually being refuelled
in space. This technique of orbital refuelling not only makes possible reductions
in the overall masses required for interplanetary voyages, but, as we shall see
later, opens up a whole range of important subsidiary projects.

[…]

**Chapter 5**

**The Earth-Moon Journey**

*Velocity Requirements*

The simplest of all journeys into space, and the
first which will actually be accomplished, is the journey to or around the
Moon, which will now be considered in detail. The conclusions reached in this
chapter will apply, it should be noted, both to guided missiles, uncontrolled
projectiles, or manned spaceships. They must all obey the same fundamental
laws.

As far as energy requirements are concerned, Figure 2
shows that the Moon is, dynamically speaking, very nearly at “infinity”,
despite its astronomical nearness. It needs a velocity of 11.2 km/sec to
project a body to infinity – and 11.1 km/sec to project it so that it just
reaches the Moon (385,000 kms or 240,000 miles at mean distance). This velocity
difference is so small that it is frequently ignored and it is assumed that the
full escape velocity is needed for the mission.

A body leaving the Earth in the direction of the Moon
would be subject of the gravitational fields of both bodies, but for
three-quarters of the way that of the Moon is completely negligible, as is
shown in Figure 8. This diagram gives the accelerations produced by Earth and
Moon in cm/sec

^{2}: in order to show the values over the region where both are significant, the scale here has been multiplied by 100.
Since the fields are opposing, they have been drawn on
opposite sides of the horizontal axis, and it will be seen that there is a
point – the so-called “neutral point” – at which both fields are equal and the
resultant (represented by the dotted line) vanishes. Up to this point the body
would have an acceleration towards the Earth: thereafter, the force acting upon
it would be directed to the Moon. It might be mentioned here that, contrary to
the vivid descriptions given by many writers, absolutely

*no*physical phenomena of any kind would take place in a rocket passing this point. Since the machine would be in a “free fall”, with only gravitational forces acting upon it, its occupants would be weightless and so would be quite unaware of the fact that the actual direction of the fall had altered. Nor would it be possible for a body with insufficient speed to be stranded at the neutral point: the equilibrium would be quite unstable owing to the movement of the Moon and the (very small) perturbations produced by the Sun and the planets.
As it receded from the Earth the rocket’s velocity
would decrease according to the escape-velocity curve in Figure 1, and it would
thus pass the neutral point at a speed of about 1.6 km/sec in its fall towards
the Moon. The Moon’s escape velocity is 2.34 km/sec, and this is the speed with
which the rocket, if it started from rest at a great distance, would crash into
the Moon’s surface. In the case we have taken the rocket has a certain
additional energy since it left Earth with a speed slightly in excess of
minimum requirements. Allowing for this, we find that in the fall towards the
Moon it would reach a terminal speed of about 2.8 km/sec (6,300 m.p.h.).
Clearly, if a safe landing is to be made, this speed must be neutralized by the
further application of rocket power.

[…]

Just as the Earth has its characteristic circular
velocity of about 8 km/sec, so has the Moon, the value for a point near its
surface being 1.65 km/sec (equivalent to a period of 1.8 hours). It may seem a
little odd to speak of satellites of satellites, but from the point of view of
the Sun this is what the Moon already is! If, therefore, when a rocket was
falling past the Moon its speed was reduced to its appropriate value by firing
its motors in the direction of flight, then it might continue to circle our
satellite, perhaps taking observations automatically and radioing them back to
Earth. If the fuel reserves were sufficient, it might at a later time be
accelerated again into an orbit which would return it to our planet. The
velocities on the return journey would be identical with those on the outward
one: the rocket would cross the neutral point at its minimum speed, and then
accelerate more and more rapidly until it reached the Earth at 11.1 km/sec –
the speed with which it originally started.

It will be seen, therefore, that as soon as it
becomes possible to build rockets which can escape from the Earth at all, a
considerable range of interesting possibilities will be opened up.

[…]

The above discussion leads us to the conception of
the “characteristic velocity” which a rockets needs if it is to carry out any
particular mission. For a rocket which is required to reach the Moon, but may
be allowed to crash on it unchecked or shoot past into space, this velocity, as
we have seen, is 11.1 km/sec, or a little less than the velocity of escape. If
it is desired to make a landing to set down instruments or, later, human
beings, then the machine’s fall into the Moon’s field must be counteracted. This
means that in some way the rocket must be reorientated in space so that its
motors point towards the Moon, and rocket braking must be employed. To put it
picturesquely, the rocket must “sit on its exhaust” and so descend slowly on to
our satellite’s surface.

If this manoeuvre was carried out in the most economical
manner possible, it would require the combustion of exactly as much fuel as the

*escape*from the Moon. Both missions are identical apart from the change in sign: it requires just as much energy to accelerate in space as to decelerate. The Moon’s escape velocity being 2.34 km/sec, the characteristic velocity for the whole trip is 11.1+2.34 or 13.44 km/sec. The rocket must therefore be designed as if it had to reach this speed, and this is the figure which must be substituted in Equation III.2.a. to obtain the mass-ratio required for the mission. The rocket, of course, never reaches this speed, since it divides its efforts between the two ends of the voyage: however, it would be capable of doing so if it burnt its fuel in one prolonged burst.*Mass Ratio Requirements*

This figure of nearly 13.5 km/sec is a theoretical
minimum value: it does not allow for gravitational loss at the take-off from
Earth and an exactly corresponding, though much smaller, loss at the lunar
landing. Taking these factors into account, the characteristic velocity for a
voyage from rest on the Earth’s surface to rest on the Moon’s is about 16
km/sec (36,000 m.p.h.). With the most powerful chemical fuels ever likely to be
available this would require an effective mass-ratio of about 35 and hence
would involve the use of rockets of at least three stages, or else the orbital
refuelling techniques mentioned before.

For a return journey the characteristic velocity must
be doubled: it would therefore be about 32 km/sec. However, an interesting and
important complication arises here. The descent on to the Moon could only be
carried out by rocket braking, since there is practically no atmosphere. In the
case of the Earth, the final landing could certainly be by parachute or some
equivalent aerodynamic means. Indeed, it is possible that the greater part of
the 11.1 km/sec which the rocket would acquire on its long fall back from the
neutral point could be destroyed by air-resistance, by the technique of
“braking ellipses.”

This procedure was worked out in great detail by the
early German writers and is as follows. Suppose that in its fall towards the
Earth the rocket is aimed so that it passes through the highest levels of the
atmosphere – at an altitude of about 100 kilometres. It will suffer a certain
amount of retardation due to air-resistance, which, if the altitude is chosen
correctly, can be of any desired value. (There would be no great danger of the
rocket becoming incandescent at these altitudes, for it would have only
one-fifth of the speed of a meteor at this level and the air-resistance would
therefore be only a twenty-fifth as great.) After “grazing” the atmosphere, the
rocket would again emerge into space, where the frictional heating produced on
its walls could be lost by radiation. It would now, however, be travelling at a
speed substantially less than escape velocity, and so after receding from Earth
to a considerable distance would return again along a very elongated ellipse.
At “perigee” it would re-enter the atmosphere, cutting through it at a lower
level but at less speed than on the
first contact.

It this way, after a series of diminishing ellipses, the
rocket could shed most of its excess speed without using any fuel. Indeed, it
has been calculated that the entire landing on the Earth could be carried out
in this manner, the final “touch-down” being by parachute. Before this can be
settled definitely much more extensive knowledge of the upper atmosphere will
be required, but undoubtedly substantial savings of fuel can be effected in
this way.

Taking the most optimistic view we can calculate the
“characteristic velocity” for the round trip as follows: –

The more pessimistic estimate, which assumes that the
whole of the landing on Earth would have to be done by rocket braking, would be
about 32 km/sec.

These performances would demand effective mass-ratios
of about 70 and 1,000 respectively with the best conceivable chemical fuels,
from which it will be seen what an important role air-braking can play if it
proves practicable. But even the lower figure of 70 would require, for a ship
large enough to carry men and their equipment, an initial mass of many
thousands of tons at take-off. This demonstrates once again the virtual
impossibility of a return voyage to the Moon, with landing, in a
chemically-propelled rocket.

The economics of the Earth-Moon voyage would,
however, alter drastically is orbital refuelling was employed.

[…]

*Transit Times*

So far, no mention has been made of the duration of
the lunar journey. If the rocket maintained its initial speed of 11 km/sec
(25,000 m.p.h.) it would reach the Moon after 10 hours, but since its velocity
is steadily decreasing the figure is considerably greater. For a body leaving
the Earth’s neighbourhood at the minimum speed which enables it to reach the
Moon at all (11.1 km/sec), the journey to the Moon’s orbit takes about 116
hours (see Appendix, Equation V.1). This, however, ignores the acceleration of
the Moon’s field towards the end of the journey, which would produce a small
but appreciable reduction of transit time.

This figure of 116 hours is therefore the

*maximum*length of time a free projectile could take on the direct journey to the Moon. A rocket which had to engage in retarding manoeuvres would, of course, be longer on the journey.
Five days is not a great deal of time in which to
make a voyage to another world[3]
and it would decrease very sharply if the rocket left the Earth with any
appreciable excess speed over the minimum 11.1 km/sec. (See Appendix, Equations
V.2, 3.) Some typical values for these transit times are tabulated below.

[…]

**Chapter 6**

**Interplanetary Flight**

*The Sun’s Gravitational Field*

In our discussions of lunar journeys in the last
chapter, it was assumed that the Earth and Moon formed a more or less closed
system and that the effects of other gravitational fields could be ignored.
This is true, to a very high degree of accuracy, of the minute fields of the
planets. The Sun’s field, however, is far more powerful since it holds the
Earth firmly in its orbit at a distance of over 90,000,000 miles, and it may
well be asked if we were justified in ignoring it in our calculations.

To a first approximation the answer is – luckily –
“yes”. Although the Sun’s influence is relatively large, the

*variation*over the whole width of the Moon’s orbit is very small – less than 1 per cent. of its absolute value. In other words, the Sun acts almost equally on Earth and Moon and on any object between them: a negligible error is therefore introduced if we ignore it completely. Its effect only appears in the third or later significant figures when more accurate calculations are required.
When we come to consider, not journeys from a planet
to its nearby satellite, but from one planet to another, the situation is
totally different. We must now alter our point-of-view from the Earth, holding
its solitary Moon in its gravitational grip, to the Sun, keeping all the
planets moving in its far more extensive field.

Everything that has been said about the Earth’s field
in Chapter 2 applies, with a suitable alteration of scale, to the Sun’s. At the
surface of the Sun, the acceleration of gravity is 28 times that at the surface
of the Earth. If we use this value for “

*g*” and the appropriate value of the Sun’s radius (695,500 kms or 432 000 miles) in the equations derived in the Appendix to Chapter 2, we can find the magnitudes of the solar escape and circular velocities and the dimensions of the orbits for the bodies moving in the Sun’s field, exactly as we have done in the case of the Earth. We can also calculate the work needed to lift a body from the Sun’s surface to infinity, and can express this in terms of a vertical distance – the “depth” of the Sun’s gravitational pit. A comparison of the two sets of figures is instructive:
We are not, of course, concerned with leaving the
actual surface of the Sun, but if we move from one planetary orbit to another
we are required to move up or down the slope of the Sun’s gravitational crater,
which is precisely similar in shape to that of Earth (Figure 2), except that it
is 3,000 times as deep. It is therefore important to consider the locations of
the Earth and planets on the slopes of this imaginary crater.

The usual scale-drawing of the Solar System, as found
in most school atlases and any astronomy book, shows the inner planets crowded
round the Sun with the outer worlds at progressively increasing distances – up
to 6,000,000,000 kms (3,750,000,000 miles) for Pluto, the most distant of the
Sun’s children. The “energy diagram” of the system, however, presents a
completely different picture. Far from being near the Sun in the gravitational
sense, even the innermost planet, Mercury, is very remote from it. Whereas the
full depth of the imaginary crater is nearly 20,000,000 kms, all the planets
are crowded together on its very uppermost slopes, within 250,000 kms of the
level plain into which it slowly flattens. This means that the work done in
moving between the planetary orbits is only a small fraction of what it might
well have been had the scale of the Solar System been different: indeed, we
will presently see that crossing such an immense distance as that between Earth
and Mars may require less energy than the journey between Earth and Moon.

In other words, the Sun’s gravitational field, though
of enormous extent, is very “flat” in the region of the planets and the climb
up its slopes requires relatively little energy. Superimposed on this field are
the much smaller fields of the individual planets. These are effective only
over very short distances, but their gradients are relatively steep and so we
have the paradox arising that the first thousand miles of an interplanetary
journey may require more energy than the next score of millions. This state of
affairs is depicted in Figure 9, which will be explained in more detail
presently.

The planets, at their varying distances, are
travelling round the Sun in orbits which are, in most cases, very nearly circular,
and all are moving in the same direction and lie approximately in the same
plane. The velocities of motion can be calculated from Equation II.8 with
suitable values for the constants: they range from 48 km/sec in the case of
Mercury, the innermost planet, to 5 km/sec for Pluto, at the known limits of
the Solar System. It will be seen, therefore, that a body on any of the planets
already possesses, by virtue of its orbital motion, a very large part of the
energy needed for interplanetary voyages.

If we calculate, from Equations II.5 and II.8, the
velocity of escape and the orbital velocity in the Sun’s field at the position of
the Earth, the values obtained are 42 and 30 km/sec respectively. The first
figure is the velocity which a body, at rest in the Earth’s orbit, would have
to be given to project it past all the outer planets and far away from the
Solar System – indeed, to the stars themselves, after many millions of years. The
second figure is, of course, the velocity which the Earth already possesses:
the difference (12 km/sec) is therefore the

*additional*speed which must be imparted to a body, moving with the Earth but free of its gravitational field, to send it completely out of the Solar System.
Similar calculations can be made for all the other planets, and some of the
results are shown in Figure 9. As far as the writer knows, this form of
representation of the Solar System is due to Dr. R. S. Richardson, of Mount
Wilson Observatory.

It will be seen that this drawing bears a
considerable similarity to Figure 2, but whereas in the earlier diagram the
ordinates were in terms of distance (and hence energy), here they are in the
more convenient form of velocity. The diagram must be imagined as extending
downwards ten times further than shown, to the 618 km/sec escape velocity needed
to leave the actual surface of the Sun. The left-hand branch of the curve shows
the additional “transfer velocity” needed by a body, already moving in a
circular orbit round the Sun, to permit it to leave the Solar System. Even for
the orbit of Mercury this additional velocity is only 20 km/sec – a very small
fraction of the enormous values needed in the neighbourhood of the Sun.

On the right-hand side of the figure, the subsidiary
escape velocity curves for the individual planets have been superimposed, so
that we can see at a glance the

*total*velocity needed to leave the Solar System from the surface of the five inner planets – assuming that this feat was carried out by (1) accelerating to escape from the planet and then,*when this has been achieved*, accelerating to escape from the Sun’s field. As we shall see on page 66, it would be much more efficient to make the velocity change in one operation, as near to the planet as possible. Nevertheless, Figure 9 demonstrates the important fact that the energies needed to cross the great spaces of the Solar System are no more, and are often much less than, those needed to leave the planets themselves. It also shows that, from the energy viewpoint, the surface of Jupiter is much nearer the Sun than is that of Mercury!*Interplanetary Orbits*

We will now consider the velocities required to make
the interplanetary journey which is perhaps of the greatest interest – that
from the Earth to Mars. The case examined will that in which the maximum
possible use is made of the planets’ existing velocities. Obviously, if one had
quite unlimited supplies of energy one could travel from one planet to another
by any route one fancied, but for a long time to come only the orbits of
minimum energy – the astronautical equivalents of great circle routes in
terrestrial navigation – will be of practical interest.

Figure 10 (a) shows the orbits of the two
planets drawn to scale, although as the orbit of Mars is actually somewhat
eccentric (

*e*=0,093) the average values of its radius and orbital speed have been taken for simplicity. This approximation will give results which are slightly too pessimistic for journeys when Mars is at its closest to the Sun, and vice versa, but the variations are very small.
The path of a spaceship in the Sun’s controlling
field must follow one of the curves – ellipse, parabola or hyperbola –
discussed in Chapter 2, and any of these could in principle be employed for
interplanetary travel. But the path which, as will be almost intuitively
obvious, is the easiest one to use is the ellipse which is tangent to both
planetary orbits, and with the Sun at one focus.

It is easy to calculate, from Equation II.10, the
velocity which a body needs to travel in such a path. When it was nearest the
Sun, i.e. in the neighbourhood of the Earth, its speed would be 32.7 km/sec. As
it grazed the orbit of Mars this would drop to 21.5 km/sec. These speeds do not
differ very greatly from those of the planets themselves – 29.8 and 24.2 km/sec
respectively.

To project a body, which is already moving in the
Earth’s orbit, out to Mars we need thus only give it an additional speed of
32.7 – 29.8 or less than 3 km/sec in the direction of the Earth’s motion. It
would then drift outwards away from the Sun along the ellipse of Figure 10 (a)
until it reached the orbit of Mars. Its velocity would then be 24.2 – 21.5 or
2.7 km/sec too low for it to remain here and it would start to drop back to the
Earth’s orbit again. If, however, it was now given this “transfer” velocity of
2.7 km/sec it would remain in the Martian orbit. It could then land on Mars, using
rocket braking against the planet’s gravitational field, or could become a
third satellite of the little world, taking observations until it was time to
start on the homeward voyage. A rather subtle point arises here. If we wish a
spaceship to reach Mars from the surface of the Earth, it must still have an
excess speed of 2.9 km/sec when it has escaped from the Earth. If it started at
11.2 km/sec, it would have no residual speed left when it had done this. Therefore,
since the problem is one of kinetic energies, the required starting speed is
given by squaring these velocities, adding them, and taking the square root. The
result is 11.6 km/sec:[4]
the

*arithmetical*sum of 14.1 km/sec gives the correct answer only if the ship waited until it had completely escaped from the Earth before accelerating into the voyage orbit – obviously an uneconomical procedure.
Similarly for the landing on Mars, when we have to
neutralise the 5 km/sec produced in falling through Mars’ gravitational field, and
change orbital velocities by 2.7 km/sec, the required total change would 5.7
and not 7.7 km/sec.

For the complete journey, therefore, the ship must be
designed to make speed alterations of 11.6 and 5.7 km/sec at the two ends of
its voyage – a total (since this time, of course, we have to add
arithmetically!) 17.3 km/sec.

In practice this minimum value would have to be
increased to about 20 km/sec to allow for gravitational losses at the landings
and take-offs, course corrections, etc. Nevertheless, this is not such a large
increase over the 16 km/sec needed for the Earth-Moon journey – yet the total
distance covered is more than a thousand times greater!

The return journey, apart from the possible use of air-resistance
braking in the Earth’s atmosphere, would be carried out in an identical manner and
would require the same total velocity. The characteristic velocity for the round
trip would therefore be about 40 km/sec, or just under 30 km/sec if 100 per
cent. air-braking could be used at the Earth landing.

It will be realised that such journeys could only be carried
out at the times when the planets were in the correct relative positions, so
that the rocket would arrive at the Martian orbit at the point also occupied by
the planet.

[…]

On the above lines it is possible to calculate the
“characteristic velocity” needed for any interplanetary journey, and a table of
such values for the more important cases is given below.

These values must be regarded as no more than approximations
based on rather conservative assumptions, so that the actual values would
certainly be somewhat less. No allowance has been made, for example, for the
fact that a spaceship taking off from the Equator would possess an additional
half a kilometre a second velocity owing to the Earth’s rotation. And if, as
some believe, the whole of the landing on Earth can be effected by air-braking
alone, the figures for the return journeys would be reduced by 10 or 11 km/sec.

[…]

*Fuel Requirements*

The characteristic velocities for interplanetary
journeys are considerably higher than for the lunar voyage, and the necessary
mass-ratios are very much higher still since they increase as the power of the
characteristic velocity. (Equation III.2.a.)

Assuming the use of a fuel giving an exhaust velocity
of 4.5 km/sec, which we have seen is probably the maximum that can ever be obtained
from chemical propellants, the return Martian journey with landing on Mars would
demand an effective mass-ratio of about 7,300, which is utterly beyond
realization. (It would mean in practice that for every ton taken on the round
trip several score thousand tons of fuel would be required at the take-off!) Even
assuming the use of atmospheric braking for the whole of the final Earth
landing, we still obtain mass-ratios for the round trip of 790 or more. Using
step construction, this would require a rocket with an initial mass comparable
to that of a battleship.

This does not mean that interplanetary travel is
impossible with chemical fuels, but it does mean that it is impossible to build
spaceships capable of reaching the planets from the Earth’s surface, landing on
them, and returning to the Earth

*in a single operation*, carrying all the fuel for the complete mission. If the task could be broken down into its components, it would become easier by several orders of magnitude, and would enter the realm of engineering possibility. In other words, we are again compelled to consider orbital refuelling.
As an example of the sort of thing that might be done
on these lines, consider a journey to Mars starting from an orbit just outside
the limits of the Earth’s atmosphere, the spaceship having been refuelled as
suggested in Chapter 4 and described in more detail in Chapter 8. It would then
escape from this orbit and enter the cotangential ellipse taking it to Mars,
the total velocity for this manoeuvre being about 3.6 km/sec. On approaching
Mars and accelerating into its orbit, the ship would not land but would become
a satellite of Mars at a distance of a few hundred kilometres from the surface.
At this height it would be possible to learn an immense amount about the planet
by telescopic observation.

The spaceship would continue to circle Mars in a free
orbit until the planet was in the correct position for the return journey. This
would involve a waiting period of 455 days, which, though long, means that it
would be possible to observe a complete cycle of seasons over the two
hemispheres. The total characteristic velocity for the mission would be as
follows: –

Assuming a rocket exhaust velocity of 4.5 km/sec,
this could be accomplished with a mass-ratio of 3.6 or, for the return trip
back into the orbit round Earth, 13. Such figures could be achieved by a
spaceship of relatively few steps, the construction of which would be further
simplified by the fact that it would never have to withstand high accelerations
since it would always be operating in low gravitational fields. […] Although
the complete project, including the fuelling of the ship in its orbit and the
eventual retrieving of the crew by an auxiliary rocket when they had returned
to the Earth’s neighbourhood, would be exceedingly expensive and would require
the combustion of several thousand tons of fuel, there would never be any
question of handling such quantities in a single operation or in a single
machine. The largest amount to be dealt with at any one time would be a few
hundred tons.

[…]

As a more remote prospect, if the materials for
refuelling spaceships could be found on any of the planets and extracted
without undue difficulty, the economics of the entire project would change
radically. (There would be little transatlantic flying even today if aircraft
had to carry their fuel for the round trip.) But even when such co-operation
makes it possible to budget for one-way trips only, and even when orbital
refuelling techniques are exploited to the utmost, flight to the other planets
will remain a fabulously expensive enterprise, which can be carried out only at
infrequent intervals. It would still be worth doing on purely scientific
grounds and for the profounder reasons discussed in Chapter 10: but even a
flourishing world-state could not afford it very often.

All this is assuming that rocket exhaust velocities
appreciably greater than 4.5 km/sec can never be attained. If this limitation
can be circumvented in any way the whole picture will be altered. To take a
specific case, consider the round trip to Mars which, as we have seen, requires
a characteristic velocity of 40 km/sec if the mission is to be carried out as a
single operation. The effective mass-ratios needed for this journey if high
exhaust velocities can be obtained are listed below.

The rate at which the figures decrease with
relatively modest increases in exhaust velocity is astonishing. The value of
exhaust velocity at which interplanetary travel begins to look a practical
proposition rather than a prodigious scientific feat is about 10 km/sec – four
times the value attainable today and twice that which seems the ultimate limit
for chemically-propelled rockets. It is, therefore, natural to ask if such
performances can be obtained by any application of atomic power.

It can be said at once that the energies released by
nuclear reactions are of such a magnitude as to make the requirements of
interplanetary travel look very modest indeed. At a very conservative estimate,
the fifty or so pounds of fissile material in the first atomic bombs liberated
10,000,000 mile-tons of energy. This is more than sufficient to take a mass of
1,000 tons to the Moon

*and*to bring it back to Earth – a feat which would require the combustion of millions of tons of chemical fuel. This fantastic disproportion[5] – 50 pounds of plutonium doing the work of millions of tons of chemicals – becomes even more astonishing when one considers that less than 0.1 per cent. of the total energy is actually liberated in present atomic explosions.
If even this 0.1 per cent. could be used to produce a
propulsive jet, the “exhaust velocities” obtained would be about a thousand
times those possible with chemical reactions. Instead of trying to design
spaceships consisting of 90 per cent. fuel – and then having to discard section
after section to get a sufficiently high final velocity – it would be quite
literally true to say that the fuel was a completely negligible fraction of the
machine’s mass – much less than 1 per cent. of the total.

This is certainly an attractive prospect after the
rather depressing figures given earlier in this chapter. As we have now
succeeded in liberating atomic energy both at controlled, low-energy and at uncontrolled,
super-high energy levels, it may well be asked why so much time has been spent
discussing the almost crippling limitations of chemical propellants, when
atomic energy can open up not merely the nearer planets but the entire Solar
System with equal ease.

The answer can be given at once. The controlled use
of atomic energy is not going to be simple even for fixed generating stations
with virtually no limitations of mass. And of all the possible uses of atomic
energy, the application to aircraft and rocket propulsion appears the most
difficult, and raises the most stubborn technical problems.

On the other hand, it is the one which offers the
greatest dividends if it can be achieved. In its “terrestrial” applications
atomic energy offers nothing essentially new. It can perform, perhaps more
economically, what can also be done in other ways. But as a means of propulsion
in space it offers – in theory at least – a solution to difficulties which
would otherwise be totally insuperable.

When the time comes to write the history of atomic
power and its impact on human affairs, it may well be found that all its other
applications – countless though they may be – will be overshadowed by the fact
that through its use Mankind obtained the freedom of space, with all that that
implies.

[…]

**Chapter 10**

**Opening Frontiers**

[…]

First by land, then by sea, man grew to know this
planet; but its final conquest was to lie in a third element, and by means
beyond the imagination of almost all men who had ever lived before the
twentieth century. The swiftness with which mankind has lifted its commerce and
its wars into the air has surpassed the wildest fantasy. Now indeed we have
fulfilled the poet’s dream and can “ride secure the cruel sky”.[6]
Through this mastery the last unknown lands have been opened up: over the road
along which Alexander burnt out his life, the businessmen and civil servants
now pass in comfort in a matter of hours.

The victory has been complete, yet in the winning it has
turned to ashes. Every age but ours has had its El Dorado , its Happy Isles, its North-West
Passage to lure the adventurous into the unknown. A lifetime ago men could
still dream of what might lie on the poles – but soon the North Pole will be
the cross-roads of the world. We may try to console ourselves with the thought
that even if Earth has no new horizons, there are no bounds to the endless
frontier of space. Yet it may be doubted if this is enough, for only very
sophisticated minds are satisfied with purely intellectual adventures.

The importance of exploration does not lie merely in
the opportunities it gives to the adolescent (but not to be despised) desires
for excitement and variety. It is no mere accident that the age of Columbus was also the age
of Leonardo, or that Sir Walter Raleigh was a contemporary of Shakespeare and
Galileo. “In human records”, wrote the anthropologist J. D. Unwin, “there is no
trace of any display of productive energy which has not been preceded by a
display of expansive energy.” And today, all possibility of expansion on Earth
itself has practically ceased.

The thought is a sombre one. Even if it survives the
hazards of war, our culture is proceeding under a momentum which must be
exhausted in the foreseeable future. Fabre once described how he linked the two
ends of a chain of marching caterpillars so that they circled endlessly in a
closed loop. Even if we avoid all other disasters, this would appear a fitting
symbol of humanity’s eventual fate when the impetus of the last few centuries has
reached its peak and died away. For a closed culture, though it may endure for
centuries, is inherently unstable. It may decay quietly and crumble into ruin, or
it may be disrupted violently by internal conflicts. Space travel is a
necessary, though not in itself a sufficient, way of escape from this
predicament.

[…]

Those new frontiers are urgently needed. The crossing
of space – even the mere belief in its possibility – may do much to reduce the tensions
of our age by turning men’s minds outwards and away from their tribal
conflicts. It may well be that only by acquiring this new sense of boundless
frontiers will the world break free from the ancient cycle of war and peace. One
wonders how even the most stubborn of nationalisms will survive when men have
seen the Earth as a pale crescent dwindling against the stars, until at last
they look for it in vain.

No doubt there are many who, while agreeing that
these things are possible, will shrink from them in horror, hoping that they
will never come to pass. They remember Pascal’s terror of the silent spaces
between the stars, and are overwhelmed by the nightmare immensities which
Victorian astronomers were so fond of evoking. Such an outlook is somewhat
naive, for the meaningless millions of miles between the Sun and its outermost
planets are no more, and no less, impressive than the vertiginous gulf lying
between the electron and the atomic nucleus. Mere distance is nothing: only
time that is needed to span it has any meaning. A spaceship which can reach the
Moon at all would require less time for the journey than a stage-coach once
took to travel the length of England .
When the atomic drive is reasonably efficient, the nearer planets would be only
a few weeks from Earth, and so will seem scarcely more remote than are the
antipodes today.

It is fascinating, however premature, to try and
imagine the pattern of events when the Solar System is opened up to mankind. In
the footsteps of the first explorers will follow the scientists and engineers,
shaping strange environments with technologies as yet unborn. Later will come
the colonists, laying the foundations of cultures which in time may surpass
those of the mother world. The torch of civilisation has dropped from falling
fingers too often before for us to imagine that it will never be handed on
again.

We must not let our pride in our achievements blind
us to the lessons of history. Over the first cities of mankind, the desert
sands now lie centuries deep. Could the builders of Ur
and Babylon – once the wonders of the world –
have pictured London or New York ? Nor can we imagine the citadels
that our descendants may build beneath the blinding sun of Mercury, or under
the stars of the cold Plutonian wastes. And beyond the planets, though ages
still ahead of us in time, lies the unknown and infinite promise of the stars.

There will, it is true, be danger in space, as there
has always been on the oceans or in the air. Some of these dangers we may
guess: others we shall not know until we meet them. Nature is no friend of
man’s, and the most he can hope for is her neutrality. But if he meets
destruction, it will be at his own hands and according to a familiar pattern.

The dream of flight was one of the noblest, and one
of the most disinterested, of all man’s aspirations. Yet it led in the end to
that silver Superfortress driving in passionless beauty through August skies
toward the city whose name it was to sear into the conscience of the world.
Already there has been half-serious talk in the United States concerning the use of
the Moon for military bases and launching sites. The crossing of space may thus
bring, not a new Renaissance, but the final catastrophe that haunts our
generation.

That is the danger, the dark thundercloud that
threatens the promise of the dawn. The rocket has already been the instrument
of evil, and may be so again. But there is no way back into the past: the
choice, as Wells once said, is the Universe – or nothing. Though men and
civilizations may yearn for rest, for Elysian dream of the Lotus Eaters, that
is a desire that merges imperceptibly into death. The challenge of the great
spaces between the worlds is a stupendous one; but if we fail to meet it, the
story of our race will be drawing to its close. Humanity will have turned its
back upon the still untrodden heights and will be descending again the long
slope that stretches, across a thousand million years of time, down to the
shores of the primeval sea.

[1] Anyone unduly disconcerted by the
occasional appearance of the mathematical fiction “infinity” can substitute “a
few million miles”.

[2] See, for example, Cleaver,
“Interplanetary Flight: Is the Rocket the only Answer?”:

*Journal of the B.I.S.*,**6**, 127-48 (June 1947); of Seifert, Mills and Summerfield, “The Physics of Rockets*”: American Journal of Physics*,**15**, 121-40 (March-April 1947).
[3] It compares quite favourably with the ten
weeks of Columbus ’
first voyage!

[4] If we desire to leave the Earth and
escape from the Solar System, this calculation shows that the starting speed
should be 16.4 km/sec.

[5] There is an apparent discrepancy here as
it has been stated that the first atomic bomb was equivalent to 20,000 tons of
T.N.T. But the greater part of the millions of tons mentioned above would be
used merely to transport a smaller quantity of fuel out of the Earth’s field:
it is this factor which reduces still further the efficiency of the chemical
fuel against the virtually weightless atomic fuel in this (highly theoretical)
calculation.

[6] James Elroy Flecker (1884–1915), “To a Poet aThousand Years Hence”. Ed.

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