How to Explore the Universe

The universe is very big

Our moon is 384,400km from Earth, which is about 68 times the distance from London to New York (as measured along the surface of the Earth). Travelling to the moon is, by far, the furthest a human being has ever travelled from his humble terrestrial origins. No space-farer before or since has made it beyond Low-Earth Orbit (LEO), which is usually defined to be an altitude of less than 2,000km above Earth. The International Space Station orbits at about 400km above Earth. Thus, the 24 lunar explorers of the 1960s and 70s journeyed 96 times further from Earth than the next most adventurous people in human history.

Though the manned missions to the moon are surely the crowning glory of human exploration so far, the moon's distance from Earth is utterly and incomprehensibly dwarfed by the distances that must be traversed to undergo further explorations of our vast universe.

The next frontier will be Mars. Since Earth and Mars both orbit the sun, the relative distance to our nearest planetary neighbour varies significantly throughout the year. At closest approach, Mars is approximately 55 million kilometers from Earth, a distance roughly 143 times further than the moon. If London and New York were just one metre apart, Mars (at closest approach) would be a full 10 kilometers away. And if a human travelled to Mars while it was near its closest approach to Earth, in order to reduce journey time, the orbit of the red planet would subsequently carry her as much as 400 million km away from Earth - this being the maximum separation of the two planets in their respective orbits. This would be over 1,000 times as far away as the lunar Apollo explorers went - and it would still be merely our nearest and most easily attainable neighbour.

The next planet outwards is Jupiter, the gas giant - the largest planet in our solar system. It averages just shy of 800 million km from Earth. Saturn is next, at about 1.4 billion km. The distances get bigger fast. After Saturn is Uranus - averaging around 3 billion km from Earth. This is nearly 1 million times further away than the moon, and we have only made it to the fourth planet away from Earth.. still well within our own solar system. Neptune, next, is about 4.5 billion km away.

Should humanity ever venture so far, we would have made it to the final true planet in our solar system. The sun continues to have a meaningful gravitational impact well beyond here, but there isn't much of great interest for humans to explore. Venture any further, though, and the distances become really big. As is now commonly known, light does not travel instantaneously from source to destination, but instead travels at a very large, though finite, speed. In fact, as we will see later, the speed of light is of critical importance in modern physics as it represents an absolute upper speed limit on all physically possible travel in our universe. The speed of light is approximately 300,000km per second.

This means that the silvery light reflected by the moon's surface takes a little over one second to reach your eyeballs as you gaze heavenward. Light emitted by the sun, 152 million km away, takes a full 8 minutes to reach Earth. Neptune, at 4.5 billion km away, can only ever be seen from Earth as it was just over 4 hours previously. If humans ever get that far away, we will have to endure an 8 hour round-trip time to send any kind of message from home and await a response. Those terse back-and-forth conversations we see in recordings between Houston and the Apollo astronauts will be completely infeasible - prohibited by the laws of physics.

But all of this is just small fry. The solar system is our microscopically tiny cosmic habitat, a minute patch of turf in an almost unfathomably large universe. The next nearest star to Earth, after the Sun, is called Proxima Centauri, a name referencing it's alleged "proximity". Actually, it is 4.2 light-years away, and part of a triple-star system called Alpha Centauri. This means that light emitted by the star embarks on a lonely and completely unbroken 4.2-year journey across the intervening expanse.

Distances like these are measured in light-years, taking advantage of the fastest thing in the universe as a reference measure to keep the numbers sane. In kilometers, the distance to Alpha Centauri is 39 trillion. The Apollo 11 mission averaged a speed of around 5,500km per hour. Travelling at that speed, a spacecraft would require over 11 million years to traverse the interstellar vacuum separating us from our nearest neighbouring star system.

Working our way further from Earth, the next star out is called Barnard's star: almost 6 light years away. Tenth on the list moving out from the solar system is Sirius, the brightest star in the next sky. It's 8.6 light years away. More generally, every individually discernible star we see in our night sky is a member of our galaxy: the Milky Way.

The diameter of the Milky Way is approximately 100,000 light years(!), and it is composed of somewhere between 100 and 400 billion individual stars. Travelling, once again, at the speed of the Apollo missions, it would take about 260 billion years to span the full extent of the Milky Way (note that the universe itself is only about 14 billion years old). And this is just our own parochial little galaxy. Merely a mote of dust lost in the vast expanse of the observable universe. In total it is estimated that there anywhere from 200 billion to 2 trillion separate galaxies in the observable universe. Each of which, similarly, contains in the hundreds of billions of stars.

The limitations of spaceflight today: the mass-ratio problem

Rocket propulsion (as well as the jet propulsion used by aircraft) relies on Newton's third law of motion, which is usually worded somewhat cryptically as "every action has an equal and opposite reaction". This is really a statement about the 'conservation of momentum'.

Consider a supermarket trolley, sitting stationary on the smooth surface of an aisle, with a child sat in the child seat. This entire 'system', taken as a whole, has no momentum. It is at rest. A remarkable fact about our entire universe is that a closed system must have fixed momentum, no matter what happens. No thing can happen which would cause the closed system to not conserve its momentum. So, if the child picks up a piece of fruit from inside the trolley and hurls it out the back, what happens? Once the fruit is flying through the air, away from the trolley it has some momentum (momentum is the product of an object's mass and its velocity; but intuitively, momentum means pretty much what it seems to mean in every-day language). Conservation of momentum tells us that the whole system has fixed momentum (which is therefore always zero, since it started at zero). But we have a subset of the system, namely the piece of fruit launched from the back, which has some definite positive momentum. The only way to reconcile this state of affairs is to conclude that the remaining parts of the system, which constitute the trolley and the child, must have an exactly equal quantity of momentum pointed in the opposite direction from the fruit, such that the total system taken together continues to have zero momentum. This therefore means that the trolley recoils slightly in the opposite direction from which the fruit was thrown.

You might recognise a variety of other examples from every-day life where this 'conservation law' is apparent. To launch a spacecraft, or manoeuvre it once in space, relies entirely on this principle. A large quantity of "reaction mass"¹ is carried on board, and to thrust the spacecraft forwards, it is ejected out of the back with considerable force, usually by igniting the reaction mass as a fuel in some way, imbuing it with a large velocity (and therefore, momentum) as it leaves the back of the spacecraft.

Jet engines work basically the same way, but they have one crucial advantage. Travelling within the Earth's atmosphere, jet engines are able to "breath in" atmospheric air through the front and then use this to significantly enhance the reaction mass available to be thrown out of the back, thus providing much more momentum to the aircraft than would otherwise be possible. Modern jet engines have very high air/fuel ratios, meaning that the vast majority of reaction mass used to propel the aircraft forwards is air, with only a small amount being fuel. This is an important feature, because fuel must be carried on board from the beginning, whereas the air comes from the medium through which the aircraft flies, and need not be packed on board.

Rocket engines, though basically the same as jet engines in terms of the physical principles involved, are far, far less fuel efficient because of this². They cannot supplement the fuel carried on board with any material from the medium through which they fly, because this medium is almost a perfect vacuum in outer space. There's nothing to grab onto and throw out the back. And this leads to a problem known as the 'mass-ratio' problem. Due to the relatively fuel-inefficient process by which rockets are forced to produce their thrust, there is a very limited amount of total thrust available through the life of a space journey. Any additional desired thrust requires more reaction mass, all of which must be carried on board as fuel/propellant from the very beginning of the voyage, which itself increases the mass of the craft to be propelled. And increasing the mass to carry the extra fuel means that the entire journey prior to the incremental fuel being used demands yet more fuel than, just to in order to propel that extra chunk of fuel!³ This leads to exponential fuel requirements as the desired amount of thrust increases.

Luckily, another important consequence of the conservation of momentum is that in outer space, once a rocket has reached its target velocity in orbit, it will remain in orbit indefinitely and not require any further thrust.⁴ This important fact (which also explains why planets and their moons do not require rocket engines attached to the back in order to maintain their orbits...) is the basis for all human space travel so far. The way we get people or satellites into low-earth orbit, or even transport them to the moon or other planets, is to establish them in desirable orbits almost immediately after launch, and then allow them to 'coast' unpowered to their desired destination. Orbital manoeuvres can be effected judiciously during a flight plan, but these are few, very carefully pre-planned, short 'burns'. It simply isn't possible to carry enough fuel for continuously powered flight in space, due to the exponential fuel requirements imposed by the mass-ratio problem.

As an example, here is Apollo 11's flight plan.

The first stage of the mission was to launch the entire spacecraft into Earth orbit. This is where, by far, the largest quantity of fuel was burned. The goal was to take the spacecraft from zero velocity relative to Earth, and accelerate it to a velocity of something like 7-8km per second - enough to establish a stable orbit around Earth with the rocket engine turned off.

Next, after a couple of orbits around Earth, you'll see a segment of the flight path labelled "translunar injection". At this point in the flight plan, the astronauts did a short, controlled burn, lasting only a couple of minutes and consuming a much smaller quantity of the precious fuel load on board. This established the spacecraft in a new orbit, an elongated ellipse, which would send them out towards the moon. For the next 73 hours, they coasted in this orbit all the way to the moon without burning another gram of fuel.

Once at the moon, you'll see a "lunar orbit insertion". Here, another short burn was used to slow the spacecraft down to a velocity which established a circular orbit around the moon. Without this, Apollo 11 would have proceeded on its long, elongated orbit and coasted right past the moon - they would not have been able to stop and descend to the surface.

The return journey essentially consisted of reversing these steps, executing two more controlled burns to coast back to Earth, re-enter a circular Earth orbit and finally descend back to the surface triumphantly.

All other space missions have had to make similar use of orbital mechanics tricks like this to succeed, including missions to Mars or the outer planets (in these cases, the exploration satellites in question have been injected into large solar orbits and left to coast out to their destinations in a precisely choreographed dance).

Upgrading Newtonian physics

To summarise the state of affairs:

1. Spacecraft travel through the emptiness of outer space, where there is little useful medium to use as "reaction mass"
2. This means that all reaction mass required for the entire journey must be carried on board from the beginning
3. Planets we might wish to visit, like Mars, are a very large distance away. Other stars are stupendously further still. Other galaxies... you can forget about it

Human missions to Mars are being planned for the 2030s. The humans embarking on this journey will have to coast the entire way from Earth's solar orbit, to Mars's solar orbit, in a specially chosen elliptical orbit that transfers from one to the other, enabled by short fuel burns at either end (just like the lunar flight plan described above). This whole process will take about 9 months each way.

So it seems that our ability to explore the universe is severly limited by the sheer vastness of the universe and the difficulty of carrying enough fuel on board to make even the tiniest dent in the problem. As noted earlier, it could take millions of years, travelling like this, to reach the next nearest star system. We'll probably never make it out of our own solar system.

Or will we?

As it turns out, physics has some more surprises in store. So far everything we've considered has been understandable within the framework of Newtonian mechanics, formulated in the 17th century. Enter Albert Einstein, in the early 20th century, who discovered revolutionary and completely mind-boggling new facts about the nature of our universe which extended Newton's understanding of dynamics considerably - particularly in the realm of high-speed travel. Newton had no idea that his theory wouldn't adequately describe reality under certain circumstances because the relevant observations hadn't, indeed couldn't, be made in the 17th century.

By the time of Einstein, however, discrepancies had been noted in experiment. It seemed that light behaved in a strange way. Imagine the following scenario. You stand on the bank of a river, while your friend sits in a kayak on the water. The river flows at 5km/h, and your friend begins to paddle, moving at 2km/h relative to the body of water. It seems clear enough that, from your perspective standing on the bank, you friend is moving away from you at 7km/h - the cumulative effect of the flowing river and the paddling.

Light, however, doesn't work like this. If you were able to actually measure the speed of light as it receded from you, you would discover the following strange phenomenon. If you release a beam of light, say from a torch, the light will be measured to travel away from you at a finite speed - call it c. Now, if you give your friend in the kayak the torch, and ask her to release a beam of light as she coasts away down the river at 2km/h, here's what will happen. Your friend in the kayak will measure the speed of the light beam as it recedes from her to be c. This is as expected. However, you, still standing still on the river bank, will also measure the same beam of light to recede from you at the same speed c - not c + 2km/h, which is what you might reasonably assume from everyday life experience.

This remains true if the kayak is replaced with a spaceship itself travelling close to the speed of light. If the spaceship turns on its headlights, the space travellers inside will see the light project out in front at speed c. If you are watching from Earth, and you see the spaceship travelling at, say, 80% of c away from you at the moment they turn on the headlights, you will see the light beam moving at speed c (relative to yourself), not 180% of c. This famous experimental discovery establishes that the speed of light is fixed at c - it has the same value for all observers. And this fact does not reconcile with what Isaac Newton understood about dynamics.

In 1905, Albert Einstein had his Annus Mirabilis (miracle year) aged just 26. He published four groundbreaking papers on physics, revolutionising many fundamental notions about the inner workings of our universe. One of these four papers was on the topic of what is now known as Special Relativity, and it started from two postulates. First, the principle of relativity: the laws of physics should be identical for any non-accelerating (often called "inertial") observer. Second, the speed of light has the same value in all inertial frames of reference (as described above). From these axioms, he derived the whole theory.

Special Relativity is a very beautiful and elegant theory, and can be built up quite straightfowardly (in hindsight!) from these two postulates. It's beyond the scope of this post to derive the theory in any detail, but here are some of the key results. (A good book to read for a very approachable introduction targeted at a general audience is Relativity and Common Sense by Hermann Bondi.)

• The notion of time as a universal absolute is abandoned. Typically, we have no reason not to think of time as being a simple, universally agreed upon quantity. If I experience 2 hours go by, I imagine that everyone else on Earth and across the whole universe has also experienced the passage of 2 hours. There is no everyday circumstance which contradicts this, which is why it had never previously been considered anything other than a self-evident truth. But Special Relativity forces this notion to be abandoned, and tells us that time is in fact relative, depending on the relative circumstances of different observers. Intuitively, you can anticipate that this might be the case from the postulate about light having the same speed in all reference frames. If the same beam of light is to have speed c no matter how you, the observer, are moving relative to the light beam, then something has to give. The notion of absolute time is what gives. A good rule of thumb to remember is this: if you are watching someone moving extremely fast relative to yourself, that person's clock ticks more slowly than your own. But note that this statement only makes sense from your reference frame. The speedy traveller still experiences the passage of time as usual. Furthermore, the situation is symmetric (i.e. from their perspective, it actually looks like you are the one moving very rapidly) and so they perceive your clock to be ticking more slowly. Weird, but true.
• The physical dimensions of the universe are also relative. As well as loosening the notion of time, we also must loosen the notion of distances as absolute and fixed. If, once again, you observe a friend travelling at a very large speed, his spaceship will be measured shorter from your perspective than he measures it. Note that this is not a question of "appearances" in the sense of tricks of the light or perspective. The spaceship actually is physically shorter in your reference frame.
• Linear additivity of velocities is untrue. If Bob moves with speed b relative to Alice, and Charlie moves with speed c relative to Bob, then it is not the case that Charlie moves with speed b + c with respect to Alice. This is what one would expect in a Newtonian framework (remember the example of your friend in the kayak), but the postulate about the speed of light's constancy in all reference frames causes this belief to break down and be replaced with a more complicated velocity addition law. Clearly, at the low speeds we are used to in everyday life, this linear additivity does hold to within an extremely high tolerance (or else we would have noticed it was wrong sooner!) but when we contemplate high velocities, the difference becomes noticeable - as was the case with light itself.
• Simultaneity is not absolute. Suppose two events happen simultaneously from your perspective. If you have a fast-moving friend, the events will no longer occur simultaneously, in general, from your friend's perspective. Once again, this is not a consequence of observational limitations (e.g. something like "it takes longer for the light from one of the events to reach the fast-moving traveller compared to the other event"). The events actually occur at different times in their reference frame. The astute reader might notice that this could pose a problem for our notion of causality in the universe, because surely if one event actually causes another event to happen, it must precede it? This is true, and studying the details of the theory and its implications shows that there is no inconsistency with respect to causality.
• All the new laws of physics derived in the theory of Special Relativity reduce to the equivalent Newtonian laws if you make the assumption that everything in question moves slowly compared to the speed of light. This is a particularly elegant consequence, and demonstrates that Newton had the right laws within his sphere of experience. One can only imagine how it must have felt to Einstein when he realised that his newly derived theory reduced down to the old theory under low-velocity assumptions. I expect realising this would have strongly suggested to him that the theory was correct.
• The theory has been tested rigourously.⁵ Many different experimental setups have demonstrated the "truth" of the theory, at least in the sense that it very accurately reflects the universe as we are able to measure it, and we are able to more accurately predict certain phenomena which involve high speeds compared to the previous Newtonian formulation.

Constant acceleration and relativistic space travel

So, what does all this have to do with exploring the universe? It turns out that the new formulation of physics, discovered by Einstein, allows some remarkable possibilities which would not have been allowed in a Newtonian universe.

Let us hypothesize a spaceship engineered somehow so that it is capable of sustaining 1g of acceleration at all times (where g denotes the rate of acceleration due to the gravity at the Earth's surface). What does this give us?

• Firstly, living conditions on the spaceship would be pleasant. Unlike the astronauts we see in orbit around Earth or voyaging to the moon, these astronauts would not be floating around weightless, but would experience the same acceleration as they are used to from Earthly gravity. They would feel the same kind of downwards force you feel in an elevator when it starts moving, except this force would precisely match the Earth's gravity, and so the physical and physiological experience aboard the spaceship would closely resemble that of life on Earth. The explorers could avoid the significant adverse effects of long-term weightlessness such as muscle atrophy and deterioration of the skeleton (among many others).
• Most excitingly of all, due to the strange and highly counterintuitive effects of time dilation and length contraction touched on above, our explorers would be able to travel truly vast distances across the universe within an ordinary human lifetime. This is absolutely amazing.

Consider, for instance, the Andromeda galaxy. It's our nearest galactic neighbour, but it's still approximately 2.5 million light-years from Earth. This means that the light we see arriving from the galaxy and entering our telescopes here on Earth has been travelling non-stop for 2.5 million years to reach us. Let's now suppose that astronauts set-off towards Andromeda at 1g acceleration, with the following flight-plan. They will keep going at 1g acceleration until the halfway point to Andromeda. At the halfway point, they will throw the engines into reverse (or rotate the spacecraft through 180 degrees, or something) in order to proceed with 1g deceleration thereafter. This would bring them to rest on arrival at the Andromeda galaxy (rather than arriving at the Andromeda galaxy travelling at almost the speed of light, which would not permit them to stop and have a look arouhexnd). After arriving at Andromeda, they have a quick look around, and preferring Earth, they decide to come back, repeating the same steps of accelerating at 1g for half the journey and decelerating at 1g through the second half. fillne year of time ticking by on Earth for every one light-year of distance covered by the travellers. This means that the total round-trip time to Andromeda would be about 5 million light-years from the perspective of Earth (twice 2.5 million light-years).

But how do things look inside the spaceship? Will it be the travellers far future descendants who arrive at Andromeda, after countless generations of humans lived claustrophobic, uneventful lives trapped on the spaceship from birth till death? A civilization in microcosm aboard a starship? The answer turns out to be no. In fact, because of the relativistic dilation of time, which causes the astronauts' clocks to tick at a different rate, as well as the contraction of lengths which literally shortens the distance they need to cover to reach Andromeda, the astronauts would be able to complete the entire round-trip in a span of just 60 years ship-time.

Let that sink in for a moment. What this means is that, if we can achieve 1g constant acceleration, humans could travel all the way to the Andromeda galaxy (2.5 million light-years away) and return back to Earth within a single lifetime on board. Most astonishing of all, in the 60 year span experienced by the crew, planet Earth would have aged 5 million years⁶. Our space-farers would also be a time travellers. They would return to a radically changed world; the human race may have long since gone extinct, or else flourished beyond anything we could imagine. If civilization remained on Earth, they may no longer be aware that explorers had been sent off to Andromeda millions of years before.

Here's a handy calculator which gives you ship-time and Earth-time for various journeys to other stars and galaxies. And here's a table showing some round-trip times for journeys using the 1g constant acceleration / deceleration method.

For a one-way trip, the entire known universe could be traversed in just 42 years of spaceship time.

The Bussard ramjet

The only remaining issue is the simple matter of building a spacecraft capable of accelerating constantly at 1g. Acceleration requires the application of a force, and this means the engines have to be turned on the whole time, consuming fuel - which means the mass-ratio problem rears its head. As described earlier, no spacecraft has yet been built which can do anything more than execute short, intermittent "impulsive" manoeuvres (i.e. burning a small quantity of fuel for a limited period of time in order to change the momentum of the spacecraft to effect a new orbital trajectory).

Returning to the relativistic space travel calculator, you can find the quantity of fuel required for a given voyage per unit of spaceship mass. Making a one-way trip to Alpha Centauri, the nearest star system, would require 39 tonnes of fuel mass for every 1 tonne of spaceship mass. This is already pretty formidable. A one-way trip to Andromeda would require 6.8 trillion tonnes of fuel for every 1 tonne of spaceship mass. So there are some big technical feasibility challenges here.

Amazingly though, there are semi-viable concepts for accomplishing this type of space travel without having to carry the entire fuel load / reaction mass on board from the beginning of the journey - like a jet aircraft which gets most of its reaction mass from the atmosphere through which it travels.

In 1960, Robert Bussard published a paper discussing the possibility of an interstellar "ramjet" (the concept of which has come to be known as a Bussard ramjet). This starship takes advantage of the fact that interstellar space is not quite as perfect a vacuum as it might appear. The universe is actually permeated by hydrogen, on the order of about 1-50 atoms per cubic centimetre, depending on where exactly you are. Although this is vastly less dense than the matter concentrations we have here on Earth, it would potentially enable a system that works something like this:

The starship would have a device attached to the front producing a very large magnetic field reaching out ahead of the craft. This magnetic field would be kilometers, or even thousands of kilometers in size. Its purpose would be to scoop up hydrogen atoms from the interstellar medium and direct them in towards the spacecraft, where they would be compressed. The spacecraft would then use a nuclear fusion reactor to release large quantities of energy from the hydrogen, and the vehicle would direct this exhaust energy out of the back opposite the intended direction of travel. This would produce a forward thrust yielding the desired acceleration.

Although there are still plenty of technical challenges to overcome, including some objections on purely theoretical grounds, the Bussard ramjet remains at least plausible as the basis for interstellar travel in some guise. One possible issue is that, once the spaceship is travelling at high velocities, the incoming hydrogen would be travelling at close to the speed of light with respect to the craft and therefore impose a drag force on the vehicle which might exceed the forward thrust produced by the ramjet engine. This could severely limit the maximum attainable speed.

Various proposals⁷ have been made over the years revising the initial concept proposed by Bussard to tackle some of these theoretical challenges. Such ideas include the "Ram Augmented Interstallar Rocket (RAIR)" which would carry a quantity of nuclear reactor fuel on board, but supplement this with interstellar gas to act as additional reaction mass - just like how a jet aircraft carries some fuel, but gets most reaction mass from the environment around the aircraft. This design is supposed to help alleviate the drag problem mentioned above.

One irony in this whole plan is that our solar system is currently passing through an area of the Milky Way with an unusually low density of hyrdrogen, making the ramjet much harder to realise in practice in our galactic vicinity. Perhaps this problem will be overcome by technical means, with a highly efficient design that can operate in low-density hydrogen. If not, we may need to wait thousands of years until the solar system has moved to a more favourable area.

Tau Zero

For a marvellous classic work of "hard" science fiction about the voyage of a group of humans aboard a Bussard ramjet, I would highly recommend Poul Anderson's 1970 novel Tau Zero. The story follows 50 humans on their mission aboard the Leonora Christine in a bid to visit the star Beta Viriginis, about 36 light-years away, in the hope of colonising a suitable exoplanet. On the journey to the star, the voyagers encounter a dense interstellar dustcloud which destroys the Leonara Christine's deceleration systems - meaning they must continue to accelerate at 1g indefinitely, attaining vast speeds. They watch countless galaxies hurtle by while eons of time elapse outside the spacecraft in mere decades of shipboard time.

The novel deals with fascinating themes, like how such relativistic travellers would cope with the effects of time dilation, knowing that their Earthly home is aging millenia without them and their loved ones will be long gone by the time they return.

Conclusion

Over the last few centuries, humanity has explored all the corners of our home planet; we have climbed every mountain, visited the depths of the oceans and spread to every continent. But far from exhausting our supply of explorable wonders, we've really barely begun. Although there are still myriad technical challenges to overcome, the Bussard ramjet and its variations give us real hope that humanity can use the laws of physics to its advantage and become an interplanetary - indeed, intergalactic - species some day in the future. We can hope to travel to far distant worlds, seeing up close the stars and nebulae which are now no more than specks in our night sky; we can hope to explore the universe in search of the life which surely teems across the cosmos. We might find other habitable planets and build fresh civilizations under the glow of new suns, perhaps long after our own planet and solar system ceases to be the welcoming oasis it is today. We just need to keep accelerating.

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Further Reading

• Relativity and Common Sense, Hermann Bondi (1964)
• Tau Zero, Poul Anderson (1970)
• The Feynman Lectures on Physics, Vol. II, Matthew Sands, Richard Feynman, and Robert B. Leighton (1963)