Carlin's observation evokes one of the core appeals of hard science fiction to some. A sufficiently hard science fiction story, even if it's set in another star system, could really happen — or at least, it should be very difficult for the readers to come up with ways that it couldn't happen.
Writing hard science fiction set in space carries with it all of the baggage of writing any other genre of literature. Your characters must be believable, your plots and descriptions must not be boring, the story must be satisfying to the reader in some way, etc.. Every piece of advice in the Write a Story article is just as sound when writing hard SF as it is when writing a western, a modern romance, a historical naval drama, or any other literary genre you can imagine.
However, to work as a piece of hard SF with space travel, the writer must go one big step farther: The technology, the mechanics of space travel, the planets, the aliens (if there are aliens), all the details of that futuristic setting must be realistic. The author must take pains to follow the known laws of physics, chemistry, biology, astronomy, and planetology, and how they apply to any areas of engineering that will appear in the story. This means the author must know the laws of physics, chemistry, etc., or have good access to someone who does. While the laws of the author's fictional universe are allowed to deviate from the laws of Real Life on occasion, the author must be consciously aware of each of those deviations, must have an excuse for them (even if he never tells the reader this excuse, he must have it in his own head), and above all must take pains to limit the damage that such departures from reality can potentially do to the story.
Since space travel is involved, it's important to remember that human beings have travelled in space for over five decades now. We know what is involved in getting from the Earth's surface to low Earth orbit. We know what's involved in landing on a rocky world 400,000 kilometers away. We know what effect microgravity has on human bones and muscles. A realistic story involving space travel must take all this accumulated human knowledge into account. The cartoonish world of 1950s B-movie astronauts having a "navigational error" that sends them to an "uncharted planet" with an Earthlike ecosystem inhabited by alien women who speak English is, and should be, a Discredited Trope — but so should portraying space travel like anything other than space travel just because it looks neater that way in your head.
One of the best resources out there for realistic future space travel is the Atomic Rockets page, which covers everything from "what designs are on the drawing board for spacecraft capable of crossing interstellar distances within a human lifetime?" to "why should my female crew members not wear skirts?"
Heartbreak HotelSadly, the rules of writing about realistic future space travel — like the rules of writing about anything realistic — are primarily a set of rules about what you can't do. The more ideas you have about what you'd like to have your characters do, the more ways reality will step in and say "No."
First off, here is a list of tropes that are frowned upon in a realistic universe:
- All Planets Are Earth-Like (at least without Terraforming)
- Faster-Than-Light Travel
- Human Aliens
- Inertial Dampening
- Reactionless Drive
- Single-Biome Planet
- Space Is an Ocean
- Space Pirates
- Stealth in Space (and most of the other subtropes of Space Does Not Work That Way)
- Green-Skinned Space Babe (and Rubber-Forehead Aliens in general)
There are sound reasons why all of the above tropes will probably not work in Real Life. It's not impossible to have them work in a way that doesn't violate the laws of science or good sense, but it will requite extra painstaking labor from the author to make that happen.
Doing the Research
This should go without saying, but:
If you're going to set your story someplace we already know something about — like Mars or Alpha Centauri — for goodness' sake, read up on what we know about the place before you start writing! We've sent space probes to every planet in the solar systemnote , we've accrued reams of data on just about every star that has a name, we've even mapped out the interstellar medium in our neck of the galaxy. The data are out there, and thanks to the Internet they're not even hard to acquire any more.
You wouldn't set a story in the Sahara Desert and have your hero go swimming in one of the "numerous lakes" there. You wouldn't set a car chase in downtown Florence, Italy and then make up the street names and city layout. Similarly, don't set your story on Mars and have your hero swelter in the unbearable heatnote , or put an Earthlike planet in orbit around Alpha Centauri without at least mentioning the bright "B" star that should be visible from time to time in the sky. Making up details about places we don't have strong data about is one thing, but making up details about places where our existing data would make those details flat-out impossible is quite another.
Doing the math
If doing an arithmetic problem like "A train leaves Chicago at 8 AM going 60 miles per hour" taxes the limits of your skills, putting realistic space travel into your story is probably not for you. Space travel is all about doing the math, and the math can get hairy — especially when dealing with speeds above 5-10% of the speed of light, where special relativity starts to rear its ugly head. But if you're up for the challenge, it's definitely worth doing. Even if you don't show your work to your readers, getting the numbers right (or nearly right) will go a long way toward your story's sense of realism.
Let's take as our example a rocket trip from Earth to Saturn. How long will it take to make the flight?
You could go the easy route, and look up how long it took for the Voyager 1 space probe to fly from Earth to Saturn, and just assume that you space ship flies about as fast as the Voyager probes did. But when you do look it up, you balk — it took nearly three years for Voyager 1 to make this trip! You can't have your intrepid space cadets waiting around for three years just to get to Saturn, they've got important space adventures to have, space wars to fight, and space women to woo. You want them to get to Saturn a lot quicker. So, you give them a space ship that never runs out of fuel — or uses fuel that's so efficient that it won't run out even if it runs its engines continuously between Earth and Saturn.
So, with the ability to accelerate indefinitely, now how long will it take to get to Saturn?
Let's say you decide to limit your space ship to a cruising acceleration of 1g, so that the crew will experience thrust equal to Earth's surface gravity. After all, this is a hard science fiction story, right? You can't just go slinging Inertial Dampening around. Any acceleration your ship undergoes will be experienced by your crew as G forces. So, if they're going to be cruising under engine power for anything longer than a few minutes, you'll probably want to keep your acceleration down to 1g. 1g works out to an acceleration of 9.8 meters per second per second — at the end of one second, you'll be going 9.8 m/s, at the end of two seconds, you'll be going 19.6 m/s, and so forth.
At speeds much less than the speed of light, which is the speed we're dealing with in the Earth-to-Saturn example, the formulas relating speed, acceleration, time, and distance travelled while undergoing constant acceleration are pretty straightforward. Ignoring the sun's gravity (which can indeed be neglected for a ship that accelerates at one g) we have:
- v = a * t + v0
- d = 0.5 * a * t2 + v0 * t
- 2 * a * d = v2 - v02
... where d is the distance travelled in meters, v is your current velocity in m/sec, a is your acceleration in m/sec2, t is the elapsed time in seconds, and v0 is your initial velocity at the start of your trip.
So, what value should we plug in for d? The distance from Earth to Saturn, right? Well, unfortunately, Earth and Saturn are both in orbit around the sun, which means they move. Their movements are more complicated than the simple equations I've written above, but for a first approximation, let's say you plan your trip to happen when Earth and Saturn are closest together, i.e. both on the same straight line from the sun (what astronomers call "opposition"). Looking up their orbital parameters on Wikipedia, we see that the average Earth-sun distance is 1.0 A.U., and the average Saturn-sun distance is 9.582 A.U., so the two will be about 8.5 A.U. apart at closest approach. (They could actually be closer. Saturn's orbit is rather eccentric, varying between 9 AU and 10 AU from the sun; but 9.5 A.U. is close enough for a first approximation. And waiting for Earth and Saturn to be at opposition when Saturn happens to be at perihelion will mean your space cadets will be sitting around tapping their toes for decades.) 1 A.U. is about 150 million kilometers, so 8.5 A.U. works out to around 1,280,000,000 kilometers.
But wait — our equations require d to be in meters, not kilometers. We have to inflate that number by a factor of a thousand. 1,280,000,000 km is 1,280,000,000,000 m. Let's hope your calculator has enough spaces for all those digits. (If not, you might need to enter it in scientific notation, as 1.28 x 1012.)
Now, how long will the trip take? Let's plug our numbers into the second equation above. We know d, and we know a. We can assume v0 = 0, if we're taking off from Earth at a standing stop. (We won't actually be; our space ship will be taking off from Earth orbit, which means it'll be moving at about 7800 m/s, and our zero-velocity reference point here is our destination — Saturn — which is orbiting at a different speed as the Earth. But our overall speed is going to be so great that these little speed differences shouldn't matter much.) This is what we get:
- d = 0.5 * a * t2 + v0 * t1,280,000,000,000 m = 0.5 * 9.8 m/sec2 * t2 + 0 * tSimplifying:1,280,000,000,000 m = 4.9 m/sec2 * t2
Unfortunately, we're trying to solve for t here, so we need to do a little algebra. Let's divide both sides by 4.9 m/s2 :
- 1,280,000,000,000 m / 4.9 m/sec2 = t2Simplifying:260,000,000,000 sec2 = t2Taking the square root of both sides:510,000 sec = t
So the trip will take 510,000 seconds. Since there are 86,400 seconds in a day, this means it'll take about 5.9 days. What will be our final velocity (v) when we reach Saturn? For that, we need the first equation above; luckily, since we now know t, it'll be a lot easier:
- v = a * t + v0v = 9.8 m/sec2 * 510,000 sec + 0v = 5,000,000 m/sec
Woops! We arrived at Saturn in less than 6 days, but now we're whooshing past it at 5 million meters per second! (That's 5000 kilometers per second, about 1.6% of the speed of light.) At that speed, we'll only have a few seconds to have adventures on Saturn before we speed right out of the Solar system.
What we'd like to do instead is arrive at Saturn with a velocity of zero, or nearly zero. That's going to require us to turn over and decelerate: We'll accelerate to the half-way point between the Earth and Saturn, then do a "skew flip" so that our engines are pointed in the opposite direction, then decelerate for the rest of the trip.
This adds an extra step or two to the math we'll need to do, but thankfully each step should be just as easy. First, we need to change d from the full Earth-Saturn distance (1,280,000,000,000 meters) to half that distance, and see how long it'll take to get there:
- d = 0.5 * a * t2640,000,000,000 m = 0.5 * 9.8 m/sec2 * t2Simplifying:640,000,000,000 m = 4.9 m/sec2 * t2640,000,000,000 m / 4.9 m/sec2 = t2Simplifying:130,000,000,000 sec2 = t2Taking the square root of both sides:360,000 sec = t
So, it'll take 360,000 seconds — a hair under 4.2 days — to get to the half-way point. Our velocity v at this point will be:
- v = a * tv = 9.8 m/sec2 * 360,000 secv = 3,500,000 m/sec
3500 kilometers per second. Slightly more than 1% of the speed of light, but that's okay, because we're in deep space nowhere near Earth or Saturn. Now, how long will it take to decelerate from this speed to a speed of 0 at 1g (9.8 m/sec2)? For this, let's plug the numbers back into the first equation. Remember, this time, our acceleration is negative (a negative acceleration is the same thing as a deceleration), and we do have an initial velocity:
- v = a * t + v00 = -9.8 m/sec2 * t + 3,500,000 m/secSubtracting 3,500,000 m/sec from both sides:-3,500,000 m/sec = -9.8 m/sec2 * tDividing both sides by -9.8 m/sec2:-3,500,000 m/sec / -9.8 m/sec2 = t360,000 sec = t
Hmmm! It takes 360,000 seconds to decelerate from 3500 km/sec to 0 — exactly the same amount of time it took to accelerate from 0 to 3500 km/sec! And if we ran the numbers, we'd see that on this second leg, we covered exactly the same 640,000,000 km we covered in the first half of the trip. The two legs of the journey are mirror images of one another. Once we've figured out how long it takes to get to the half way point, we know that it'll take exactly as long to go the rest of the way (assuming our deceleration during the second leg is equal in magnitude to our acceleration during the first leg).
So ... using our constant-acceleration trajectory, it takes 360,000 seconds to reach the half way point, and another 360,000 seconds to go the rest of the way, for a total of 720,000 seconds to get from Earth to Saturn. That's 8.3 days, a little over a week. It's still not something your space cadets can do on their day off, but it's a heck of a lot quicker than the 3 years Voyager 1 took to make the trip — and unlike Voyager 1, your space ship ends up at rest relative to Saturn so it can stay there as long as you need it to.
By the way, that constant-acceleration trajectory may be fast, but it is ferociously inefficient in terms of fuel use, and no real spacecraft actually use it. (For just how inefficient it would be, see the "Why Rockets Are So Big" section farther below.)
Now ... what if our heroes can go faster than this? Let's say we've decided we need shorter flight times, so screw it, we're introducing Inertial Dampening technology into our story, like in the Honor Harrington or Star Trek universe. Now our space ships can accelerate at 1,000 g, or 9,800 m/sec2, and we should be able to get to Saturn much faster. In fact, using the first equation above, it looks like we should be able to accelerate to 30,000,000 m/sec in less than an hour — that's a tenth of the speed of light.
And there's where we run into problems. Because above about a tenth of the speed of light, acceleration doesn't affect velocity in a straightforward manner any more. Your clock runs a little slower to a fixed observer than it does to you. Your momentum is slightly higher to a fixed observer than your acceleration history says it should be. The universe shrinks slightly in the direction you're moving. In short, you run smack-dab into special relativity, and now the math gets a lot more complicated. For one, the change in your velocity per second, given a constant acceleration from your space ship's reference frame, now depends on your current velocity — which turns the relationship between the two into a first-order differential equation.
The basic relativistic equation for determining your "gamma factor" — the amount by which your mass goes up, time slows down, or distances in the direction of motion shrink — is as follows:
- γ = 1 / sqrt (1 - v2/c2)
... where sqrt means square root, and c is the speed of light in a vacuum (about 300,000,000 m/sec). As you can see, it varies according to how fast you're going (that pesky v2 term in the denominator).
Here are some typical gamma factors:
|At rest||γ = 1|
|At 10% of c||γ = 1.005|
|At 50% of c||γ = 1.15|
|At 86.6% of c||γ = 2|
|At 90% of c||γ = 2.29|
|At 99% of c||γ = 7.09|
|At 99.9% of c||γ = 22.37|
|At 100% of c||γ = ∞|
(As you can see, a massive object such as a space ship can never achieve 100% of the speed of light, because its momentum would be infinite — it would take an infinite amount of energy to accelerate to c.)
The Atomic Rockets website lists many, but not all, of the useful equations that come into play for a rocket travelling at these relativistic speeds. These include:
- T = (c/a) * ArcCosh[a*d/(c2) + 1]
- t = sqrt[(d/c)2 + (2*d/a)]
- v = c * Tanh[a*T/c]
- v = (a*t) / sqrt[1 + (a*t/c)2]
- γ = Cosh[a*T/c]
- γ = a*d/(c2) + 1
... where T is "proper time" (the number of seconds elapsed in your space ship's frame of reference), t is the number of seconds elapsed from a fixed observer's frame of reference, d is distance travelled from a fixed observer's frame of reference, a is acceleration in the space ship's frame of reference (which is assumed to be held constant), Tanh is hyperbolic tangent (there's a button for this on most scientific calculators), and ArcCosh is inverse hyperbolic cosine.
So, let's say you want your inertial-dampener-equipped space ship to accelerate at 1,000g, or 9800 m/sec2, and you want to follow the same course you did with your piddling little 1g space ship — accelerate to the half-way point between Earth and Saturn, 640 million km away, and then decelerate for the same distance to arrive at Saturn with v = 0. How much time will that take, as far as the folks back on Earth are concerned? For that, we can use equation 2 above:
- t = sqrt[(d/c)2 + (2*d/a)]t = sqrt[(640,000,000,000 m / 300,000,000 m/sec)2 + (2 * 640,000,000,000 m / 9800 m/sec2)]t = sqrt[4,550,000 sec2 + 130,600,000 sec2]t = 11,600 sec
The folks back on Earth measure 11,600 seconds, or about 3.2 hours, for the space ship to reach the half way point. Meanwhile, how much time has elapsed for the folks on board the space ship? For that, we need equation 1 above:
- T = (c/a) * ArcCosh[a*d/(c2) + 1]T = (300,000,000 m/sec / 9800 m/sec2) * ArcCosh[9800 m/sec2 * 640,000,000,000 m / ((300,000,000 m/sec)2) + 1]T = (30,600 sec) * ArcCosh[0.06969 + 1]T = 11,360 sec
Your intrepid spaceship crew measures the elapsed time as 11,360 seconds, which is only slightly less than the time t measured by the folks back on Earth. How fast will you be going at this half-way point? For that, we'll need equation 3 above:
- v = c * Tanh[a*T/c]v = 300,000,000 m/sec * Tanh[9800 m/sec2 * 11,360 sec / 300,000,000 m/sec]v = 300,000,000 m/sec * 0.3549v = 106,500,000 m/sec
... or a tad over 1/3 of the speed of light. This explains why our proper time T and our Earth time t are so close together: At 1/3 of light speed, the gamma factor is only about 1.07, and our space ship was only going this fast near the end of this leg anyway. If we'd taken a longer trip — say, from Earth to Sedna in the Kuiper belt, or from Earth to Alpha Centauri — we'd have more distance in which to accelerate, which would let us get closer to the speed of light, and the relativistic effects would have been more pronounced.
Unfortunately, these equations only address the situation when your space ship starts out at 0 velocity. If you want to apply these equations to a situation where you start out already moving at (say) 1/5 of light speed, they get even more complicated, and often times will not have already been derived for you. For example, the equation for the amount of time a fixed observer measures that it takes your accelerating space ship to cross a given distance, assuming you started out with a velocity that gave you an initial gamma factor of γ0, is this hairy beast:
If your space ship is close to a large gravity source like a planet or a star, and is moving at a low enough speed, it isn't going to travel in a straight line. The gravity of the big object will cause your spacecraft to follow an orbital trajectory.
The equations for an orbit are more complicated than the equations for straight-line movement, because your acceleration is always changing; it depends on how far you are from the big object at that particular instant. Whole volumes have been written on how to calculate an orbit precisely, but there are some simple straightforward cases that are at least somewhat easier to calculate.
All orbits are shaped like conic sections. If your space ship is moving slower than the "escape velocity" — or more precisely, if its total kinetic energy and gravitational potential energy is less than the gravitational potential energy it would have at an infinite altitude — its orbit will be shaped like an ellipse. If it's moving precisely at the escape velocity, its orbit will be shaped like a parabola. If it's moving faster than the escape velocity, its orbit will be shaped like a hyperbola. This is assuming, however, that your space ship spends all its time from this moment forward in free-fall, without firing its engines.
Parabolic and hyperbolic orbits are basically escape trajectories. The spacecraft leaves the big object in question and never comes back. An elliptical orbit, on the other hand, is stable, and allows your space ship to go around and around the big object over and over again. It's what most people think of when they hear the word "orbit." An ellipse looks an oval-ish shape, with two points inside it called the "foci" (plural of focus). In an elliptical orbit, the center of the big object you're orbiting is going to be at one focus, while the other focus won't contain anything at all.
The formula for how long it takes to make one complete orbit was first deduced by Johannes Kepler when studying the motions of the planets around the sun. Sir Isaac Newton expanded on this formula so that it applied when orbiting any object. The formula is:
- P2M = A3
.. where P is the period of the orbit in years, M is the total mass of all objects involved in the orbit in solar masses, and A is the semi-major axis of the orbit's ellipse in Astronomical Units.
The simplest kind of elliptical orbit is one with no eccentricity at all. We call this a circle. In a perfecly circular orbit, both foci are at the same point in space, which is at the center of the circle. The semi-major axis A of a circle is just its radius (half its diameter).
Suppose you want your space ship to orbit the Earth in a perfect circle 200 kilometers above the surface, like the Space Shuttle does. What will the period (P) of that orbit be? If we want to use the equation above — P2M = A3 — we'll first have to find the combined mass of the Earth and your space ship in solar masses. The Sun's mass is about 2 x 1030 kg, while the Earth's mass is about 6 x 1024 kg. Let's say your space ship weighs in at 1000 tonnes, i.e. a million kg. Here's the mass of the Earth in solar masses:
- 3.003740720000000000 x 10-6
... and here's the combined mass of Earth and your space ship in solar masses:
- 3.003740720000000001 x 10-6
As you can see, unless the two objects involved in the orbit are of comparable mass, the mass of the teensy tinsy little orbiting object really doesn't matter for this equation. We can just use the Earth's mass by itself, and be done with it. We don't even need all those decimal digits — the real Earth isn't a perfect sphere, so its gravity is a tiny bit "lumpy", which means that our answer for how long the orbit will take is only going to be approximate anyway. The value we need for M is 3 x 10-6 solar masses.
Now, we need the semi-major axis, that is, the radius of the orbit. We're at 200 kilometers altitude, so that means the orbital radius is 200 kilometers, right? Wrong. The radius is the distance from our space ship to the center of the Earth. The Earth is 6371 kilometers in radius, on average, so the orbit's radius is 6571 km. For our formula, we need this expressed in Astronomical Units. One A.U. is 149,598,000 km, so the value we need for A is:
- 4.39 x 10-5 A.U.
Plugging those two numbers into the formula, we get:
- P2 * (3 x 10-6) = (4.39 x 10-5)3P2 * (3 x 10-6) = 8.47 x 10-14P2 = (8.47 x 10-14) / (3 x 10-6)P2 = 2.82 x 10-8P = 1.68 x 10-4 years
... which works out to 88.4 minutes. And, indeed, the space shuttle does take about this long to orbit the Earth once.
Now, let's try it with a 100 kilometer orbit above the surface of Mars:
- Mass of Mars = 6.4 x 1023 kg = 3.2 x 10-7 solar massesRadius of orbit = 100 km (orbital altitude) + 3397 km (radius of Mars) = 3497 km = 2.3 x 10-5 A.U.P2 * (3.2 x 10-7) = (2.3 x 10-5 A.U.)3P2 = (2.3 x 10-5 A.U.)3 / (3.2 x 10-7) = 4 x 10-8P = 2 x 10-4 years = 105 minutes.
Not surprising that this is similar to the period for our low-Earth orbit above. Mars is only about 1/10 the mass of the Earth, but our orbital radius was about half as high as before (and 1/2 cubed is 1/8), so the two factors nearly cancel each other out.
Note that you don't have to do these calculations in solar masses, A.U.s, and years. If you want to use other units, you can introduce a constant k that adjusts for the differences in your unit system, like so:
- P2M = kA3
This is usually done with a k that converts everything into kilograms, meters, and seconds; but in the olden days, you might have picked a different k that converts your units into pound-masses, feet, and seconds. There's even a video about orbital mechanics here that uses furlongs!
Why rockets are so big
You've doubtlessly seen the footage of the Apollo moon mission launches. An enormous Saturn V rocket, hundreds of feet tall, lumbered off the launch pad on an enormous column of flame. Yet the actual Apollo spacecraft was just a tiny cylinder perched atop it, with an even smaller cone on top of that where the crew actually lived. Why was the rocket so big, and the actual usable space so small?
Cars can pull themselves along the ground by spinning rubber tires. Boats can push water through their propellers. Airplanes can push air through their propellers or turbines. Rockets, on the other hand, have none of these options. Every ounce of thrust their engines produce has to come through the expenditure of onboard propellant — in other words, they accelerate forward by throwing material backward. (Boats and airplanes also accelerate forward by throwing material backward, but they get this material from the environment around them. Rockets have to carry all this "reaction mass" on board.) This severely limits the efficiency of a rocket engine when compared with a fluid-breathing or surface-friction engine, even moreso than the need to carry their own oxygen to combust with their fuel. Even worse, it means that at the start of your flight, you have to produce that much more thrust just to push all your unburned fuel along with you, so each kilogram of fuel you add provides progressively less and less total acceleration. This cascade effect can add up very quickly. The equation for how much total acceleration your rocket can undergo before it runs out of fuel — the total "delta-v budget" of your rocket — was derived by Tsielkovsky over a century ago:
- Total delta-v = ve * ln(M/Me)
... where ve is the exhaust velocity of your engines, ln means "natural log" (there's a button for this on all scientific calculators), M is the mass of the rocket with fuel, and Me is the mass of the rocket without fuel (the empty weight). M/Me is sometimes called the "mass ratio" of the rocket.
The ve for, say, the Space Shuttle's main engines is about 4500 meters per second. In order to orbit the Earth, the Space Shuttle must travel at 7800 meters/sec, and it must be about 300 kilometers above the Earth's surface (it requires at least another 1600 m/s of delta-v to lift it that high and overcome atmospheric drag along the way). This means it needs a total delta-v of around 9400 m/s, which is over twice its own exhaust velocity. From the rocket equation above, this means its M/Me ratio must be more than e2, or 7.39. The shuttle's weight with fuel must be over seven times as high as its weight without fuel! Discarding its spent solid rocket boosters in mid-flight (a trick similar to staging) can help a little, but not much.
With such a stultifying mass ratio just to get into Earth orbit, you can see why flying to other planets in a matter of days — or worse, flying to another star within a human lifetime — just isn't practical for modern chemically-propelled rockets.
How impractical is it? Well, let's take the example of the trip to Saturn discussed above, where our space cadets undergo a continuous 1g acceleration to the half way point, and a continuous 1g deceleration for the rest of the trip. We established that their velocity is 3,500,000 m/s at the half way point, so we need 3,500,000 m/s of delta-V to get that far, and another 3,500,000 m/s of delta-V to brake to a halt, for a total delta-V requirement of 7,000,000 m/s. If their space ship's engines had an exhaust velocity of 4,500 m/s, the same as the Space Shuttle's main engines, what mass ratio (M/Me) would be required to attain 7,000,000 m/s of delta-V?
- delta-v = ve * ln(M/Me)7,000,000 m/s = 4500 m/s * ln(M/Me)Dividing both sides by the exhaust velocity:(7,000,000 m/s) / (4500 m/s) = ln(M/Me)1555 = ln(M/Me)To get rid of the natural log, we need to take the natural exponential of both sides:e1555 = M/Me
e1555 works out to an absolutely gargantuan 3.7 x 10675. In other words, your space ship must carry 3.7 x 10675 times as much fuel as its own empty mass! To put that into perspective, the estimated mass of the entire observable universe (excluding exotic forms of mass such as dark matter) is only some 1053 kilograms. A space ship with a very modest 1000 kg empty mass would have to carry 3 x 10625 observable universes' worth of fuel.
Most hard SF authors will solve this problem by using more exotic forms of rocket propulsion which have much much higher exhaust velocities, or which can derive their propellant from someplace other than the rocket's fuel tanks. These include:
- Nuclear fission (NERVA) engines
- Ion engines, such as those on the Dawn and Deep Space One spacecraft
- The Orion Drive
- Controlled nuclear fusion engines
- Ground-based laser pushers
But even if controlled nuclear fusion does become a reality (allowing what Robert A. Heinlein called a torch), that still won't eliminate the need for big rockets if you want to get anywhere in a reasonable amount of time. Sure, your exhaust velocity might now be on the order of (say) 2% of light speed, but the rocket equation still applies. Let's try the trip to Saturn under a continuous 1g acceleration again, only this time let's give the space ship "torchship" engines with an exhaust velocity of 2% of light speed, or 6,000,000 m/s. The trip still requires 7,000,000 m/s of delta-V, so:
- delta-v = ve * ln(M/Me)7,000,000 m/s = 6,000,000 m/s * ln(M/Me)Dividing both sides by the exhaust velocity:(7,000,000 m/s) / (6,000,000 m/s) = ln(M/Me)1.17 = ln(M/Me)To get rid of the natural log, we need to take the natural exponential of both sides:e1.17 = M/Me
e1.17 works out to 3.22. So the space ship's fuelled weight will need to be 3.22 times its empty weight. This means it's still going to have to carry 2.22 times as much fuel as its empty mass. You're still stuck with a big rocket. And when you get to Saturn, you'll be out of fuel. You'll need to completely refill your fuel tanks if you want to make the return trip to Earth. Forget about the notion of a "ship" patrolling the "seas of interplanetary space" for months on end, hopping from planet to planet without refuelling.
Realistic World Building
We humans evolved on, and (so far) all grew up on, Earth. We instinctively expect the air to be breatheable, the temperature to be liveable, the gravity to be 9.8 m/s2, the days to last 24 hours, trees and grass, animals and plants and fungi, et cetera, et cetera.
The sad fact is, though, that no other planet we've detected thus far is even remotely habitable by human standards. The bigger ones are Jupiter-like balls of gas, while the smaller ones are almost universally airless. The few worlds we've found that do have both an atmosphere and a solid surface have been blanketed in gases that no human can breathe, at pressures anywhere from near-vacuum to 90 times Earth's sea level. While it's theoretically possible that a planet out there might harbor life as we know it, it would have to fit a long, narrow list of parameters, and even then, the kind of life that might have actually evolved there will most likely be very different from the multicellular-eukaryote-rich biome inhabiting Mother Terra.
In order for a planet to be able to support life as we know it on its surface at all, it will have to lie in a very narrow range of distances from its parent star. Too close, and any water would evaporate. Too far, and any water would freeze. Liquid water — and life as we know it requires liquid water — can only exist if the planet lies within that narrow zone where it's receiving just the right amount of energy from its star for the surface temperature to allow it. This is called the star's "comfort zone," or "Goldilocks Zone" (as in: not too close, not too far, but juuuuuuuust right). The exact width of a star's Golilocks zone is a matter of some debate, due to the fact that some atmospheres can trap heat (*cough* Venus *cough*) and some can't, and a number of other factors that astrogeologists can make whole careers out of. All we can say for sure is that, for a star as bright and hot as the sun, Venus is too close, Earth is clearly within the Goldilocks zone, and Mars is probably close to the tail end of it.
How far away from the star the Goldilocks zone is depends on the star's energy output. A very dim red dwarf star, like Wolf 359, would require a planet to be only about 1.5 million kilometers away from it to receive as much energy as Earth does from our sun — that's only 0.01 A.U., 1% of the Earth-sun distance. A bright and powerful star like Sirius A, on the other hand, would require a planet to be 5 A.U. away from it to receive as much energy as the Earth does from the sun.
Interestingly, both of those distances have potentially disastrous consequences. If a planet is only 0.01 A.U. away from its star, the star's tidal influence is going to be enormous. The strength of tidal forces varies directly with the larger object's (i.e. the star's) mass, but inversely with distance cubed. The tidal forces on a planet only 0.01 A.U. from a star 1/10 the mass of the sun are, therefore, going to be 0.1 / 0.013 = 100,000 times as strong as the tidal forces the Earth experiences from the sun. This all but guarantees that the planet will be locked in synchronous rotation with its star — that is, its rotational period must match its orbital period, so the same side is always facing the star. One side of such a planet would be in perpetual daylight, while the other would be in perpetual night. The climate on such a world would be much different than the climate on Earth.
Dim stars also have the disadvantage that their Goldilocks Zones are going to be narrower. There is disagreement as to exactly how wide the Goldilocks Zone around the sun is — different models compute widths anywhere from 0.5 A.U. down to 0.02 A.U. — but however wide the zone actually is, it will be proportionally narrower with a dimmer star (and wider with a brighter star). The star 61 Cygni is about 1/10 of the sun's brightness, so its Goldilocks Zone will be (the square root of 1/10) of the sun's, or a little less than 1/3 of the sun's Goldilocks Zone distance. But this means both the inner edge and the outer edge of the Goldilocks Zone will be 1/3 of the distance compared with the sun — and that means the zone as a whole will only be 1/3 as wide. The narrower the Goldilocks Zone, the less a chance that a planet would happen to have formed within it.
Worse, many red dwarf stars — Wolf 359 included — are flare stars, which emit semi-regular bursts of X-rays every bit as powerful as those emitted from a flare taking place on the sun. At 0.01 A.U., that much ionizing radiation can easily disassemble the organic molecules necessary for life. And X-rays can scatter (e.g. bend around corners), which is why the dental hygienist always leaves the room and closes the door when (s)he takes an X-ray picture of your teeth. Regular flare outbursts so close by probably means that any life would have to be buried underground.
A planet orbiting Sirius A at 5 A.U. wouldn't have any of these problems, of course, but it runs into another issue. Sirius is a binary system. Sirius B (a white dwarf) makes one complete orbit around Sirius A every half century, and at one point in this orbit the two stars come within 8 A.U. of each other. As any budding astrophysicist will tell you, the three-body problem is a chaotic one for which there is no solution. Any planet orbiting Sirius A farther away than 1/4 of this 8 A.U. closest-approach distance will be thrown out of the star system by Sirius B's gravity. The farthest a stable planetary orbit can be from Sirius A is, therefore, only 2 A.U. — which is barely 2/5 of the Goldilocks Zone distance. Therefore, no planet can exist in the habitable, liquid water zone around Sirius A. (A planet could theoretically orbit both Sirius A and Sirius B as a pair, but then its minimum orbital distance has to be at least four times the greatest separation distance between the two stars in their orbit of each other. Sirius B's orbit is rather eccentric, and at one point in its orbit it's over 30 A.U. away from Sirius A. A planet orbiting both Sirius A and B would therefore need to be at least 120 A.U. away from their common center of mass, and at that distance the combined brightness of Sirius A and Sirius B would be far too weak to keep the planet from freezing.)
Even if a planet happens to lie within the Goldilocks Zone, that's no guarantee that it can harbor surface life — let alone that life will actually arise there on its own, or that said life will have had sufficient time to evolve to the point where space-faring beings can emerge. The atmospheric pressure must be high enough for liquid water to exist, and that can't happen unless the planet has sufficiently strong surface gravity to keep its atmosphere from escaping into space. The formula for determining the surface gravity of a planet is as follows:
- surface gravitational field strength = G * ρ * 4/3 * π * R
... where G is Newton's gravitational constant (6.6738 x 10-11 m3/(kg s2) ), ρ is the average density of the planet in kg/m3, π is 3.14159, and R is the radius of the planet (half the planet's diameter) in meters. The result will be in meters per second squared.
As an example, the Earth's radius is 6,371,000 meters, and Earth's average density is 5515 kg/m3. Plugging those into the formula above, we get:
... which is, in fact, how fast things accelerate downward near the surface of the Earth when you drop them. Mars, by contrast, only has a radius of 3,380,000 meters and an average density of 3930 kg/m3, so its surface gravity is only 3.71 m/s2, about 38% of Earth's.
You'll note that the Martian atmosphere is extremely thin, less than 1% of the surface pressure of Earth's atmosphere. One factor that contibutes to Mars's thin atmosphere is this low surface gravity.note Despite being farther from the sun than the Earth, and thus receiving less heat that could potentially boil its atmosphere away into space, Mars still has less of an atmosphere than the Earth does. A resonably strong surface gravity may be required for a planet to retain a thick atmosphere. There are exceptions in our own solar system, of course: Saturn's moon Titan has less than a sixth of Earth's surface gravity yet its surface atmospheric pressure is higher than Earth's, and while Venus is both closer to the sun and has only 90% of Earth's surface gravity its surface pressure is ninety times that of Earth's atmosphere. But you need at least some gravity, and possibly quite a lot of gravity, to retain an atmosphere within the Goldilocks Zone.
Another factor that can mean no life-bearing planets are possible in a given star system is the lack of heavy elements. The Milky Way galaxy is over ten billion years old. When it first formed, it consisted almost entirely of hydrogen and helium; almost no heavier elements (like carbon and the other elements necessary for organic life) existed. Several generations of stars have been born and died since then, and some of the more spectacular star deaths have peppered the interstellar medium with heavy elements synthesized by those stars' death throes. The sun, for instance, is a third-generation star — the cloud of gas and dust out of which it formed contained material expelled by a supernova which, in turn, had formed out of an earlier cloud that contained material from an even earlier supernova. This is why there was enough carbon, oxygen, silicon, iron, etc. to form solid, rocky planets and organic molecules. Astrophysicists refer to all elements heavier than helium as "metals" (even if the element in question is oxygen or neon), and sometimes call a star system's heavy element abundance its "metallicity."
By contrast, Barnard's Star (a red dwarf approximately 6 light-years from the sun) formed in the Milky Way's first wave of star formation. It has almost no heavy elements. If the star itself is metal-poor, that means the cloud out of which it formed was also metal-poor, and therefore any planets that would have formed out of that cloud would be metal-poor as well. There might be some Jupiter-like balls of hydrogen or helium orbiting Barnard's Star, but there isn't going to be anything with a solid surface.
So, to sum up, the requirements for a habitable Earth-like planet are:
- The planet must lie within the Goldilocks Zone for its star.
- The star cannot be too dim, since this will mean its Goldilocks Zone will be too narrow, any planet in the zone will be in synchronous rotation with the star, and the Goldilocks Zone will lie within the Danger Zone for stellar flares.
- If a binary star system, the companion star cannot come closer to the primary than 4 times the Goldilocks Zone distance.
- The star system cannot be metal-poor, or (if its metallicity isn't known) so old that it would have formed when the galactic medium was still metal-poor.
- The planet cannot be too small or light, as this will prevent it from retaining an atmosphere.
Note that if you're willing to accept non Earth-like planets, many more possibilities open up. For example, Europa, one of Jupiter's moons, is thought to contain liquid water despite being nowhere near the Goldilocks zone. A thick or rapidly rotating atmosphere like Venus's can distribute heat evenly around the planet, thus solving the problem with tidal locking mentioned above. Greenhouse effect atmospheres, tidal heating from a nearby planet, and internal heating from other unknown mechanisms note can all lead to potentially habitable conditions in unexpected places. However, these all lead to new problems and obviously won't resemble Earth.
For that matter, even liquid water might not be necessary. There are theories that life might be possible with alternate biochemistries based on liquid ammonia, methane, or even interstellar gases. Since all we have to go on is observations of Earth, there's no way to tell for sure if this is actually possible. But the less Earthlike you get, the more problems you have with an actual story involving anything other than Starfish Aliens. A hypothetical ammonia based organism, for instance, would constantly argue over the thermostat with Earthlings given that ammonia boils at -28F. note
If you want anything more interesting than bacteria to have evolved, another problem arises. The star must have been shining at roughly the same energy output for at least a couple billion years, in order to give time for complex life to have evolved.
This last requirement is a real buzzkill, as it eliminates damn near every bright star you can see in Earth's night sky. Big, bright stars like Sirius A only live for a few hundred million years before they run out of gas. (The candle that burns twice as bright lasts half as long, after all.) Red giant stars like Arcturus had a long, stable lifetime as a dimmer star in the past, but will only last for a couple of million years at the red giant stage — so if they did harbor life bearing planets in the past, those ecosystems were snuffed out when the star expanded to its current red giant state, and any planets in the star's new Goldilocks Zone won't have long enough for evolution to run its coursenote .
See the Useful Notes article on Local Stars if you want to pick a home for your theoretical planet from among our stellar neighbors. See the Useful Notes article on Planets if you want to put even more realism into the worlds you create.
Oh ... and if your planet has any moons, don't forget to use our old formula P2M = A3 to calculate how long their orbital periods are!
Two separate "So You Want To" articles now exist to deal with the realism aspects of creating your own aliens. They are:
Of particular import to any story involving space travel is the "Believable space-faring aliens" section of the first article.
Deviation: Limiting the Damage
Let's say the idea of a spaceship carying 10 times its empty weight in fuel sickens you. You want the space aboard your space ship to house your colorful characters, dazzling weapons, holodecks, shopping malls, and other fun and excitement — not deck after deck full of boring old propellant. And you want to allow for long patrols without having to refuel at every destination. So, you elect to go the route of the Honor Harrington series, and equip your spaceship with a gravity-manipulation Reactionless Drive that allows her to accelerate without throwing material out of her tailpipe. Problem solved, right? And now that you've given your civilization gravity-manipulation technology, that also eliminates your problem of having your characters float around in zero gee; they can now spill liquids without spraying them all over the walls and play ping-pong to their heart's content while riding between the planets.
But hold on. You've also opened up a can of worms.
First, if you allow them to accelerate without pushing anything, they are now violating one of the most basic laws known to physics: the conservation of momentum. In the real world, you can't apply a force to an object in one direction without causing an equal-and-opposite force on some other object. Rockets fly up because their exhaust flies down. Jumping up pushes the Earth ever-so-slightly downward; falling back to the ground afterward pulls the Earth ever-so-slightly up. By letting your space ship violate this basic law, you're saying that momentum is not always conserved. What other circumstances in your universe will cause momentum not to be conserved? Do the laws of Newton simply get held in abeyance every time someone switches on a gravity generator? Are there natural phenomena that accomplish the same thing?
Second, are you also violating the conservation of energy? A 1000 tonne spaceship traveling 1/10 of the speed of light has a kinetic energy of 450 quintillion Joules, equal to 100,000 megatons of TNT. That energy had to come from somewhere. Did it come from burning some sort of fuel on board your space ship, to power the generators? If you used the thermonuclear fusion of hydrogen into helium as your fuel source, and you managed to Hand Wave a fusion reactor technology that's nearly 100% efficient, you'd have to burn at least 350 tonnes of hydrogen to obtain that much energy, which is a third of your spaceship's own mass. (This isn't as bad a mass-ratio situation as if you'd used a plain-old momentum-conserving fusion rocket, but it's still pretty significant.) And you'll have to burn just as much again to slow your space ship back down at the end of your trip. If this is too much for you, and you decide your reactionless gravity drive simply works by tapping into the magical gravity waves of the universe and surfing along them with only minimal power requirements, then your space ship's kinetic energy is being created ex nihilo. You've got yourself a free energy machine! Just strap your space ship to one end of a long lever, strap the other end to a huge electric generator, and fly in circles. You can generate enough energy to power your entire civilization this way, with no cost in natural resources. This will play absolute havoc with your fictional economy. You'll have to throw away that whole book you were going to write about your space empires' war over Space Oil.
Third, if any 1000 tonne space ship can easily accelerate to a tenth of light speed, then every two-bit spaceship owner has in his possession a weapon of mass destruction. Those 100,000 megatons of TNT-equivalent kinetic energy will act like 100,000 megatons of actual TNT if they strike a planet. Want a future populated by plucky tramp space-freighters and sneaky space pirates? It ain't gonna happen if every ship is a Hiroshima-on-steroids waiting to happen. Every spacecraft captain will be on too short a leash. Any spacecraft that even looks suspicious will be killed before it can become a threat. (And, yes, all fast-moving spacecraft, and even stationary spacecraft, will eventually be detected — there ain't no Stealth in Space.) Any civilization that didn't take these precautions wouldn't be a civilization for very long. This might work as a setting for your future totalitarian dystopia, but is hardly the right world for romantic swashbuckling adventures.
The potential damage done to your story by a Reactionless Drive is just one example of the broader principle. Any technological marvel that sidesteps the Real Life roadblocks facing space travel has the potential for unintended consequences. Thermonuclear torchships? They've got the same "spaceship = weapon of mass destruction" problem that reactionless drives do, albeit on a more manageable scale.
So what do you do when you need your characters to be able to move between the stars faster-than-light, or teleport, or have a Tractor Beam, or do any of the other myriad things that our current best guesses at the law of nature say are impossible? You set the technology up in such a way as to limit the damage to your story and your setting. Maybe your Deflector Shields are magnetic, and can only affect charged particles and ferromagnetic metals — and your spaceship needs to open up holes in its shields to shoot iron slugs or particle beams at an enemy. Maybe the high speeds needed to traverse interplanetary distances in days or hours are imparted not by your space freighter's own engines, but by planetside pushers that will only push it onto a predictable course, thereby eliminating the threat of rogue spaceship commanders turning their vehicles into WMDs. Maybe your transporters only let you beam between one transporter pad and another (unlike the transporters in a certain softer SF franchise). Maybe the violations of the Laws of Thermodynamics needed to make Stealth in Space work are curtailed in some way that prevents you from getting useful energy out of any warm object (which, like some types of Reactionless Drive, would have driven your Space Oil companies out of business).
FTL Travel is one of the bigger thorns in the side of the Hard SF genre. Special Relativity makes it absolutely clear: it is physically impossible to accelerate an object with any kind of mass so that it's moving faster than the speed of light. Even accelerating an object to the speed of light would require an infinite amount of energy. However, we've also pretty much established that there are no other technological species on any planet in the Solar system other than Earth. If we want to have space adventures involving high-tech aliens, we'll have to travel to other star systems, and the distances involved are so enormous that it would take years to get from one star to another if you were limited to sub-light speeds. Science Fiction writers have had to compromise, note and allow some means of travelling faster-than-light which didn't turn their universe into something totally unrecognizable to a modern reader. Therefore, the ability to move faster-than-light has received more attention in SF than any other fantastic concept as to ways to Limit The Damage of having it around.
The very worst problem with FTL travel (or even just FTL Radio) is a certain niggling consequence of Time Dilation. When travelling at any speed, even a brisk walk, relative to somebody else, you'll see his clock move slower than yours — but he'll see your clock move slower than his. This way-counterintuitive state of affairs means that some distant events in the universe which are in your future are in the other guy's past, and vice-versa. Without FTL travel, though, this isn't a problem. Einstein and Minkowsky established that for any event that's in Oberver A's future and Observer B's past, no matter how far in Observer A's future the event is, it will always be far enough away that any light-speed signals from this event would not reach Observer A until the event was also in Observer A's past. When plotted on a space-time graph, the signals from the event would stretch out in spacetime in a "light cone," which guarantees that the signal will not reach any observer in the universe until the event is in that observer's past. To put it another way, let's say that in Observer A's reference frame, Event 1 occurs before Event 2, but in Observer B's reference frame, Event 2 occurs before Event 1. Light cones maintains causality by ensuring that, if Observer A would find out about Event 1 before Event 2, Observer B cannot find out about Event 2 before information about Event 1 is theoretically available to him.
Here's an example: Suppose Observer A is standing on Earth, and Observer B is in a space ship, coasting in a straight line at 86.60254% of the speed of light. This gives him a gamma (γ) factor of exactly 2. When the space ship passes by Earth, both Oberver A and Observer B synchronize their clocks at 5:00 PM. In Observer A's frame of reference, when his clock reads 7:00 PM, Observer B's clock will read 6:00 PM. However, in Observer B's frame of reference, when his clock reads 7:00 PM, Observer A's clock will read 6:00 PM. At 6:20 PM on Observer A's clock, an event happens on Earth — the winning State Lottery numbers are announced. At 7 PM on Observer A's clock, this event is 40 minutes in Observer A's past; but at 7 PM on Observer B's clock, this event is still 20 minutes in Observer B's future. It's not just that Observer B perceives it to be in the future, it really is in the future, it really hasn't happened yet. What prevents Observer B from knowing about the event before it happens in his reference frame is that it takes time for any information about the event to reach him. At 6:20 PM in Observer A's reference frame, Observer B's clock would only read 5:40 PM, but Observer B would be 69.282 light-minutes away from Earth; if Observer A radioed the winning lottery numbers to Observer B at this moment, they'd take 521 minutes in Observer A's reference frame to reach Observer B's space ship, at which point Observer B's clock would read 9:40 PM and the event would be 4 hours in Observer B's past. Even if Observer B magically reversed his velocity at 5:40 PM on his clock, so that he was headed toward Earth at 0.866c instead of away from it from that moment onward, the radio signal would still take 37.128 minutes in Observer A's frame of reference to reach the space ship.
But by going faster than light, even just FTL Radio, you can receive information about events that are in your own future. You can perceive Event 2, which was caused by Event 1, before Event 1 actually occurs in your reference frame. In our lottery-winning scenario above, suppose Observer A and Observer B had a Subspace Ansible that allowed instant communication no matter how far apart they were. Observer A could send the winning lottery numbers to Observer B's space ship at 6:20 PM on Oberver A's clock. With instantaneous communication, the numbers would arrive on board the space ship at 5:40 PM on Observer B's clock. If Observer B then sent the same numbers back to Observer A over the same subspace ansible, they'd arrive on Earth at 5:20 PM on Observer A's clock. Observer A would have the winning lottery numbers an hour before they were announced.
In other words, Time Travel.
How do veteran SF writers handle the time travel consequences of FTL travel? Most of them don't. They simply sweep it under the rug and hope no one will notice. Those authors who do address it often end up with bizarre universes where wars are fought before they've even started, and characters can shoot their own grandfathers.
The other main problem with FTL travel is what it can do to life in your universe even without time travel. If your space pirates can just jump into hyperspace at the first sign of trouble, you'll never have any exciting space battles. If you can ram a planet or another spacecraft while travelling at FTL speeds, you risk turning even the tiniest FTL shuttlecraft into a planet-killer that will put even the largest, fastest slower-than-light kamikaze to shame.
Maybe faster-than-light travel only works between certain rare points in space, and your ships must maneuver in normal space to get to and from them. Maybe FTL movement is impossible within some large distance from a gravity source, requiring your space ships to leave the solar system — or at least leave Earth orbit — before they can go FTL. Maybe your space pirates can jump to hyperspace at the first sign of trouble, but so can your space cops, and they have FTL weapons they can shoot at each other while in hyperspace.
The third problem with FTL travel is more practical: we don't know how to do it in Real Life. Every attempt to come up with a way to do so has run into intractable problems. Quantum entanglement can occur instantaneously across vast distances, but it can't convey any actual information faster than c. The Alcubierre space warp requires the energy output of an entire sun just to create, and there's no guarantee that you could actually make the space warp move — and even if you could, there's even less of a chance that it could move faster than c. Wormholes, if they even exist, will spontaneously collapse faster than it's possible to traverse them. You, as the writer, will have to invent a way to travel faster than light, and then cover all the repercussions of the method you come up with.