# Prior to putting spacecraft on a trajectory going a significant fraction of the speed of light, would some things need to be tested on Earth?

Except for particle accelerators, I don't think we have made any macro object go anywhere near the speeds planned for spacecraft like the one planned in Project Orion.

But would there be something learned first by attempting to get a multi-kg mass object moving at say 1% of $$c$$, especially if we could place an animal in such a craft? Surely one would not (eventually) send humans on a 1% $$c$$ journey without such experimentation?

The issue of course is that perhaps there is no good way of reaching such speeds on Earth although I would guess something like a cyclotron (with some major modifications) could do it except the centrifugal forces would be perhaps too large. And a linear accelerator approach might not be practical/possible/safe at all.

Nonetheless, would there be some benefit to testing issues with communication, control, and even perhaps crew health before sending people on such an eventual journey in space?

EDIT: To me, the most interesting part of the question is whether there is any plausible way to accelerate a macro object on Earth to .01 c -- perhaps as mentioned, this really can't practically be done on Earth because of many practical problems. I know that rail guns are both not even close to providing that speed and the acceleration they produce would probably destroy conventional electronics let alone what would happen to a human or an animal.

I think I am right in saying that a circular track would also produce destructive acceleration.

Last Edit: My question is not whether such trips are being planned but if they were being planned, whether Earth-bound testing is possible or not, whether it is a good idea (which of course it would be) and finally how such testing on Earth would be done.

• "Surely they do not plan on sending humans on a 1% c journey without such experimentation?" No one plans on this at all. – Organic Marble Jun 7 at 4:04
• no one plans on a 1% c journey at all? or not on one without Earth-bound experimentation first and if so, how will such speeds be achieved on Earth? – releseabe Jun 7 at 4:52
• I’m voting to close this question because no one plans on this at all. – David Hammen Jun 7 at 4:58
• I've adjusted the wording of your question so that it is a better fit to the site. The complaints were that this is not going to happen any time soon, so it was trivial to edit out that particular premise and leave an answerable question. Feel free to adjust further if you are uncomfortable with the wording, and Welcome to Space! – uhoh Jun 7 at 5:08
• @DavidHammen: How can you say no one plans on 1% c space travel, given that it was planned on 60 years ago and more recently it is being discussed using anti-matter and light sails? I would guess given Musk's and Bezos extremely large commitment there might well be teams working on this right now, if only for inter-planetary travel. – releseabe Jun 7 at 6:27

First of all we are confident enough that special relativity is correct that we know we would not need to worry about the speed as such: everyone is travelling all the time at any speed you like less than $$c$$ relative to something, and we don't all explode or die or anything. We also know how to deal with the related issues around communication. This is all very well-tested physics.

## Hitting things

What you would certainly have to deal with is the problem of the spacecraft meeting crud in space (dust, gas) which is more-or-less stationary in the frame of the Sun, say, but very much not stationary in its frame. If you hit something with a mass of $$.01\,\mathrm{g}$$ then it's going to dump about $$5\times 10^7 \,\mathrm{J}$$ of energy into you. I make that the equivalent of about $$10\,\mathrm{kg}$$ of TNT. This is probably a significant problem for any vehicle which intends to travel at a significant fraction of $$c$$: impacts on spacecraft are already a problem, and they get worse as the square of speed: when the spacecraft itself is travelling at a significant fraction of the speed of light, almost anything it hits will be travelling at a significant fraction of the speed of light. This is as much a problem for interstellar travel as it is for interplanetary travel: there's less stuff, perhaps, but you are out there for longer.

## Why this is all absurd

Although the person asking the question seems to have repeatedly changed what they're actually interested in in comments, it seems that they're interested in testing things on Earth for use in interplanetary (not interstellar) travel. In the following two sections I'll show why testing such a thing on Earth is not possible, and why such high speeds are impractical for interplanetery travel.

Since the maximum velocities here are only 1% of the speed of light, I'll do all the calculations without relativistic corrections: there will be some, but they'll be small. I'm also generally rounding to 3 significant figures, although some of the values are probably less accurate than that: if you assume $$\approx$$ whenever I have $$=$$ it's probably safe. I haven't quoted values for constants like $$c$$ & $$g$$, but they're the usual ones.

### Testing on Earth is absurd

In order to test anything like this on Earth we would need to accelerate some massive object to $$v_\text{max} = 0.01c$$. There are two ways we could do this: in a straight tube, and in some ring.

There's a longest straight tube we can make due to the curvature of the Earth: let's say it has $$l = 100\,\text{miles} = 1.61\times 10^5\,\mathrm{m}$$. We can easily now compute the smallest acceleration (this is simply the case where acceleration is constant) needed to achieve a given $$v_\text{max}$$ along such a tube, which is:

$$a = \begin{cases} \frac{v^2_\text{max}}{l} &\text{object slows down again}\\ \frac{v^2_\text{max}}{2l} &\text{object allowed to hit end of tube} \end{cases}$$

And given $$v_\text{max} = 3\times 10^6\,\mathrm{ms^{-1}}$$, we get, for the first case, $$a = 5.59\times 10^7\,\mathrm{ms^{-2}} = 5.71\times 10^6\,g$$, and for the second $$a = 2.80\times 10^7\,\mathrm{ms^{-2}} = 2.85\times 10^6\,g$$.

For both these cases the experiments would last hundredths of a second.

If the object being accelerated had a mass of $$1\,\mathrm{kg}$$, the energy required would be $$1.5 \times 10^{12}\,\mathrm{J}$$: this is about equivalent to 359 tonnes of TNT: it's a rather small nuclear weapon's worth. In the case where the object hit the end of the tube this would all be released at that point.

Experiments like this are unlikely to be useful for testing anything: the conditions are so extreme that, while it might be possible to design electronics to survive the version where the object is slowed down again, such electronics would be utterly unlike anything in a spacecraft.

The second version is to test an object which is being run a round a ring. Well, what's the largest ring we could build on Earth? It's a ring which runs all the way around the equator, with radius $$R = 3.38\times 10^6\,\mathrm{m}$$. So we can now easily compute the acceleration felt by an object running around such a ring:

\begin{align} a &= \frac{v^2_\text{max}}{R}\\ &= \frac{9\times 10^{12}}{6.38\times 10^6}\,\mathrm{ms^{-2}}\\ &= 1.41\times 10^6\,\mathrm{ms^{-2}}\\ &= 1.44\times 10^5\,g \end{align}

So this is better: we now only need to design electronics which can survive hundreds of thousands of gravities. We also have the small problem of building an evacuated tube around the equator and somehow steering some macroscopic object around it (how you do that I have, really, no idea at all: the approach used for charged particles in particle accelerators definitely won't work).

This is the kind of thing the ringworld engineers might consider: it's not the sort of thing that humans are going to be doing any time soon.

And, even if you could do this, it's still completely unrelated to the kind of conditions in a spacecraft: the electronics will be completely different, and the accelerations involved are hundreds of thousands to millions of times greater than what is survivable by a human being.

So even if we could do this sort of experiment on Earth, it would be entirely unuseful for spacecraft design. Some things you can only do in space, and this is one of them.

### Velocities this high for interplanetary travel are impractical

So, let's look at what sort of interplanetary travel (as opposed to interstellar) might involve velocities this high. We can use the same equations we used before to compute the minimum acceleration involved for a trip of a given length. I will assume here that at the end of the trip you want to stop, because if you don't want to stop then you're definitely talking about the acceleration phase of interstellar travel. And we can treat all the boring orbital velocities as zero, since they're all very small compared to the velocities we're interested in.

We'll take $$v_\text{max} = 3\times 10^6\,\mathrm{ms^{-1}}$$ again, and this time $$d = 5\,\mathrm{AU} = 7.48\times 10^{11}\,\mathrm{m}$$. This is about as far as Jupiter.

\begin{align} a &= \frac{v^2_\text{max}}{d}\\ &= \frac{9\times 10^{12}}{7.48\times 10^{11}}\,\mathrm{ms^{-2}}\\ &= 12.0\,\mathrm{ms^{-2}}\\ &= 1.23\,g \end{align}

So for a trip to Jupiter during which you accelerate for half the trip and decelerate for the rest this is habitable, For anything shorter than that it rapidly becomes unsurvivable (a trip to Mars would be something like $$5\,g$$ all the way, which would almost certainly kill the crew I should think).

Well, Jupiter is somewhere interesting to visit, so this is OK. What sort of spacecraft would we need?

Well the first option is a light sail. Let's say the spacecraft weighs $$1000\,\mathrm{kg}$$ and the sail is a perfect reflector and weighs nothing. How big does it need to be? The pressure on the sail due to light at the orbital radius of the Earth is $$P = 2\times 1360/c\,\mathrm{Pa} = 9.07\times 10^{-6}\,\mathrm{Pa}$$.

We're going to Jupiter so we need $$a = 12.0\,\mathrm{ms^{-2}}$$. $$F = ma = PA$$ so $$A = ma/P$$, where $$A$$ is sail area. Plugging in the numbers we get

\begin{align} A &= \frac{ma}{P}\\ &= \frac{1000\times 12.0}{9.07\times 10^{-6}}\,\mathrm{m^2}\\ &= 1.32 \times 10^9\,\mathrm{m^2} \end{align}

If the sail is square, it is about $$36\,\mathrm{km}$$ on a side. It has to be bigger than this of course, because you want to sustain the acceleration beyond Earth's orbit.

So, maybe this is feasible: it's huge but it's not absurd (better make sure you don't use it to focus the reflected light on anything though: it's about a Trinity test every minute's worth of power).

Except ... you can't stop. We don't have a convenient second Sun so when you reach the half way point and want to turn around, you can't. This thing is the canonical example of the acceleration stage of an interstellar trip. So, not useful for interplanetary travel with speeds this high (light sails are potentially useful for much lower speeds where you can rely on the target object capturing you, unfortunately $$0.01c$$ is much higher than the escape velocity of any planet).

So what about rockets. Well, now we can use the rocket equation:

$$\Delta v = v_e \ln\left(\frac{m_0}{m_f}\right)$$

or

$$m_0 = m_f e^{\frac{\Delta v}{v_e}}$$

Where

• $$m_0$$ is the launch mass;
• $$m_f$$ is the final mass which we will take to be $$1000\,\mathrm{kg}$$
• $$\Delta v$$ is the total change in speed, which we'll take to be $$c/50 = 6\times 10^6\,\mathrm{ms^{-1}}$$, as you want to stop at the destination;
• $$v_e$$ is the exhaust velocity.

So I'll assume some super-duper ion drive which will:

• have enough thrust (they don't);
• have $$v_e = 5\times 10^5\,\mathrm{ms^{-1}}$$, about 5 times better than anything I know about.

So now, we can plug these numbers in and we get

\begin{align} m_0 &= m_f e^{\frac{\Delta v}{v_e}}\\ &= 1000\times e^\frac{6\times 10^6}{5\times 10^5}\,\mathrm{kg}\\ &= 1000 \times e^{12}\,\mathrm{kg}\\ &= 1.63\times 10^8\,\mathrm{kg}\\ &= 163\times 10^3\,\text{tonnes} \end{align}

This is less than twice the mass of a large aircraft carrier.

And this is for a one-way trip: if you want to come back you need to get that mass to the other end. And that means you need a launch mass of $$m_0 = 2.65 \times 10^{13}\,\mathrm{kg}$$. This is still light compared to the Moon, fortunately.

There are ideas for drives with higher $$v_e$$ than this but they are increasingly science-fiction devices. Even a high-thrust ion drive is fairly science-fiction: almost certainly, even if it were possible it would require a fusion reactor to power it, and those don't exist yet, let alone ones we can put in spacecraft. The heat-dissipation problems would also be formiddable.

So no plausible kind of propulsion will achieve these speeds for interplanetary travel: they're only interesting for interstellar travel, currently only with light sails of some kind.

### Other confusions

One thing the person asking the question was interested in was guidance: how you steer spacecraft travelling at $$v\approx 0.01c$$. This is a non-problem: if you have a propulsion system which will accelerate you to this kind of speed, you also have one which will change your course when travelling at this speed. The problem is having a propulsion system which will get you to $$0.01c$$ in the first place.

## Conclusion

Travel at $$v\approx 0.01c$$ is extremely impractical for interplanetary travel: it's not survivable for short trips and the fuel requirements are absurd for all trips. Testing such a system on Earth is completely absurd. This seems to be a case of too-much-science-fiction combined with no real intuition about just how fast $$0.01c$$ is, how much energy is required to get to that kind of speed, and the implications of the rocket equation.

• This is not about special relativity. It is about collisions and other perhaps unexpected things. – releseabe Jun 7 at 12:12
• @releseabe: then your question makes no sense. You're not going to learn anything about collisions by tests in a cyclotron, or on Earth at all. And if you read my answer you'll see that most of it ... is about collisions. – tfb Jun 7 at 12:27
• But there are dozens of other things besides collisions that must be tested when a craft is moving so fast that human reactions are of no use. How is it steered, slowed down? How does it, perhaps, interact with other craft? Bottom line, if we really were planning on very fast ships, it would be crazy not to do a lot of Earth-bound testing if it is possible to do so. – releseabe Jun 7 at 14:56
• @releseabe: I can't work out what you're confused about, but it's something. We know how to steer and slow down spacecraft: nothing changes (except you need absurd amounts of fuel to slow down). Astronauts do not run spacecraft by looking out of the windows and relying on their reaction time being good enough to avoid obstacles: computers run them. Finally no experiment you could do on Earth involves accelerations less than tens or hundreds of thousands of gravities: these are things that you can only test in space. – tfb Jun 7 at 15:16
• wow, we know how to steer 1% c spacecraft? i sure did not know that. in fact, that is almost certainly wrong. – releseabe Jun 7 at 15:43

No.

## Speed

I don't think there is anything about the speed that would need to be tested. Every time we experimentally test special or general relativity theory we get results that perfectly match. As a reference point, the fastest spacecraft speed designed for is 0.1% $$c$$, and that's the Parker Solar Probe. For more on that see Parker Solar Probe passing extremely close to the Sun; what relativistic effects will it experience and how large will they be?

As far as communications is concerned I can't imagine anything that would have to be tested at such high speed. The regular Doppler effect and relativistic Doppler effect are well understood, and there should be no challenge to building transmitters and receivers for the expected red-shifts from relativistic flight. See answers to Relativistic effects in space mission communications for more.

Just because there "shouldn't be" though doesn't mean that someone won't make a mistake!

From The Space Review article:

The combination of Cassini’s tremendous speed and the sharp air-drag deceleration of the Huygens probe creates a significant Doppler shift in the probe’s signals as seen from Cassini (the expected Huygens-Cassini velocity shift would have been up to 5.5 km/sec). Engineers at Alenia Spazio, the Italian company that built the radio link, properly anticipated the need for adequate receiver bandwidth to accommodate the frequency shift.

[...] Here was the crucial flaw. The Doppler shift did not only change the frequency of the incoming signal, it also squeezed it into a slightly shorter time period. As a result, Cassini’s receiver would have been unable to recognize the timing pulse in its expected location, and thus the incoming data stream would become unreadable.

## Acceleration

Acceleration is another matter entirely! If you provide significantly less than 1 g then there are health effects; the longest an astronaut has lived in microgravity at a time is a little more than a year, so you'll need to supply some to keep them healthy on a long journey, and your propulsion may not be strong enough to do that. If it is, then you'll reach 0.1 $$c$$ in about a month, and then what?

If your acceleration is even stronger and you subject your crew to significantly more than 1 g then there may be health effects related to long-term exposure to enhanced acceleration. But that could definitely be tested with reasonably built centrifuges.

• i would guess and have in fact read that much has to be considered when traveling so fast and one big concern is hitting smallish rocks in space. So any system for dealing with such rocks (magnetic field or plasma field) would need to be tested as realistically as possible. – releseabe Jun 7 at 6:29
• @releseabe now that is an excellent point! Certainly spacecraft are hit by meteorites all the time at 0.01 $c$ (about 30 km/sec) but those tests can be and are done by accelerating just the tiny particles to high speeds, rather than "a multi-kg mass object moving at say 1% of 𝑐, especially if we could place an animal in such a craft?" Other people can continue to post answers here about accelerating a craft, but why don't you go ahead and post a second question about accelerating tiny dust particles to relativistic speeds? – uhoh Jun 7 at 6:46
• @releseabe That's something much more doable, and those collisions nearly impossible to simulate accurately and will require a lot of experimentation! – uhoh Jun 7 at 6:46

Getting to high velocities is actually very simple. Not much difference between the earlier and later phases of, say Reaching half light speed.

It’s the time factor. Even with high thrust, it can take a very long time. Lifetimes with current technology.

• I would guess that reaching the high speeds if that's all one was concerned about would be fairly straightforward. But steering, slowing down, dealing with obstacles, especially at .5 c would have almost unimaginable problems. A man-made object going thousands of times faster than what we have now, just mind-boggling. – releseabe Jun 7 at 15:47
• Re Getting to high velocities is actually very simple. This is incorrect. It is very, very hard. Read up on the ideal rocket equation. – David Hammen Jun 9 at 13:56