# Is it possible to create a relativistic space probe going at least 0.1c with present day technology?

That's pretty much it:

Is it possible to create a relativistic space probe going at least 0.1c with present day technology?

Present day meaning as of April 2020. If it is actually possible, how could it be done, what would it cost, what could be gained from doing it, and why has no one done it before?

• en.wikipedia.org/wiki/Breakthrough_Starshot could be interesting source of ideas and some pointers. Not exactly present day technology, so it is not an answer directly, but quite close to it, at least theoretically. – Martin Apr 8 at 18:00
• Could the two users who posted answers please elaborate on why the rocket equation specifically prevents such a probe from existing? At the moment both answers just say "no, it's not possible because exponentials". Perhaps a better question to answer would be: given current fuel tank and power technologies and the most efficient production engine we have, what is the most delta V achievable today? – Michael Stachowsky Apr 8 at 18:12
• en.wikipedia.org/wiki/Starwisp suggests it might be technically possible. I remember Carl Sagan talking about something like this as early as the 1970s, but I can't find a reference. – user7073 Apr 8 at 18:15
• @MichaelStachowsky That's 1 tenth of 1% of the speed of light, still 100x slower than OP is looking for. – Russell Borogove Apr 8 at 20:03
• The question "why has no one done X?" is a strange question; we are not required to give you reasons to NOT spend billions of dollars. Stuff gets done when there is a reason to do it, not when the reasons to not do it are all exhausted. Put another way: why haven't you learned any French this morning? You were perfectly capable of learning French before breakfast so why didn't you? There are infinitely many things you could have done this morning, and you don't expect people to ask you why you didn't do all of them. – Eric Lippert Apr 9 at 17:37

No.

10% of the speed of light is about 30,000,000 m/s. Our fastest space probe to date, New Horizons, left Earth at less than 1/1000 of that speed. With a large propellant tank and a high-efficiency ion thruster we could reach something like 300,000 m/s, about a tenth of 1% of the speed of light. Due to the exponential nature of the rocket equation, reaching higher speeds requires exponentially larger amounts of propellant.

• Is there a launcher available to start that space probe with a large propellant tank and a high-efficiency ion thruster? Some scientifc payload of the probe should be possible too. – Uwe Apr 8 at 18:43
• With present day technology, yes, with present day equipment, no. (There's not actually a hard line between the two concepts, so take this as my opinion.) – Russell Borogove Apr 8 at 19:59
• It's worth noting that this more-science-than-fiction answer was the top answer, until the question hit the Hot Network Questions. Now the top answer is more-fiction-than-science. Interesting. – DrSheldon Apr 9 at 11:51
• Isn't the Parker Solar Probe the fastest man-made object? It had a max velocity of about 192 km/s at perihelion, albeit it didn't get to that speed using propulsion. – Star Man Apr 9 at 15:53
• You accelerate all the way towards the sun, then decelerate all the way back out, for zero net gain. If you were coming from outside the solar system, you could use the sun for a gravity assist that would increase your speed relative to your origin and/or destination. Gravity assist only changes the direction of motion relative to the assisting body, not the speed. – Russell Borogove Apr 10 at 15:41

I'm showing the calculations for Russell Borogove's excellent answer.

You've asked to accelerate an object to 0.1 times the speed of light. Mathematically, $$\left( \frac{\Delta v}{c} \right) = 0.1$$

The exhaust velocity $$v_e$$ of an ion thruster is 20-50 km/s. Let's pick $$v_e=30,000 \text{ m/s}$$, thus $$\left( \frac{v_e}{c} \right) = 10^{-4}$$

And let's say the mass of our payload is 1 kilogram: $$m_1 = 1 \text{ kg}$$

The special relativity form of the rocket equation is $$\Delta v = c \tanh\left(\frac {v_e}{c} \ln \frac{m_0}{m_1} \right)$$

Solving for the initial (fueled) rocket mass $$m_0$$, $$m_0 = m_1 e^{\left(\frac {c}{v_e}\right)\tanh^{-1}\left(\frac{\Delta v}{c}\right)} = 1 \text{ kg } e^{10^4 \tanh^{-1}0.1} \approx 10^{435} \text{ kg}$$

The mass of the observable universe is estimated to be only 1.5x10$$^{53}$$ kg.

I would say NO.

• Comments are not for extended discussion; this conversation has been moved to chat. – called2voyage Apr 13 at 13:34

Breakthrough Starshot claims to be capable of attaining 0.15c to 0.2c. But, the concept is based on a swarm of tiny probes (centimeter scale). They would be propelled by a "ground-based" laser; no on-board propellants circumvents the tyranny of the rocket equation. Breakthrough Starshot depends on a number of technologies not yet available or sufficiently advanced to meet required parameters. For relativistic spaceflight, it seems like the closest thing to achievable today, if you measure "close" in decades.

• Are you sure it depends on technologies not yet available? We have lasers and probes, what's keeping us? Is scaling the lasers technologically impossible, or is it just a solvable engineering problem (like sufficient cooling)? (I just made the technology/engineering distinction up -- a "technological" problem to me would mean we need scientists to solve it because the engineers say "can't do".) – Peter - Reinstate Monica Apr 9 at 7:41
• This really isn't present day technology, the question seems to be what can be built right now, not in decades... – GdD Apr 9 at 9:55
• I am somewhat surprised to see that laser propulsion has been demonstrated up to 3.5mN with a quite modest power supply. Now all you have to do is keep the beam on target at distances measured in AU... researchgate.net/publication/… – Russell Borogove Apr 9 at 14:13
• @Peter-ReinstateMonica: I believe the problem is not of power, but one of accuracy. Hitting a target on the other side of the solar system that's centimeters wide with a laser is.... tricky. – Mooing Duck Apr 9 at 22:07
• @MooingDuck : ... as is collimating a laser beam to be only a few times bigger than that target over such distances. – Eric Towers Apr 10 at 15:31

# Yes, with nuclear pulse propulsion.

The fastest manmade object is a "hubcap" that was used to cover a nuclear blast testing site, which was clocked at 125,000 miles per hour. With a spacecraft designed to use nuclear bombs for propulsion, it has been suggested that it may be possible to build a spacecraft that can reach .1c with modern technologies, though doing so would require solving some engineering challenges first. NASA's Project Longshot, for instance, was calculated as having a top speed of .045c on a trip to Alpha Centauri, and would presumably be able to reach a speed of approximately double that if they used all their fuel without leaving any for deceleration.

• I don't think that's working tech yet. Nice find though. – Joshua Apr 9 at 3:32
• @Joshua We could have built a nuclear pulse rocket in the 1960s if we'd had the political will to do so. You "just" need to hook a giant metal plate to an equally giant set of shock absorbers and then throw nuclear bombs onto the other side of it. – nick012000 Apr 9 at 3:35
• Orion style nuclear pulse propulsion only gets you about twice the specific impulse of an actually existing ion thruster. The more efficient variations are fantasies that might be possible once we have fusion power plants, which are just 10-20 years away, as they have been for the last 50 years. – Russell Borogove Apr 9 at 4:31
• For those wondering about Russell's comment above: that's unfortunately very true. ITER is supposed to be the milestone proving to the world it's not just possible but remotely viable and it has been planned since Reagan and Gorbachev in 1985. In 2010, people were convinced they'd be ready around 2018. Current timeline states ITER's first plasma is scheduled for 2025. We'll see... – Mast Apr 9 at 10:20
• @EricTowers: "The fastest manmade object is a "hubcap" that was used to cover a nuclear blast testing site, which was clocked at 125,000 miles per hour." And the link talks about how Operations Plumbomb Pascal-A launched a manhole cover into space. – Mooing Duck Apr 10 at 16:31

Given that rockets are clearly not cut for this, I find it rather weird that, despite a couple mentions in the comments, Breakthrough Starshot isn't getting more discussion here even though it was literally the first thing that came to my mind when I saw this question up. And that leads one to naturally consider the state of the art of beam propulsion, for that is what is relevant here.

Beamed propulsion, of course, circumvents the rocket equation by leaving the fuel on the ground, so that the "have to lift fuel to lift fuel to lift fuel to ..." business that creates the exponential problem with rockets no longer applies.

Now, the simplest method to do beamed propulsion, perhaps, is a laser and, indeed, BTSS aimed to use exactly such. Given that BTSS is not expected to produce results for some 50 years or more (iirc), then I'd say this isn't "present day" by your definition but, given that posts have at least examined the feasibility of using existing rockets, I find it is only fair to try a similar at least cursory analysis of the existing possibilities for laser beam propulsion.

Beam propulsion, of course, works on the principle that light carries momentum as well as energy and, so, if suitably directed at a craft, can create a force (transfer of momentum) upon it. The relevant equation is Einstein's

$$p = \frac{E}{c}$$

where $$E$$ is the energy in the beam of light. If the spacecraft is an ideal reflector, it will manage to acquire twice this much because the beam is reflected back, and that back-reflection must be balanced by an extra forward momentum equal to the whole original beam thanks to the conservation of momentum.

Note, of course, that there is the factor $$c$$ in the denominator, which, in human scale units, is crazy big: as a result, even a modest energy will only produce a little extra momentum and, hence, only minimal acceleration of a spacecraft. In particular, using $$p = \gamma mv$$ for a general relativistic spacecraft, we see the energy required to accelerate to speed $$v$$ is

$$E_\mathrm{accel} = \frac{\gamma mc v}{2}$$

for the ideal-reflection case. Likewise, if we are alloted a certain amount of energy and want a certain goal speed, we can figure the maximum mass:

$$m_\mathrm{max} = \frac{2E}{c\gamma v}$$

So how much laser energy can we reasonably muster? Well, there apparently was one laser from as far back as the 1980s called "MIRACL", which was a chemical gasdynamic laser meaning that instead of electric power it was fueled directly by a special chemical fuel and obtained a peak power exceeding 1 MW and 70 s firing time, which means you can have 70 MJ to play with.

Since it has been built, it could be again and, perhaps better now. Thus I'd say - while I don't know if this is the state of the art now - it could definitely be a reasonable value for "today". Suppose we build 100 of these lasers - that would be 7000 MJ, and we want to figure out the largest mass. Using speed $$0.1\ \mathrm{c}$$, so that $$\gamma \approx 1.005$$ and

$$m_\mathrm{max} = \frac{2(7000\ \mathrm{MJ})}{(3.00 \times 10^8\ \mathrm{m/s})^2 \cdot 1.005 \cdot 0.1} \approx 1.54 \times 10^{-12}\ \mathrm{MJ \cdot {s^2/m^2}}$$

or $$1.54 \times 10^{-12}\ \mathrm{Gg}$$ (gigagrams). Taking those units down we see this is about 1.5 milligrams.

The question then becomes whether you can do anything useful with 1.5 mg of total payload, most of which will have to be taken up by the light sail - indeed, if such a light sail is possible at all. Hence whether this qualifies as "a probe" is something for which I would exercise considerable caution and mind you that I am much more of a theoretician than an engineer, so those who are more savvy with the latter may want to chime in and complete this answer. Moreover, note that this has some very optimistic hidden assumptions such as that we can reflect 100% of the laser light (impossible), and that we can keep 100% of the beam focused on the craft (this is a big issue with the real BTSS project). Hence maybe you could say that 0.15 mg might be a better target and, it doesn't then start to sound too good for the sail.

One can, of course, work the other way, too: given the energy and a craft mass, how fast can we get it? $$0.1\ \mathrm{c}$$ may be out, but what about if we're willing to at least send an interstellar precursor, e.g. something like the "thousand astronomical units" (TAU) that was once upon a time proposed a very long time ago. Suppose we were to take a craft mass of, say, 1 gram, or 1000 mg. Using the same equations, we can solve for $$\gamma v$$ by

$$\gamma v = \frac{2E}{mc}$$

so that with now $$E = 7000\ \mathrm{MJ}$$ and $$m = 10^{-9}\ \mathrm{Gg}$$, we get a $$\gamma v$$ of about $$46\ \mathrm{km/s}$$, so this is about the actual velocity. Not much better than chemical rockets, but could get you to 1000 AU - 150 000 Gm - in (noting that km/s is the same as Gm/Ms) ~3200 Ms which, while longer than a typical human lifetime of 2200 Ms (~70 years) or even a long one of 3000, is still within range of a few who'd be lucky. Still rather abysmal though esp. given what I said about this being very idealized as in the previous case.

So I'd say that, yeah, it is probably not feasible to get a space probe going with this route either. Nonetheless, I'm at least a little surprised by how and that is actually something you could perhaps at least see with your eyes that we just might, were we to deem it worthy of spending the money, loft, if not right now then quite sooner than 50 years (1577Ms). Keep in mind that "cool" can, if nothing else, be inspiration for better.

One more angle I'd point out is that in order for the lasers to be really useful, you'd ideally not want to launch this from Earth, but rather from the Moon, because of the atmosphere. Fortunately, a chemical gasdynamic laser is near-ideal for that due to the fact that it contains its own powerplant; the downside is MIRACL was a pretty big thing, and would require a lot of launch capacity to get 100 of them to the Moon. Nonetheless, it could be possible esp. with Elon Musk's BFRs - though that still is "not today".

New Horizons was the fastest man made object in space reaching 16.26 km/s after launch. After gravity assistance 23.3 km/s was reached later.

The speed of light is about 300,000 km/s. 0.001 c is 300 km/s, roughly 20 times the speed of New Horizons and 400 times the kinetic energy. Due to the rocket equation 300 km/s is impossible with present day technology.

The heaviest things we are capable of accelerating to 0.1c today are heavy atoms or small molecules.

You can always strech the definition of "probe", of course.

Is it possible to create a relativistic space probe going at least 0.1c with present day technology?

Of course! A child could do it! A child could do it!

Let's get the logarithms out of the way first. With $$m_f/m_i = 20$$ and ignoring special relativity we'd need an exhaust velocity $$v_E$$ of $$0.1 \ c \ / \ \ln(20) = 0.033 \ c$$.

What energy protons would we need from an ion engine for their velocity to be $$0.033 \ c$$?

$$E = \frac{1}{2} m v^2 = \frac{1}{2} m c^2 \left(\frac{v}{c}\right)^2$$

The mass of a proton $$m_P c^2$$ is about 938 MeV, so the energy would have to be

$$E = \frac{938}{2} 0.033^2 = 0.54 \text{ MeV or } 540 \text{ keV}$$

So if you built a spaceship that was 95% by mass liquid hydrogen and the other 5% were an electric powered low voltage proton RFQ linac or even just a gridded accelerator at 540 keV, you're good to go! You have space to be your vacuum pump and if you are clever the coatings of your resonators can be superconducting to minimize ohmic $$I^2 R$$ losses that copper would produce so you might be able to keep your power fairly low. You'll still need an ion source that makes protons and you'll have to recycle all the unionized hydrogen and protons that can't be bunched into your linac's acceptance if you use one, but them's the breaks.

If your system is having mass efficiency problems (losing hydrogen) then just crank up your RFQ to a few MeV.

See this answer to If specific impulse is directly related to exhaust velocity, would a ion post-accelerator improve the Isp of a propulsion system? for further reading.

Here's a 5 MeV RFQ (that tiny thing on the left) followed by another booster: LIGHT: A Linear Accelerator for Proton Therapy

• @RussellBorogove this is an interesting topic and probably deserves a question or three by itself. Xenon and krypton are used because while they are relatively easy to bottle and because they are relatively easy to ionize and so the robust, maintenance-free ion sources for spacecraft limited by solar power have found easiness-to-ionize worth the loss of Isp. For a given acceleration potential, the theoretical Isp scales with $\sqrt{Q/A}$ where those are the charge and mass of the species being accelerated. Going from xenon to hydrogen would boost Isp by 11.5 times, or to 4He would be 5.7 – uhoh Apr 12 at 3:35