I wonder whether it is impossible. How can I be launched into space without using a rocket? If the planet has some super volcanoes, can a volcanic eruption be used to launch a vehicle into space? How can a vehicle launched into space survive the volcano?
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2What technology level is available? Is the vehicle supposed to carry humans or intricate machinery? – Oct 13 '16 at 11:42
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2We have today the technology to build rockets, but not to survive volcanic eruptions. Why is a volcano more practical in this case? – kingledion Oct 13 '16 at 11:44
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1@ZhuPeng - This question has a few answers with votes from users. Removing the content of your opening question destroys the question for anyone in future who might have the same question as you. If you wish to resolve this question, please mark your preferred answer with the "tick" to show it answered your question. – Feb 22 '17 at 09:09
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Rockets aren't modern technology... – Durakken Feb 22 '17 at 09:13
3 Answers
It's extremely difficult, but somewhat plausible
(That's a very, very cautious "yes"). There are many challenges, not the least of which is building a tube angled into the sky some 416km in length, capable of sustaining a massive amount of energy from a volcanic eruption. I have serious doubts as to whether this could work, but it might work.
Reaching escape velocity
Mars has an escape velocity of 5.0 km/s. You didn't specify a size or mass of your spacecraft, but for argument's sake, we'll go with 25 tonnes (close to the mass of the STS (Space Shuttle)). The space shuttle had a sustained acceleration of around $30 m/s^2$. That gives us a force of $F = ma = 25\,000\text{kg} \times 30 \text{m/s}^2 = 750 \text{kN}$.
Now, at 30 m/s/s, how long does it take to reach escape velocity? That's simply $\frac{5.0 \text{km/s}}{30 \text{m/s}^2} = 166.\bar6 \text{s}$.
A very, very long barrel
Next, your volcano's blast energy would need to be directed and focused, so some kind of launch tube (like a gun barrel) would be required. How long would that barrel need to be? That length is $s$ in the following equation:
$$s = \frac{1}{2}at^2 = 30 \text{m/s}^2 \times (166.\bar6 \text{s})^2 = 416\,333\text{m}$$
Thus you would need a tube some $416 \text{km}$ in length, and it would need to be angled, because "going to space" really means going sideways very fast. That is a very, very huge engineering task, especially if it needs to contain a blast with the energy of a volcano.
Given the difficulties of creating a "simple" space elevator, I have my doubts as to whether you would be able to come up with strong enough materials for this tube, but since it doesn't need to support its own weight, that's why I'm not giving this an outright "no", but I'm still highly skeptical.
Energy Requirements
How much energy are we talking about?
The launch requires $750 \text{kN} \times 416\,333\text{m} = 3.12 \times 10^{11} \text{J}$. Obviously you would need a little more than that because the energy transfer will not be 100% efficient. Volcanic eruptions vary greatly, but Krakatoa released $8 \times 10^{17} \text{J}$, although it destroyed most of the island around itself in the process. However, since that's around a million times more energy than you need, it is at least plausible that there would be enough energy for launch with much smaller eruptions.
Survival
This will be difficult.
First, you will need a heat shield (or some kind of buffer/insulated sabot), but more importantly, you will need some way to regulate the eruption itself. Perhaps you can have some kind of valve or muzzle brake to vent excess gases.
Building the tube some distance from the volcano would probably help; that would give you some protection from the most extreme heat and larger projectiles from the eruption. Add in some heavy duty screening at the tube entrance to catch as many of the smaller projectiles as possible.
Without knowing a great deal more about your spacecraft design, it's hard to predict how feasible this will be, but there's nothing intrinsically impossible about the idea.
Predicting Eruptions is Hard
There is some speculation that Mars is still volcanically active, but we haven't seen any recent eruptions.
But since you are merely talking about a Mars-like planet, then the above doesn't matter—just be careful have a planet with active volcanoes. However, predicting eruptions is difficult to say the least (almost certainly harder than inventing rockets), and scheduling launch dates around essentially random natural events would be problematic.

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1It sounds like by the time you have the infrastructure to build a non-rocket solution, you could just build a rocket. – Azuaron Oct 13 '16 at 14:36
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1@Azuaron Pretty much that was my thinking as well. However, the question is pretty adamant about the no rockets rule, so I went with it. – type_outcast Oct 13 '16 at 20:08
You'd better take Io instead of Mars. Io jets materials up to 500 km into space; the Lagrangian point between Io and Jupiter is, presumably, 8000 km above Io's surface. If you teak the sizes of planets (lighter Io, heavier Jupiter, smaller distance between them), volcanic debris could probably end on Io's or Jupiter's orbit.
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1Heh, and then what? Die in the vacuum of space? Die by radiation from jupiter? Die by falling back down into a volcano? Not a lot of options :p – Innovine Oct 13 '16 at 14:18
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3@Innovine, the question is merely about escape. Without rockets, they couldn't navigate the space at all, so, yes, the crew is doomed in any case. Io and Jupier have heavy radiation, yes, but the planets have to be changed to allow eruptions reach L1 anyway. And the entire point of being on the orbit is that you won't fall back onto the planet. – Oct 13 '16 at 17:56
You would need a vehicle of some sort to protect and manoeuvre yourself while in space don't you? If you were able to build yourself a capsule of some sort that could survive the extremes of space, it would also be tough enough to survive small volcanic forces.
I think you're on the right track with the idea of using another option to propel yourself into space, but I don't think you'll realistically and reliably get far with a volcano! There's far too many "if's" and "buts".
On the propulsion idea, the first thing that occurred to me was to build yourself a gigantic gun that could fire a capsule into space. The bad points on this is that the capsule itself would have to be strong enough to survive terrific forces, the pressure, heat, shock etc. However this wouldn't necessarily involve the use of tech, you just need a gigantic stick of dynamite or similar explosive.
Although the use of a rail-gun or coil-gun to propel a capsule into space would involve some tech, there's a possibility that they could be fashioned from elements on the planet itself - use mineral deposits for the power source, etc. If these options are possible, they are more realistic, and the forces can be controlled and governed. There isn't so much shock as using an explosion to propel you into space, but both options can be scaled up to do what you want.
You either have to be propelled into space, or you need to propel yourself. I think the second option could only realistically work with a rocket, or similar. Using a lighter than the atmosphere craft (a balloon of some kind) occured to me, but I wouldn't think you could reach outer space with this.

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Sorry just re-read the question and realised the title states no tech tools, so I'm guessing a coilgun / railgun would fall outside of this. Failing that, I guess you will need to use a skyhook. :) – AutoBaker Oct 13 '16 at 11:52
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1Space sucks. Pretty literally, pressure inside is higher than outside. Volcano pushes. Space is cold and thermally insulating. Lava is hot and conducts heat relatively well. First paragraph is very wrong, because hazards are opposite, and solutions different. – Mołot Oct 13 '16 at 21:49
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Christopher priest's SF novel THE SPACE MACHINE: A Scientific Romance (1976), combines elements of HG Wells' THE TIME MACHINE and WAR OF THE WORLDS in a scientific romance hommage/pastiche. It has Wellsian Martians launching their invasion vehicles using a gigantic space gun. Priest had had the calculations done to demonstrate that the passengers launched into space via space guns fired on Mars could survivable. Your answer's fine. Just leave out rockets. Plus one from this little black duck. – a4android Oct 14 '16 at 04:08
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@Mołot - both volcano and space would put massive pressure on the vessel - and if the vessel is strong enough not to explode in space, it'll be strong enough not to explode in a volcano. If it can survive the stresses and friction of exiting the atmosphere, it should survive the heat of a volcano. If it needs to be insulated from heat in a volcano, the same insulation will also insulate it from cold in space. So yes, as you say, the hazards may be opposite, but they can be reduced in similar ways. – AutoBaker Oct 14 '16 at 11:41
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@Tomy-rex you're so wrong. Imagine brick arc. Pushing from above does nothing to it. Push from below, and it'll break easily. "strong enough" is not direction independent! – Mołot Oct 14 '16 at 12:22
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@Mołot Yes I do understand what you mean. However, in both cases the pressure will be forcing the capsule to explode, and not implode. The vacuum in space will mean the pressure inside the capsule will try and force it's way out, and as heat expands, the heat of a volcano would also make the capsule explode, as the pressure is trying to force it's way out. However, if you had a spherical capsule (the strongest pressure-resistant shape there is), it will implode and explode at equivalent pressures as the pressure is equal on all surfaces - in your example the pressure is not applied equally. – AutoBaker Oct 14 '16 at 13:08