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This question was inspired by the one here:

Is there a self-rounding celestial body from which an Olympian could jump into space?

regarding the, apparently shown infeasible, idea of jumping off what was determined to be Saturn's tiny moon Mimas (~400 km diameter, 0.04 Yg mass), solely under one's own human power, because the escape velocity from that moon is about 153 m/s.

Which made me start wondering - if not by jumping, could it be possible to do this with a rocket pack, that is small enough to carry on your person, perhaps along with your air tank? How small, and how feasible would it be, to engineer such a rocket pack for this job?

Going the other way, what would be the largest body you could escape from using a rocket pack small enough to carry on your person and buildable with today's technology?

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Not only could it be done, but you could in fact get the hardware right now.

Behold, the RB2000 rocket belt: Rocket belt

We can work out the probable $\Delta_v$ of the rocket via the good old rocket equation:

$$\Delta_v = g_0 \cdot I_{sp} \cdot \ln \left( \frac{M}{M_e} \right)$$

Where $g_0$ is a standard gravity, $M$ is the fully fuelled mass of the rocket and $M_e$ is its dry mass. High-test peroxide monopropellant has an Isp of ~140 seconds. Given a desired $\Delta_v$ of 153m/s to escape Mimas, you'd need a mass ratio of ~1.12.

If the rocket belt weighs 60kg (wikipedia says "equipped" so lets assume that's the wet mass) and it has 23l of peroxide fuel, the dry mass of the rocket alone would be 26.65kg. An average human is ~62kg. A fancy lightweight spacesuit might be 40kg (this is perhaps a little optimistic). This would give a fully dressed and fuelled up weight of 162kg, and a dry mass of 128.65kg. That gives you a mass ratio of ~1.26 and a $\Delta_v$ of 316m/s... more than enough (which is good, because I'm ignoring complications like gravity drag as being too much like hard work).

Obviously the RB2000 as it stands wouldn't work in a vacuum, but clearly it has enough thrust to do the job (it works on Earth) and more than enough fuel, and there's still plenty of scope for adding additional fuel tanks if needs be.


For the second part of your question, you can work out the size of a spherical body with a given escape velocity $v_e$ and density $\rho$ by fiddling with the simple escape velocity equation like this:

$$\frac{M}{r} = \frac{v_e^2}{2G}$$ $$M = \frac{4}{3}\pi r^3 \rho$$ $$r^2 = \frac{3v_e^2}{8\pi G \rho}$$

Where $v_e$ is escape velocity. With density similar to Mimas (1.15g/cm3) and an escape velocity of the rocket belt's $\Delta_v$ of 316m/s, you'll get a radius of about 394km, which is coincidentally about twice that of Mimas, and a mass of about 2.95x1020kg.

Obviously on such a small world the surface gravity will be lower (its about 0.013g) so you'd be able to carry a much heavier rocket which in turn would help you lift off from a larger body, but its hard to pin down precisely what counts as "a rocket pack small enough to carry on your person", as Hohmannfan's comment showed. A limit purely by weight $W_l$ gives rise to this inequality in terms of radius $r$ and density $\rho$:

$$\sqrt{\frac{8\pi G \rho r^2}{3}} < g_0 \cdot I_{sp} \cdot \ln \left( \frac{3W_l}{4\pi G \rho rM_e} \right)$$

which I shan't attempt to simplify. A weight limit of 1000N (and neglecting any increase in fuel tank mass, which is obviously lazy and wrong) will give you enough delta-V (2440m/s) to escape from Europa (surface escape velocity ~2025m/s) and a mass ratio of ~5.77, which is about ~423l of fuel... dubiously "small enough", but should give you a rough upper limit. The Moon is just a bit too hefty to escape from with this weight limit, but all smaller bodies with no atmosphere would seem fair game.

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  • $\begingroup$ why wouldn't it work in a vacuum? $\endgroup$ – JCRM Jan 25 at 12:06
  • $\begingroup$ @JCRM for the same reason that any other bit of kit built for use in a temperature atmosphere wouldn't work in a vacuum? $\endgroup$ – Starfish Prime Jan 25 at 12:08
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    $\begingroup$ such as? pressure fed peroxide thrusters have been used in a vacuum (I'm not saying it would work, just that the reasons for it not doing so are not obvious) $\endgroup$ – JCRM Jan 25 at 12:10
  • $\begingroup$ @JCRM did you read the actual sentence I wrote? Let me repeat it for you. "Obviously the RB2000 as it stands wouldn't work in a vacuum". I've emphasised a bit you may have missed. Also, in my last comment, "kit built for use in a temperature atmosphere wouldn't work in a vacuum" is really, quite clearly, not the same as using equipment designed for use in a vacuum, is it? $\endgroup$ – Starfish Prime Jan 25 at 12:11
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    $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – called2voyage Jan 25 at 17:56

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