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Imagine I'm writing a sci fi thriller novel set in the modern day, on a space station orbiting the Moon. The crews are supposed to deliver supplies to a lunar station on the Moon, they board a shuttle docked on the space station and leaves for the lunar surface.

To nobody surprise, I will introduce an emergency situation that could endanger everyone onboard the shuttle while they are at a certain altitude above the lunar surface. I need the crews to suit up on something quite similar to the one our chinese astronaut wears today but fancier, then they must evacuate as the order to ditch the doomed shuttle is issued. Now I just want those wearing red to K.I.A by being crushed from the falling debris as the shuttle disintegrated mid air and some to simply die from hypoxia due to equipment failure. I am wondering at what range of altitudes from the lunar surface should the remaining crews to begin their skydives from the shuttle?

This Goldilock range is very crucial for my story, one red suit panicked and jumped prematurely and died on the spot as he crash landed while another red suit suffered a third degree burnt since the shuttle suddenly exploded and produce a giant fireball and engulf him. I suppose a fall from height within this Goldilock range would allow my story to continue on, a few broken bones and some internal breeding here and there is okay they just need to hit the ground and not die immediate. No exosuit, no mutant, no nano-biotechnology, no magic, no alien, no gravitational anomaly and no superhero landing.

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    $\begingroup$ If the shuttle is falling freely in a vacuum, then it makes little difference when anyone jumps, because they'll hit the ground at the same speed anyway... may as well get out immediately. "shuttle disintegrated mid air", apart from the slightly inappropriate language for the moon, doesn't really give enough clues as to what's happening, though. $\endgroup$ Dec 8, 2023 at 8:19
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    $\begingroup$ "hypoxia due to equipment failure" could of course include the suit rupturing on landing $\endgroup$
    – Chris H
    Dec 8, 2023 at 16:18
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    $\begingroup$ What's the horizontal speed of the shuttle? Note that you can't safely jump out of a speeding car, despite the fact that it's at an altitude of 0m. Falling from height will make you go faster, but if you're already going too fast to survive, that doesn't really matter. $\endgroup$ Dec 8, 2023 at 18:12
  • $\begingroup$ Don't worry: your goldilock range is presumably going to be extremely large, if you allow some people to fall head-first and some people to fall feet-first, because head injuries are easily deadly and feet injuries are easily not deadly. That's for dying from hitting the ground. If we're talking about dying from falling on a pointy item or dying from being crushed under a heavy debris, then you don't need any altitude at all ;-) $\endgroup$
    – Stef
    Dec 8, 2023 at 20:08

7 Answers 7

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The "LD50" for "impact velocity against a hard surface" is around 17 m/s. If we give a small bonus for wearing spacesuits (provide limited armoring) and the fact that the lunar surface may have a little give and dampen the fall, lets bump this up to 20 m/s.

On Earth this is a fall of about 15 meters, which would equate about 120 meters in Lunar gravity.

One complicating factor is that your shuttle presumably isn't stopped in ""midair"" when the people jump out, so you'll need to apply some $\sqrt{a^2+b^2}=c$ to combine the velocity vectors.

This means your final formula is:

$$v_{impact} = \sqrt{3.25 * h_{jump} + v_{horizontal}^2}$$

where $v_{impact}$ should be less than 20 m/s, $h_{jump}$ is the altitude in meters, and $v_{horizontal}$ is the horizontal speed of the shuttle in m/s.

Should be noted that a LD50 means that 50% of people die because of this, however those that are, eg, crippled for life or wouldn't survive without hospital intervention are counted as survivors.

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    $\begingroup$ There are some important factors for and against that probably should be considered as well. People in space are going to be wearing something like 50% their body weight in suit since they're often very picky about "breathing" and "not freezing or boiling". A well-designed suit might protect various joints and spread out or even absorb some of the impact, but I don't think that's a feature in modern suits. $\endgroup$
    – William
    Dec 8, 2023 at 18:31
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    $\begingroup$ The other is that horizontal velocity matters a lot less in terms of the injury from the initial impact. High vertical velocity means you squish, high horizontal velocity means you roll or slide until you hit something. $\endgroup$
    – William
    Dec 8, 2023 at 18:32
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    $\begingroup$ @William True about the horizontal velocity part. I considered adding a fudge factor to reduce its effect, but the Moon isn't flat and it's quite possible that they, for example, hit the wall of a crater, some boulder, or similar. Generally, due to the lack of conventional erosion, I assume the Moon is rather rough. Could be a storytelling point though. Those who jump to Early pancake against a cliff-face while those who time it just right land in a flat area with few rocks where they can slide for quite a bit. $\endgroup$
    – Dragongeek
    Dec 8, 2023 at 21:06
  • $\begingroup$ You may also want to factor in that most astronauts are physically fit specimens and have probably been given some training in how to land safely from a drop from height. That should increase their LD50 chances significantly. $\endgroup$
    – Richard
    Dec 9, 2023 at 0:27
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    $\begingroup$ Also, severe injury on Earth is bad. Severely damaged life support in vacuum is fatal. $\endgroup$
    – Dale M
    Dec 9, 2023 at 11:43
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There's no atmosphere on the moon, so the shuttle isn't gliding.

If all the shuttle thrusters have failed, it will keep going according to whatever speed vector it had, plus acceleration from gravity.

Anybody jumping from the shuttle will inherit the shuttle's speed vector, plus whatever extra speed they get from jumping. Then they will also accelerate downward according to gravity.

In other words, if the thrusters fail while the shuttle is at lethal speed, then anybody jumping from it will splat. You just get to choose if you splat in your seat or as a free floating spaceman.

To have survivors, the accident should happen when the shuttle is at survivable speed, for example hovering over the landing pad preparing to land. Then it loses thrust. Unfortunately, that leaves a lot to be desired regarding drama and foreshadowing, and the scene will be too short.

So perhaps they get some foreshadowing to make them panic and put on the suits, like a propellant leak inside so they have to vent atmosphere before it goes boom, or the shuttle misbehaving in other ways.

Now they're missing some fuel, and they don't know if they have enough deltaV to stop before hitting the ground. It's still leaking, so if they decelerate now it will just take longer before they get down, so more fuel will leak, which means they're even more screwed. The only option is a last second suicide burn.

At this point Redshirt #1 does an EVA to try to fix the leak and gets flung into space. He will splat quite close to the crash site.

Now they reach the landing site and do the suicide burn. Someone who watched too much SpaceX landing videos yells "I know how it ends", jumps off too early, overtakes the decelerating shuttle, and splats right on the landing site.

Meanwhile the shuttle is decelerating, then as it looks like it's gonna make it, it's almost hovering at the altitude mentioned in every other answer... the thrusters puff out. Those who jump off right at this moment should survive, if they jump as hard as they can towards the sides to get far away from the explosion.

Jumping up only means you will fall down from a higher altitude. Jumping down means you gain extra downward speed to break a leg. So really if you have to pick a direction it's gotta be horizontal.

Now of course all the thrusters don't puff out at the same time so the shuttle goes sideways and rotates, and as the pilot frantically tries to save the day one of the thrusters finds some leftover fuel and goes to max, sending it in a spin and away from the lucky guys who jumped at the right moment.

It bumps into a building, then lands on its nose and stays still. At this point the guy who's still strapped in his seat because he'd rather die comfortably says "See? I told you so." Everyone else jumps off. As he unclasps his seat belt, he falls and crashes into the windshield, hitting the cargo hatch release lever. Miraculously, the hatch still works, it opens, bumps against the building, pushes the shuttle and tips it over. It crashes on the ground on top of a fully fueled vehicle, which explodes, blowing up the smartass.

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  • $\begingroup$ The more people that jump off early, the easier it is for the shuttle to decelerate - a selfish person who is more aware of physics than others on the shuttle could try to convince people to yeet early in the hopes or reducing weight enough that they can decelerate to a safe/survivable speed. It'd have to be a very lightweight shuttle for that to matter, but it seems like it could make for interesting fiction. $\endgroup$
    – William
    Dec 8, 2023 at 18:37
  • $\begingroup$ (FWIW, I think this is the most correct answer and should be picked, even though it's basically a frame challenge.) $\endgroup$
    – William
    Dec 8, 2023 at 18:38
  • $\begingroup$ One thing this answer overlooks is that EVA suits are going to have some thrusters of their own. Definitely not enough to make a huge difference, but maybe pushes it over the edge from "certain death" to "probable death" for some lucky astronaut? $\endgroup$
    – Hearth
    Dec 9, 2023 at 3:50
  • $\begingroup$ @Hearth damn, you found a plot hole! That's true, without atmosphere, the ejected astronaut would simply drift slowly and be able to come back... unless he just has magboots and no thrusters, or they do a deorbit burn in a hurry and that's too much deltaV for spacesuit thrusters to catch up... $\endgroup$
    – bobflux
    Dec 9, 2023 at 9:27
  • $\begingroup$ @bobflux - There is no "drifting slowly" when moving at low-altitude orbital speeds, so whether this is relevant or not is very dependent on the descent profile the lander uses. The wiki page for the manned maneuvering unit shows they have 100-250 feet per second (f/s) of delta-v. This page gives an velocity of 5,480 f/s at a 20km orbit. Anything going slower than that will eventually impact the surface... going even faster. $\endgroup$
    – William
    Dec 11, 2023 at 18:48
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It's not the fall that kills you, it's the sudden stop at the end.

That said, if we look at the statistics, we find that free falling from the range between 3 meters (10 feet) and 4.5 meters (15 feet) significantly increases the fatality rate.

Falling from that height on Earth gives an impact velocity between 7.7 m/s and 9.4 m/s. On the Moon, with its reduced gravity, that impact velocity would be achieved when falling from between 18 meters and 27 meters.

Considering that the chances of soft landing of the Moon (splashing in water, impact dampened by vegetation or other obstacles, etc.) are rather slim, and that the crew would be jumping with a non null horizontal speed, which would make the stopping even more energetic, I would trust the Earth statistics to be valid also on the Moon.

More in general, gravity on the Moon is 1/6 than on Earth, so you can take the fall range from Earth and multiply it by 6 to get the equivalent range on the Moon to have the same impact velocity.

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There is no atmosphere. If the shuttle has no thrust, and you jump out of it, the speed you hit the ground will be basically the same regardless of when you jump (or, if you don't jump at all).

The shuttle is trying to land. When in orbit, it is flying around the moon, mostly horizontal to the surface, at a very fast speed. The Lunar Gateway does this somewhat quirky orbit (from the perspective of Earth orbits) that is elongated and not at all circular, as the gravitational attraction of the Earth distorts lunar orbits.

Regardless, your shuttle is landing. We get fictional control over HOW it lands in order to make the story work in a way that makes sense.

I think your best bet is to have the shuttle shed its horizontal velocity first, and land "strait down". This can be described as a matter of near-lunar flight path control: landing shuttles from orbit show up as descending dots, not as lines flying over the surface.

They then fall towards the surface, decelerating to keep velocities reasonable as they go. The lower altitude they thrust the more efficient it is, but also the less safe it is, and if your rocket has constrained thrust rates you might not have time near the surface.

As the shuttle lowers itself, it can have partial engine failure. It no longer has enough thrust to come to a halt before crashing into the ground.

So it could be a matter of working out how much remaining thrust it has, how hard the remaining thrusters can burn, how fast fuel is leaking, and the like to determine the "ideal" time to bail out.

Your space suits may also have small, weak EVA thrusters.

A problem here is that the space shuttle will end up impacting at about the same velocity. And in most impacts, having a shuttle crumple zone around you will increase your chance of survival. For you to impact slower than the shuttle, you need to have more rocket delta-v than the shuttle does when you separate. This is tricky, unless your EVA thrusters are quite strong, or you have something else like that available.

Lunar surface gravity is 1.6 m/s^2 -- and at speeds much over 20 m/s^2 you aren't going to survive. This means you have to bail out under 13 seconds before impact in almost every situation; if you bail out of a stationary object and take more than 13 seconds to hit the ground on the moon, you are really likely going to die.

A final idea would be to take aim for something on the moon that would help you not die. Imagine if there is a plastic membrane surrounding a garden - your plan is to jump, blast a hole in it, then use the expanding air to cushion your fall.

Doing so perfectly would be insanely hard, and missing by a bit would result in you being thrown into orbit (which ... might be better than splatting! You can be rescued from orbit.)

1/3 of an Earth Atmosphere is 30 kPa. If you are hit by 30 kPa for 5 seconds, a 1 m^2 human would be flying at 1 km/s (and have died from the impact). But the point is, there is more than enough oomph in near-earth-atmosphere air to throw a falling astronaut into lunar orbit.

So I'm imagining a precision jump that makes you fly right above a dome, blowing the dome to get a shockwave of air, then using that shockwave of air to knock you back into lunar orbit.

Those that jump early or late ... miss the key moment.

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Your big issue on the Moon is that there is virtually no atmosphere to slow you down, so there is basically no terminal velocity. The higher you start from, the faster you will get, no limit there.

On Earth a skydiver in belly down position (the slowest possible) will reach a terminal velocity of $55\space m/s$ (about $200\space km/h$) after a few seconds.

On the Moon, nothing will stop you from accelerating, and your vertical speed (in $m/s$) when you "land" (crash) will be about $1.79 \times \sqrt{h}$ where $h$ is your initial height in meters, if you start with no speed at all.

The lowest orbital altitudes are around $100\space km$, so even if you ship was midway when your protagonists started their fall (and they were magically standing still relative to the Moon when they did), you would still crash at $400\space m/s$, or $1440\space km/h$. Ouch. Even at $10\space km$ that's still $179\space m/s$, over 3 times terminal velocity on Earth.

If we consider that the terminal velocity on Earth is about the maximum one can possibly survive (there have been such instances, but usually with a lot of mitigating factors, such as snow, vegetation, etc, none of which exist on the Moon), then the corresponding altitude is less than $1000\space m$.

Given the lack of soft surfaces on the moon (yes, it's covered in dust, but as we saw when missions landed there, you don't sink in it as you would in fresh snow, it's a hard surface), it's probably a lot less, on the order of hundreds or even tens of meters. Basically your spacecraft is just about to land.

To make it survivable from higher altitudes you need something to slow down. Again, since there's virtually no atmosphere, anything which uses drag to slow you down (i.e. a parachute or sail) won't be of any use. Your suits would need to be equipped with some other device which is able to counteract gravity during the whole descent (or alternatively, to slow you down before landing). Exactly what type and size/weight that would mean is probably for another question, but I fear this would largely exceed what you could have in some sort of MMU.

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There are so few actual scenarios that would allow anyone to survive as to make this look really quite made up.

Given you are landing on an airless object, you'd want a trajectory with a minimum energy expenditure to get you to zero horizontal and zero vertical velocity at the landing pad. Or as close to zero zero as is reasonable.

There just wouldn't be enough time do do anything like getting in to suits, or even getting to a door to get out in this LD50 window. [remember the max velocity you get LD50 from is about 20m/s]. So your survivability window would begin with your lander stopping all Vel in both directions at 120m and everyone bailing out all at once you fall for about 12 seconds. It ends with when you could get out of the lander with your initial velocity [from the falling, no longer decelerating lander] plus your freefall acceleration rate adding up to 20m/s. So something considerably less than 12 seconds and 120 meters up.

Maybe a better scenario is to have the ship explosion happen, but use automatic escape pods with built in rockets. Some crew get killed in the explosion, some with damaged pods, some not being able to get to safe landing zones, etc. I think that is a much less contrived circumstance.

Orbital mechanics is a bitch!

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EDIT: People are having no fun on a question not tagged or . The default on this Stack is

So, let's up the ante. Terminal Velocity on Earth is 53 m/s. That's the speed (give or take, we'll ignore that) that Ms. Vulović achieved on her descent. L.Dutch's worry about vegitation and snow are irrelevant. At that velocity the apparent solidity of both and thickness of either are irrelevant. But, if you wish to insist they are relevant, then so, too, is the astronaut's space suit. Further, while the surface of the moon is nothing at all like a sponge, it isn't hard as granite, either.

So, simplifying this and having established that a human can survive a 53 m/s descent, we ask ourselves, at what altitude above the surface of the moon would 53 m/s be achieved? Using a free fall calculator we discover that happens at about 870 meters.

Therefore, based on known survivability conditions and actual physics, ignoring both the theortetical value of vegitation and snow vs. space suits, your astronaut's upper limit is 870 meters.

But he/she can still die by tripping on a rock.

This answer assumes a straight descent

Since we're getting into specifics... Orbits only happen when things move and move fast. The proposed Lunar Gateway extraterrestrial space station is planned to use a near-rectilinear halo orbit that also uses an Earth-moon lagrange point. In other words, the shuttle will be a long way away from that space station or the tangential speed of the astronaut would make the rest of this discussion entirely irrelevant (assuming he/she hit the moon in the first place).

But at 870 meters altitude a shuttle will have lost all but the horizontal approach velocity... but that velocity matters, too. Thanks to air resistance, Ms. Vulović couldn't exceed 53 m/s in any direction. Not so your astronaut.

Speaking generally, the approach velocity of an airplane on Earth must be about 1.3X its stall velocity (the speed at which the plane can't sustain flight). For example, small planes often have a stall velocity of 26 m/s and thus an approach velocity (for landing) of about 34 m/s. That's below the 53 m/s known maximum limit, but thanks to no atmosphere on the moon, the aggragate vector velocity exceeds 53 m/s. Except... no air on the moon means no stall velocity. Shuttles will for the sake of efficiency slowly shed tangential velocity to match the surface of the moon and then descend, fighting against gravity, and I've already linked a source that explains the landing velocity of the Apollo missions could have been higher than the 3 m/s they planned on due to the cushion of the lunar surface. (Note that because efficiency demands a gentle transistion from orbital velocity to an approach velocity of 0 m/s there could still be an approach velocity condition that lowers the 870 meter practical limit.) But whether or not you can account for that depends on how you design your shuttles and landing surfaces. They'll have a non-trivial contribution, but for the moment, we must ignore them.

Practical maximum: 870 meters.

Party poopers... 61km sounds so much more impressive.


Your biggest problem is "what's fatal?"

Vesna Vulović holds the world record for surviving the highest fall without a parachute...

10.16 kilometers (6.31 miles).

Other, not so lucky people die from tripping on sidewalks.

Therefore, using Ms. Vulović's experience as a worst-case (best-case?) analysis and given Earth's gravitational acceleration of 9.807 m/s2 vs. the moon's 1.625 m/s2 I'd say...

Anything less than 61 kilometers could be reasonably believed to not be fatal — although the closer you get to 61 km the "luckier" your astronaut would be.

  1. I'm not entirely convinced that a fall from any height to the surface of the moon could be fatal. I'm probably wrong about that, but I seriously doubt the threat.

  2. Then there's the issue that while your mass is hitting the moon, you simply don't have the weight that you would on Earth. Watch those NASA movies of people bouncing along the lunar surface. The astronaut's muscles would be far more capable of absorbing impact energy on the moon than on Earth.

  3. Frankly, how you land is as much or more an issue of survival as how far you fall. Land on your head from almost any height and you're dead. But that begs the question of how much the helmet-to-suit connection can absorb and how much force the suit's shoulder construction can absorb. But, since that's 100% within your control as a worldbuilder, it means so long as the astronaut falls on his/her head, whether or not they die is entirely up to you, the author. But if they don't fall on their head... they probably won't die under any circumstances.

Whether or not they need serious hospitalization after the fall is quite another matter.

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    $\begingroup$ The circumstances which lead to her not being killed by the fall are hardly replicable on the Moon, though: air drag, falling through vegetation on snow. $\endgroup$
    – L.Dutch
    Dec 8, 2023 at 9:08
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    $\begingroup$ This doesn't make much sense. A fall from 61km on the Moon would result in an impact velocity of around 450 m/s (or about 1000mph). At these speeds, the astronauts would be transformed into meat-paste on impact no matter where they hit regardless of how lucky they are. $\endgroup$
    – Dragongeek
    Dec 8, 2023 at 10:32
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    $\begingroup$ On Earth, there's no difference between falling from 10 km or from 500 m, you will reach the same terminal velocity. On the Moon there's no air so no terminal velocity, the higher you start from, the faster you go, and it's not your weight but your speed (or rather your energy, which is based on your speed) which is the issue. $\endgroup$
    – jcaron
    Dec 8, 2023 at 17:14
  • $\begingroup$ @L.Dutch I'll give you air drag... but vegitation and snow? The depth of either comptared to the distance fallen is irrelevant and the compressive capabilities of either compared to the velocity fallen is also irrelevant. Had she hit a pile of hay a half kilometer thick, maybe then... But air drag only means terminal velocity of 53 m/s. But what's irrational is ignoring the rest of the post... maybe it would have been easier to VTC:TSB since there's no distance short enough to guarantee survival. $\endgroup$
    – JBH
    Dec 8, 2023 at 18:43
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    $\begingroup$ I do feel using Vulović as a basis is the most fair, she was an extreme fringe case. I feel that OP is asking moreso for an average, not the most extreme possible case scenario. Especially if they are falling without the protection that Vulović luckily had. $\endgroup$ Dec 8, 2023 at 20:36

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