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Let's say I have a normal, space-suited human who, for various reasons, must climb a very long, indestructible ladder in space. Air, heat, food, water and waste are already accounted for. What I want to know is what their rate of progress up the ladder will be ? How many kilometers a day can they travel ? How much rest do they need? Also, how long before ambient radiation begins to affect them? How likely are they to be hit by micro-meteors or other space debris ?

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    $\begingroup$ "Climb"? Why not just coast along beside it? $\endgroup$ – JDługosz Dec 11 '15 at 2:00
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    $\begingroup$ The specific location in space will determine the presence of radiation/debris. Is this ladder in deep space, or orbiting a star, or what? $\endgroup$ – DaaaahWhoosh Dec 11 '15 at 2:03
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"The" Assumption

Since your human is in a spacesuit, I will assume the ladder is in a (near) vacuum.

Zero gravity v. microgravity

The use of "zero gravity" versus microgravity—which is the common feeling of "weightlessness" felt by astronauts in orbit—is an important distinction. I will assume you mean microgravity. The gravity they experience is almost as high as on the surface of the Earth, and they are falling! The trick is, they're moving sideways (in orbit) fast enough that they basically fall "around" the Earth. That's kind of an oversimplification, but with the links I've provided, you can get into as much detail as you like.

Now, back to your guy/gal in the space suit.

Acceleration

Since the human doesn't have any gravity to pull them down, or air drag to reduce their velocity, they could, in theory, accelerate to very fast speeds. Each time they push "down" on a ladder rung, the equal-and-opposite force (see Newton's 2nd law) imparts a force on them in the "upward" direction, which is felt as acceleration.

The acceleration in this case is momentary; it lasts only for as long as they are pushing on the ladder in the opposite direction. Think of it like a spaceship firing its maneuvering thruster. That momentary acceleration imparts a permanent increase in velocity (or at least until some other force acts to accelerate them in a different direction).

So in a sense, they're not "climbing" the ladder so much as accelerating themselves along. In real EVAs (spacewalks), astronauts always tether themselves to the frame of what they're working on, so they don't "accelerate" themselves to deep space. So, realistically, safety concerns would probably be the bottleneck. However, there's a way to get those tethers out of the way:

Maybe you build a cylindrical cage around the ladder to obviate the need for tethering. You still have a problem with protrusions on the suit getting caught or sheared off on the way "up" if the velocity is too high, but I'll recommend some high(er) tech solutions for that. (So far, all you need is a decent welder.)

Micro meteors

This risk is very minimal, at least near Earth. If you're talking about another planetary system, I would need to know more to say with certainty. But especially given the cylindrical cage idea, above, most small meteor/debris impacts would impact/deflect/ablate on the cage itself, rather than injuring the astronaut or her suit.

Km/day

This is where I take all of my soft descriptive text and turn it into hard numbers.

A useful equation for acceleration is:

$$a = \frac{\Delta v}{\Delta t}$$

Reasonable values? Let's say your astronaut can grip that rung for 0.5 seconds and push "down". The force he can exert on that would certainly be less than his mass (including suit), but let's say he can manage (50kg, or let's round up to 500N). With some unit conversions and basic algebra, we get:

$$\Delta v = a \cdot \Delta t = 5 m/s^2 \cdot 0.5 s = 2.5 m/s$$

So every time he pushes off a rung, our astronaut's speed increases by $2.5 m/s$. Now there's a limit to how many times he can do that, because at a certain speed, he's more likely to break a finger than actually increase his speed, plus the interval ($\Delta t$) will decrease. Think of this like trying to "speed up" a thrown baseball already in the air.

Thus, it's a little hard to estimate, but let's say, from a standstill in the ladder's reference frame, the astronaut could manage ten good, equal pulls on the ladder. Her speed would increase to a final velocity of $2.5 m/s \cdot 10 = 25 m/s = 90 km/h$, which is a reasonable freeway speed in many cities (and about as fast as I would reasonably like to travel in a narrow tube, in a spacesuit!).

Air, heat, food, water and waste are already accounted for. ... How many kilometers a day can they travel ? How much rest do they need?

Distance: $90 \frac{km}{h} \cdot 24 \frac{h}{day} = 2,160 \frac{km}{day}$

Rest

No more than usual. Those "ten pulls" would be nothing for a trained astronaut. In fact, most terrestrial office workers could pull that off.

Deceleration

At the end of the ladder, the same process must happen in reverse: the astronaut must find a way to decelerate (which simply means acceleration in the opposite direction), so they don't go head-first into a bulkhead at 90 km/h. There are many methods they could use, such as manual (lightly grab the rungs to slow down), or mechanical (the "station" has built-in decelerator flaps near the end that work like a series of nets to gently slow down the astronaut).

High tech options

To keep the astronaut aligned in the center of the tube, you could use strong (electro)magnets in a ring to repulse the astronaut, pushing her into the center of the cylinder. Her suit would also need a magnet (strong earth magnet would do well enough).

Going a step further, you could even use those magnets to accelerate (and decelerate) your astronaut automatically, similar to a coilgun, which would allow for very high speeds (safer, due to the magnetic containment idea, above). If safety is sufficiently addressed, the same daily journey could easily traverse a 3-5 times the distance of a manual launch, however any failure in the magnetics could easily prove fatal.

Rest

No more than usual! With either solution, the manual effort required is minimal (just a few minutes of work), and only related to stopping and starting the journey.

Radiation

I'm not exactly sure where your ladder will be located (it makes a big difference), but for reference, have a look at the Health Threat from Cosmic Rays on Wikipedia; it has some charts that compare the levels with mean sea level dose, with durations listed. You might have to do a little arithmetic to make it relevant to your story, but you can always ask another question if you run into any uncertainty there.

Conclusion

I believe I've hit all of your sub-questions as accurately as I possibly can. My goal here (as with many of my answers) is not only to give you the specific answers you're looking for, but provide a little bit of the background information so you can understand the basics a little better, and be able to adapt them as needed to fit your story/work.

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  • $\begingroup$ This is great! Very thorough and quick answer. May I ask about an alternate scenario? What if the ladder was tethered to the Earth and continued until geosynchronus orbit ? (assume that there's a platform at the top with a counterweight on the other side for balance.) What is the climbing speed then? Would it change if there were some type of device (insert handwavium tech here) that reduced the climber's relative weight to zero? $\endgroup$ – mytallest1970 Dec 11 '15 at 4:37
  • $\begingroup$ @mytallest1970 You may be interested in Couldn't I escape Earth's gravity traveling only 1 mph? on Space Exploration. $\endgroup$ – a CVn Dec 11 '15 at 12:29
  • $\begingroup$ We know that the ladder is indestructible, but we don't know what it is attached to. Again Newton's second law of motion say that for every action there is an equal and opposite reaction. When you push down on the ladder to "climb" it, there must be something arresting the ladder's downward momentum, or you end up wondering, as it was once so eloquently put, at what time Oxford stops at the train. (I think that was in reference to Einstein's theory of relativity, but it works here, too.) $\endgroup$ – a CVn Dec 11 '15 at 12:32
  • $\begingroup$ @mytallest1970 That scenario is completely different, since you are now climbing an ordinary ladder on the Earth's surface, with familiar gravity. When you include life support (as specified in the question), suits are commonly in the 100kg range. GSO/GEO orbit is a 42164km - 6371km = 35793km climb. I think you'd be hard-pressed to find anyone who could make that climb with 100kg of dead weight. For the first 200km or so, gravity is at least 90% of that on the surface. There are other problems, too. Post a new question with specifics if you want to see math/sources. Look up "Space Elevator". $\endgroup$ – type_outcast Dec 11 '15 at 13:05
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Type_outcast has really explained the crux of the matter. Here I would comment on a few flaws in the environment presented in the question.

In open space (as in, with no artificial gravity) there is no (negligible) gravity so the very idea of building a "ladder" is questionable. You can achieve the same results with simply having one metal pole of 3-4 inch diameter. The rungs would actually make it harder for the astronaut to traverse through because it would make it hard for him/her to tether to the ladder while moving along it. If you have one really long, smooth metallic pipe, the astronaut can easily build a loose curl with his/her rope and attach firmly to the pole without any hindrance to motion. You only need to hold the pipe once and push it down to get yourself moving upwards forever. Do it a few more times and you would be moving at a car's speed on a highway. I would not go into details as that has been sufficiently explained by Type_outcast.

Rest? None is required, really. Since your astronaut is going on a free trip, all his/her time is rest already.

I cannot say anything about the probability of getting hit by a meteor, since it really depends on your settings. If your dude/girl is going anywhere between mars and Jupiter, good luck is all that could save him/her. However if he is going between Earth and Venus, there would be other concerns (heat) to attend to, instead of meteors. One important thing to notice about meteors is that the damage done does not only depend on the speed of the falling meteor, but also on the speed of the astronaut. It is the relative speed of the two (alongwith their masses) which determines the damage done.

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The type_outcast estimate breaks at the very first assumption that the astronaut may grip the ladder for half a second. On the contrary, faster you go, less time you have to accelerate. The ultimate speed is limited precisely by how fast you can move your limbs.

Some data indicate that a world class boxer delivers a punch at 11 to 14 mps while an average person may reach 7 mps. In a space suite I guess 5 mps (i.e about 10 miles per hour) is the best one can hope for.

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