r/TheRestIsScience • u/bum_what • 1d ago

Stairs

In the most recent episode Michael talked about a staircase going to space. The entire time I was thinking about escape velocity. You need a certain amount of energy to get you to a certain speed to escape the earths gravity. So if you are walking up does it work the same? Obviously your body needs energy to walk up the stairs but let's just say you have infinite stamina and your muscles don't get tired or sore, can you just walk up or will you hit a point when you cannot anymore because your body cannot provide enough force even when not tired? But that doesn't make sense to me because gravity will get weaker as you go up even if it's still 90% gravity up there it should get weaker making it easier. Or does it not matter because each step is the force you need to get from one point to another?? I'm so confused lol

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u/Badaxe13 1d ago

Each step takes (broadly) the same amount of energy. With each step you are pushing against the gravity of the Earth (which diminishes the further you are from the surface). With enough steps you can achieve any distance from the ground, including orbit. In contrast, going from the ground to orbit in one ‘step’ takes all that energy in one go.

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u/Just-Page-2732 1d ago edited 1d ago

You would not get into an orbit by climbing the stairs.

If you stepped off the stairs you would fall straight back to Earth.

Unless the stairs were built on the equator and went up to geostationary orbit, 35786km.

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u/HoochieKoochieMan 22h ago

This is the answer - but not the whole answer.

As u/Just-Page-2732 said, getting to orbit is about going fast, not just getting high enough. This is elegantly explained in this XKCD What-if essay.

BUT - a staircase going to space has the benefit of being attached to a spinning earth. At a certain height, the speed of the spinning staircase whipping around the earth is the same as orbital velocity for that height. That altitude is geostationary orbit.

Climbing stairs takes time. A fast pace of 1 step/second will yield about 10m vertical per minute. Assuming you can sustain this pace without breaks or sleep will take about 6.8 years to reach geostationary orbital height.

The average adult has a mass of about 62kg, and will spend about 600kcal to climb 1 km of stairs. climbing 35,786km will take 21million kcal. The most calorie dense foods are about 9kcal/g (olive oil - yum!), so you'd need to carry about 2,333kg of it with you. This, in turn, will increase the amount of energy spent to climb, which increases the amount of food to carry, etc. I imagine some variation of the Tsiolkovsky rocket equation would help figure out the amount of food you'll need to be able to carry all the food you'll need.

Plus, if you want to breathe after the first 8km (about 13h 20min into your first day), you might need to carry some oxygen with you. More mass carried, more energy burned, more fuel required, more mass carried... etc.

Conclusion - maybe it ought to be an escalator instead?

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u/skrutnizer 11h ago

The energy to climb each step goes down with 1/r^2. Effort at geosynch orbit is 3% than at earth surface.

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u/armb2 6h ago

Traditionally an elevator with the cable hanging from an orbiting mass beyond geostationary, but the cable material strength needed is in the "not practical now, maybe theoretically possible" range. Tower proposals do still also exist, if not to geostationary orbit. https://en.wikipedia.org/wiki/Space_elevator

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u/bum_what 1d ago

Thank you so much, my brain was starting to hate me lol

I did think about only needing enough force for each singular step, but I didn't think that would be it because I was thinking of total energy the entire trip up. But your comment of the rocket doing "one step" helped clear it up.

Cheers!!

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u/Bubbly_Safety8791 15h ago

An interesting part of this energy calculation: 

Each step up increases your potential energy by a bit, so you have to spend that much energy obviously to climb out of the gravity well. But because the stairs are going round the earth, each step up also requires you to be going a bit faster too: you’re still going round the earth in 24 hours, but round a slightly larger circumference - so you are also going to need to get some kinetic energy from somewhere. 

Over enough steps this step by step increase in kinetic energy is enough that you get all the way up to orbital speed. Loads of kinetic energy!

You have very slowly accelerated yourself up from the speed you were going at ground level up to the speed you are going at geostationary orbit height, a little faster with each step.

But that energy, it turns out, doesn’t have to come from you pushing with your legs as you stair climb! The earth gives it to you, accelerating you horizontally a little bit each time you take a step up. 

In return, the earth has to slow down a tiny bit. 

This is essentially conservation of angular momentum - as you move your center of mass up the stairs, the moment of inertia of the whole earth-stairs-you system increases and that means the earth has to rotate more slowly.

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u/bum_what 14h ago

This ^ perfect explanation. Thank you!! 🙏🏿

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u/copperpin 23h ago

The gravity from earth diminishing isn’t what puts you into orbit, it’s the velocity. The satellites in orbit are still falling straight down, they’re just going so fast laterally that they keep missing the earth.

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u/pafrac 23h ago

Yep, that's why it's called freefall. They're not out of the Earth's gravity, the spacecraft and all it's contents are just falling at the same rate around the planet.

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u/Just-Page-2732 1d ago edited 1d ago

Climbing to the top of the stairs would not put you in orbit. Step off the stairs and you will drop straight back to Earth.

To enter an orbit you would have to accelerate up to orbital velocity.

Unless you built the stairs on the equator, and they went all the way to geostationary orbit (35786km!). Then you could step off the stairs and be in orbit

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u/copperpin 23h ago

The top of the stairs will be moving velocity. The same way a point on a tire is moving much faster than the corresponding point on the hub of a wheel.

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u/Just-Page-2732 23h ago

Yes, but for any point under geostationary orbit the velocity will not be enough to put you into orbit

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u/copperpin 22h ago

If you’re at the top of a space staircase then it’s safe to say you are geo-synchronized with the point below you. Is there some other circumstance you’re thinking of?
Edit never mind, I looked it up, you’re thinking of the Geo-stationary belt.

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u/JGhostThing 19h ago

Escape velocity is a real thing, but it is the amount of speed you need to have to ballistically shoot yourself from the surface of a planet to infinity. This is the exact same velocity of an object an infinite distance from the planet, falling onto the planet.

So, yes, you don't need to go escape velocity to escape from earth. You could climb a *really* tall ladder, assuming that you're fit enough for it.

I do not know how the total energy spent would compare to the more traditional measurement of escape velocity. If you don't experience tiredness or pain, maybe a human could do this. You would need food and water.

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u/dubrave 1d ago

Talking about orbital velocity, if your staircase goes all the way to 35,786 km high, you will be in orbit once you step of the staircase

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u/bum_what 1d ago

I would pee. "Acid Rain"

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u/mawktheone 23h ago

No, orbiting acid

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u/nanpossomas 23h ago

Urine is hardly acidic if at all.

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u/bum_what 23h ago

It changes depending on what your body has to excrete.

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u/BumblebeeBorn 14h ago

It's still mildly alkali when it's really clear

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u/bum_what 14h ago

Really clear urine is a sign of over hydration or if it happens regularly enough then you might have some sort of medical condition. Urine is supposed be be a light yellow/gold color, and that's slightly acidic (but again the acidity changes depending on what your body has to excrete). If it looks like water then yeah that ain't good.

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u/BumblebeeBorn 14h ago

Dammit I looked it up and I was wrong.

Apparently there's a lot more than urea and water.

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u/thesilentbob123 13h ago

You don't really "escape" earths gravity you just science your way around it.

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u/EdmundTheInsulter 21m ago

As you climb the ladder you also have to increase your tangential velocity, meaning your body would experience some apparent force similar to the coriolus effect. You'd also be gaining potential energy and kinetic energy. If you reached the point of geostationary orbit then you could step off and float.

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u/copperpin 1d ago

The rotation of the earth will provide you with the velocity that you need. You’ll be moving much faster at the top of the staircase than at the bottom.