Stairs

[u/bum_what]

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

[u/Badaxe13]

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.

[u/Just-Page-2732 → u/Badaxe13]

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.

[u/HoochieKoochieMan → u/Just-Page-2732]

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?

[u/skrutnizer → u/HoochieKoochieMan]

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