Suppose you were able to build an infinitely high staircase, could you escape earth's gravity at walking pace?

Answer 1

No.

The force of gravity:
F = G*M*m/d^2

G is a constant, always bigger than 0
M mass of Earth (also constant, bigger than 0)
m = your mass (may decrease if you do not bring food; as long as you are alive, m is bigger than 0)
d = distance between you and centre of Earth.

Therefore, F is always positive, although it gets smaller and smaller as you climb away.

If you were to climb very high and jump off, you'd be "weightless", but still affected by gravity: if you do not have enough sideways motion, you fall back to Earth's surface.

If the staircase is rotating with Earth (and let us assume that the rotation does not destroy it), the angular speed of the staircase is the same at all heights (15 degrees per hour); However your actual speed (in km/s) would increase because the circle you trace in 24 hours has a bigger and bigger radius as you climb. You would feel a centrifugal force, "pushing" you away from Earth's centre. Because your angular speed is constant, the centrifugal force varies as the radius (the distance from the centre of Earth).

Then you could arrive at an altitude where the centrifugal force equals the force of gravity. At that step, you'd feel weightless. At the next higher steps, the centrifugal force is slightly bigger AND the gravity is slightly lower. You would feel a net push away from Earth.

At the "magic" point, you could step off the staircase and be in a stable orbit around Earth without touching the staircase. This is the altitude at which we put geostationary satellites (they turn around the Earth at exactly the same rate as the Earth rotation, so they appear stationary). 35,786 km. (At a pace of 1 meter per second -- very fast for such a long climb with space suit -- it would take a little over a year; pack a lunch)

You would still be affected by Earth's gravity: you would fall. However, because of your sideways speed, you would fall down at exactly the same rate as the Earth surface curves down under you, so you always stay at the same distance above Earth's surface: you are in orbit.

PS: You would not burn up. Earth's atmosphere is rotating along with Earth. However, you would have to put up with some very strong high altitude winds. Once you are high enough, you'd get above the ozone layer (no more protection from UV rays). You may also have to dodge a few meteor coming at you at speeds of 20 to 70 km/s.

The thermosphere, where air molecules have very high temperatures, is not really a problem: the density is so low that even if individual molecules are extremely hot, there is not much heat (not enough molecules per cubic metre to cook you).

Then you have to cross the Earth's low orbit levels, with tens of thousands of "things" in orbit, plus lots of smaller junk.

In space, the Sun's flux is 1370 W per square metre (on only one side of your suit). With a proper heat distribution system, you should have no more problems than modern astronauts. Of course, there is all that heat that you produce, climbing at a rate of 1 m/s in a space suit...

Answer 2

Every step you take increases the distance between you and the center of the earths mass. Thus gravity effect gets smaller as you rise.

Your problem will be air. You need air to breath so at walking pace you would suffocate before you reach a point where earths gravity is not sufficient to hold you on the stairs.

Answer 3

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Answer 4

It would only work for a staircase placed on the equator. You would be weightless once you get to geostationary orbit at 22,240 miles. Below that your orbit speed would not be enough to keep you up.

What the staircase is does is to increase your orbital velocity for every step up that you take. This is because the earth is rotating so you move faster the higher that you get.

If the staircase was on the pole then you would need to go many millions of miles further because there is no speed gained with height.

Answer 5

Yes, you can.
Because when you use a sustained effort to escape from earths gravity, and you get far enough, gravity gets so weak, that you can escape from it with the same force that you maintained trough the flight. The Altitude where you can escape gravity, depends of that sustained force, vs. the mass of the space ship

Answer 6

This sounds like a similar concept of the space elevator. See the reference below. I would say yes but you wouldn't need an infinitely high staircase just one that goes into orbit much like the space elevator. This would allow humans to travel into space without rocket propulsion.

Answer 7

If u do so ,u ca'nt completely escape from the gravity ,if u exceed from it there u can't have oxygen to inhale ,if u have arranged all the needs ,u can't build it since if there is no gravity u can't build them since they will fly

Answer 8

Probably not. You'd die of O3 before ever escaping Earth's gravity.

Answer 9

of course!
because you have a stair.
if you don't have a stair, you should exceed the escape velocity of the earth's gravity.

Answer 10

You mean a "SPACE ELEVATOR"? I searched for it in google and found that scientists are thinking of making one...Well, they are kind of started. They are going to finsh it in 2021 or somewhere at that time.