Not sure if this has been asked before but here goes.
I was thinking about this in relation to a question I had about what would happen if Earth’s gravity shut off. Long story short, the end of the world. Then I started pondering what it would look like: the various fates of those who would float up but be stopped by a ceiling above them (i.e. indoors) versus those who would simply float into the atmosphere. I mean, everyone would die from lack of breathable air, I believe. But some would float away, and others would simply hit the ceiling.
All this leads to a couple of questions. Is there a way to calculate or estimate how many people are located indoors vs. outdoors at a given moment? Or in general, is the number of people indoors at a given moment with a ceiling above them higher than those outdoors with nothing above them but sky? My guess is yes, but beyond that I would have no clue. Lots of people are out and about during the day or have no homes. And how many people are currently driving a car?
I ask these questions to get context to whether in the awful hypothetical of gravity stopping and the world ending, if there would be more people floating away or hitting the ceiling. This is a weird question, but I figured if anyone could enlighten me, you all could.
I think you’ll find that the world’s population is not evenly distributed by longitude. A really hefty fraction of humanity lives between the west edge of India and the eastern edge of Indonesia. But that’s only about 20% of the world’s circumference.
There are more people indoors when it’s night than when it’s noon. So my bet is if gravity switches off when it’s daytime in the India-Indonesia zone, lots more people float away than are trapped by a ceiling.
OTOH, if it’s between 11pm and 3 or 4am local time in the India-Indonesia zone when gravity switches off, so many of those folks are indoors sleeping that it really doesn’t matter how many are indoor vs. outdoor in Europe, Africa, West Asia, or the Americas. The vast number of indoor Asians ensure the majority of humanity doesn’t float past their ceiling.
Also, what keeps the ceiling in place? Mostly gravity, pressing the ceiling into the walls, And the walls? gravity again, pressing into the foundations. And the foundations? Yup, gravity again.
So turn off gravity, and the ceiling will be floating (or flung) out just about as briskly as everything else.
The velocity is not going to be the same everywhere. The closer to the poles, the lower the velocity. To find out how much at your location, multiply the equatorial velocity by the cosine of your latitude. Unfortunately, you have to get pretty close to the pole before the velocity becomes not immediately fatal in a collision. For example, Edmonton, at 53.5° N, still has a velocity of 595 mph. Anchorage, at 61.2° N, has a velocity of 482 mph.
Anyway, if you turn off gravity, the whole Earth is going to fly apart. It may take a little while longer than the loose stuff on the surface is lost, but probably only by a few minutes, if not seconds. There’s a huge amount of pressure in the inside of the Earth that will be released. It’s going to blow.
Some structures may stay in place for a little bit because of the cohesion/friction of the foundation to the soil. But I suspect that wouldn’t last very long. You’d end up floating in your floating house.
This is how I was thinking about it. There is also the seasonal aspect - winter in the northern hemisphere means more people likely indoors during daytime.
And of course, if this effect extends to the sun, then a few minutes later you will be experiencing it going nova. Most likely everyone is dead before that, but maybe the people on ISS simply go flying off faster than the debris from the Earth, and get to watch in horror as the planet dissembles itself beneath them, until the wave of rapidly expanding stellar material from the sun vaporized them.
But it’s gravity holding the soil in place. If the gravity turned off, there would be no more Earth. Everything would go flinging into space, including all of the water, dirt, trees, mountains, etc.
You’d still have a bit of “gravity” from acceleration. The Earth is under a tremendous amount of pressure, materials under substiantal compression due to gravity.
Even without the rotation, turning off gravity would cause the Earth to expand rapidly. It would be less than a full G, but by how much I have no idea how to even begin to calculate. But there would be a downward force of some kind as objects on the surface are accelerated upwards due to the expansion.
As @dtilque correctly says, at the equator the circumferential velocity is ~1000 mph and declines to zero at the poles per the cosine of latitude. But we’re not talking about the earth stopping rotation. So we’re not talking about anyone or anything suddenly going from e.g. 1000mph to zero at the equator or 595mph to zero in Edmonton.
The actual centripetal force due to Earth’s rotation is very, very close to zero. Don’t forget the Earth turns at one rotation per day, which is 1/1440 or about 0.0007 RPM. Yup, seven ten-thousandths of one RPM. Yes, the lever arm is long at ~4000miles radius, but the rotation rate is really, really tiny.
Doing the math in US customary units, the centripetal force on 1 lb is 0.003 lbf.
So when gravity switches off, everyone and everything on the surface is no longer being pulled downwards at 32 ft/sec^2. Instead they’re being accelerated upwards at roughly 0.1 ft/sec^2. So about 0.003G.
That’s a very gentle waft upwards. It’s inexorable, but it’s gentle.
The various later comments about what’s holding the houses onto the ground and what’s holding the interior of the Earth compressed are 100% valid. Maybe the Earth is going to burst pretty spectacularly. But not from centripetal force. but just from the sudden absence of compressive force on the interior.
Or maybe not. I’m not enough of a geophysicist to know, but consider this idea:
Things only rebound if they’re compressed. e.g. Water is nearly incompressible. If you have a vessel filled with water at umpteen hundred thousand psi of pressure and magically disappear the container the water doesn’t explode outwards since it was perfectly happy sitting there under that pressure. The same container full of a gas would see the gas very rapidly expand to a much larger volume. That would be explosive; the water not so much.
I’m going to suggest the interior of the Earth is under tremendous pressure, but I’m not sure how compressed it is. If the answer is “not much” we may not get the Earth bursting as much as bulging a bit. Which would still be mongo violent on a human scale, but it wouldn’t look like it had been hit by the Death Star beam.
Another thought:
We might all be surprised at how well-anchored buildings are to the ground and how well anchored roofs are to buildings. They sure aren’t designed for the sudden cessation of gravity. But they do have to withstand dynamic wind and earthquake loads. Which amount to the various parts needing to be connected together, and connected to the Earth, more strongly than just sitting there.
Something mobile like a car, train, or boat of course will be wafting upwards at the same rate as any occupants.
Interesting and thought-provoking point about submarines.
Initially I was going to say that they cruise underwater in an equilibrium between their weight and their buoyancy. And when weight suddenly disappears the forces would suddenly be unbalanced and they’d pop to the surface like uncontrolled corks. Upon a bit more thought, I realized the buoyant force disappears at the same time gravity does for the same reason. So the net change is zero.
To the degree water is not absolutely 100% incompressible there will be an upward rebound of the ocean of course. Along with the upward rebound of the whole Earth I mentioned before.
While the question was prompted by the concept of gravity being turned off, that’s not the actual question, here. The actual question is just, at any given moment, what proportion of the population has a roof over their heads.
An answer to this can at least be approximated by looking at any single person (such as oneself), and asking how much time that person spends inside vs. outside. It changes seasonally, of course, but even in summer, I’m pretty sure I spend more than half of my time inside, probably even more than half of my waking time (i.e., over two thirds of my total time).
But, how close are you to the average person? Anyone in agriculture or construction is going to spend a lot more time outside. Anyone who drives for a living, whether that be truckers, mail delivery, or DoorDash is going to not have a ceiling over their head through much of the day. That doesn’t count the people in their cars commuting to or from work.
Just kinda doing Fermi estimation in my head, I’d think that at any given time, there are more people in the world that are outside than inside, but it’s probably fairly close, and does depend on what part of the world is in day and what part of the world is in summer when the switch gets flipped.
Here’s an interesting map of geographic population distribution.
Compared to my expectations / recollections the Europe / Africa / Mideast bulge is bigger than I expected. But for sure the India-China-Indonesia-Japan bulge is the lion’s share of humans.
As long as the earth continues to rotate the effect of gravity ending would be very slow. If you were on the equator (say standing on solid rock), while you would be travelling at over 1000 mph so would the ground. Gravity ending would mean you would go in a straight line and the ground would slowly move away from you as it travels in a very large arc. If my maths is right the rate of accelleration from the surface would be about 1 inch per second per second. (about 0.3% of g). Building foundations would easity resist this force so those inside would be retained ceiling though the acceleration would be so low you would be essentially weightless.