According to this article freefall speed is anywhere from 120mph to 200mph for a human depending on position, that’s roughly 190-320km/h. The radius of Earth is 6,371 km so you’d be traveling one Earth every 40-60 hours. In 80 years you’d cover between 133 and 224 million kilometers (82-139 million miles), traveling an entire Earth 28 to 47 million times. Interestingly this is still only roughly 10% the radius of the solar system, but it would get you to the moon and back 173 - 291 times. Space is big.
With the parachute open obviously you’re a little slower, this article says 16-32 km/h. That’s close enough we can just divide the other estimates by 10, so you’d travel about 13-22 million km (8-14 million miles) or 1% the radius of the solar system.
There’s a very good chance these numbers are a bit off, rough calculations that I didn’t bother to double-check.
I wonder… How does gravity affect you inside the earth?
In very simple thoughts: You fall down to the middle of the earth and accelerate (ok, friction would get you to the stated terminal velocity) and the decelerate on your way “up” on the other side.
A bit more complicated: But this is just a hole, meaning there’s mass all around us. So this attracts us. But right in the center, we should be attracted by all mass around us in all directions. So I guess it pulls is into the center of mass? Or maybe it cancels all out and there is no gravity?
I dont think the difference in mass from either side makes enough difference to effect your velocity and pull you towards a side.
I think You fall towards the center, pass it, deceleration, reverse, fall back towards the center, decelerate and reverse again, losing momentum each time until you come to float in the center.
The part I wonder is if the earth’s rotation will crash you into the side, depending on where the hole is in relation to its axis. Say your hole was on thw equator- When you jumped, straight down in reference to the earth, you were actually traveling forward at the same speed the ground was moving, ~1000 mph.
As you approach the center, the Earths’ movement in direction tangetial to the equator is 0- from your frame of reference -1kmph. As you approach the other side, its 180° to that direction- now -2000 mph from your frame of reference.
What im curious about, is if this is self correcting; does gravity slow this forward acceleration, then start imparting the opposite force while your on the far side of the earth each time? (Making your path look something like the spokes in a wheel, getting smaller until you stop moving)
Or do you quickly crash into the side of your hole?
That is a really interesting question. The exact acceleration depends on the density profile of the earth. But you are correct there is no gravitational pull in the center of the earth, it cancels out.
This is actually true for every spherically symmetric shell - gravity cancels out everywhere inside the shell. Something probably every physics undergrad had to prove as homework. See https://en.wikipedia.org/wiki/Shell_theorem for more information.
So when calculating gravity you only have to take into account the part of the earth below you, everything above you cancels out (yes the earth is not a perfect sphere but this is a pretty good approximation).
The end result for a large hole through the earth is oscillating around the center and slowing down until you are stuck in the middle. Oh and you would also be melting, it’s still ~6000° C down there.
Yes, in the center of Earth gravity cancels itself out. Even if there’s a huge hole making it asymmetric.
With the parachute open, you’ll fall slower and slower until you barely go past the center and then continue to slow down while you oscillate around it. At 32 km/h, you would need about 3 months to get there, but with all the slowing down you’ll probably stay on the path for a few years.
This is getting well outside my area but my understanding is that if you were approaching the center of the earth gravity would gradually decrease until you have effectively no net pull at the core. This is because the mass above you is still attracting you too so at the core you’re pulled equally in all directions. Using the same principle you’d essentially be free-floating if you found yourself in a hollow “shell” planet, presumably because the pull from whichever area of the shell is close to you is offset by there being more shell pulling you away.
Let’s say, for argument’s sake, that they are falling in “ideal conditions” and it takes the person 2 days to die (they had the shits when they jumped) and a further two days to dry out. With a parachute open they could be falling at about 10mph (or possibly even slower as they lose further moisture!). 4 days at 10mph is 960 miles
The live person is the best person at skydiving to have ever lived, and spends most of the time not in the panels at 350mph (almost at the speed record). 960 miles at 350mph only takes 2.7 hours.
Maybe not so long after all?
My maths could be completely off though - haven’t used it much in years.
You can use the math below and correct the years to be close to 5. But we would end up with a mummy because of the conditions (wind leading to dessication).
Assuming you don’t bring any food, the usual survival times: 3 days without water, 3 weeks without food. So a minimum 3 days… on the other hand, the time to turn into a skeleton would be much, much longer.
Edit: Since I wanted to do some math, it looks like skydiving is about 120mph in free fall and then 20mph with the parachute open. Let’s say you got scared/bored of free falling after an hour and open your chute, that would be 71 hours before dying. So you would have traveled 1,540 miles (assuming earth gravity, wind resistance, etc). Someone who hasn’t pulled their cord would catch up to you after 12 hours, so very much within the “alive” window.
No, then it would have a bottom. For this pit to be truly bottomless (and considering someone died before hitting anything, it appears to be) it has to go on forever in a supernatural way.
I think you can also have a bottomless pit by simply having a large hole that goes all the way through a planet, directly through its center. But then you’d just go back and forth until wind resistance stops you.
I suppose you’re technically correct, as it has two tops, but no bottom. But the positioning of the corpse doesn’t make sense for a body that’s been going back and forth rather than just one direction the whole time.
Now I’m wondering how long a person would have to be falling at parachute speeds to die and become skeletal.
depends on his/her rations
80-120 years
I meant how far, not how long.
According to this article freefall speed is anywhere from 120mph to 200mph for a human depending on position, that’s roughly 190-320km/h. The radius of Earth is 6,371 km so you’d be traveling one Earth every 40-60 hours. In 80 years you’d cover between 133 and 224 million kilometers (82-139 million miles), traveling an entire Earth 28 to 47 million times. Interestingly this is still only roughly 10% the radius of the solar system, but it would get you to the moon and back 173 - 291 times. Space is big.
With the parachute open obviously you’re a little slower, this article says 16-32 km/h. That’s close enough we can just divide the other estimates by 10, so you’d travel about 13-22 million km (8-14 million miles) or 1% the radius of the solar system.
There’s a very good chance these numbers are a bit off, rough calculations that I didn’t bother to double-check.
I wonder… How does gravity affect you inside the earth?
In very simple thoughts: You fall down to the middle of the earth and accelerate (ok, friction would get you to the stated terminal velocity) and the decelerate on your way “up” on the other side.
A bit more complicated: But this is just a hole, meaning there’s mass all around us. So this attracts us. But right in the center, we should be attracted by all mass around us in all directions. So I guess it pulls is into the center of mass? Or maybe it cancels all out and there is no gravity?
I dont think the difference in mass from either side makes enough difference to effect your velocity and pull you towards a side.
I think You fall towards the center, pass it, deceleration, reverse, fall back towards the center, decelerate and reverse again, losing momentum each time until you come to float in the center.
The part I wonder is if the earth’s rotation will crash you into the side, depending on where the hole is in relation to its axis. Say your hole was on thw equator- When you jumped, straight down in reference to the earth, you were actually traveling forward at the same speed the ground was moving, ~1000 mph.
As you approach the center, the Earths’ movement in direction tangetial to the equator is 0- from your frame of reference -1kmph. As you approach the other side, its 180° to that direction- now -2000 mph from your frame of reference.
What im curious about, is if this is self correcting; does gravity slow this forward acceleration, then start imparting the opposite force while your on the far side of the earth each time? (Making your path look something like the spokes in a wheel, getting smaller until you stop moving)
Or do you quickly crash into the side of your hole?
That is a really interesting question. The exact acceleration depends on the density profile of the earth. But you are correct there is no gravitational pull in the center of the earth, it cancels out.
This is actually true for every spherically symmetric shell - gravity cancels out everywhere inside the shell. Something probably every physics undergrad had to prove as homework. See https://en.wikipedia.org/wiki/Shell_theorem for more information.
So when calculating gravity you only have to take into account the part of the earth below you, everything above you cancels out (yes the earth is not a perfect sphere but this is a pretty good approximation).
The end result for a large hole through the earth is oscillating around the center and slowing down until you are stuck in the middle. Oh and you would also be melting, it’s still ~6000° C down there.
Yes, in the center of Earth gravity cancels itself out. Even if there’s a huge hole making it asymmetric.
With the parachute open, you’ll fall slower and slower until you barely go past the center and then continue to slow down while you oscillate around it. At 32 km/h, you would need about 3 months to get there, but with all the slowing down you’ll probably stay on the path for a few years.
This is getting well outside my area but my understanding is that if you were approaching the center of the earth gravity would gradually decrease until you have effectively no net pull at the core. This is because the mass above you is still attracting you too so at the core you’re pulled equally in all directions. Using the same principle you’d essentially be free-floating if you found yourself in a hollow “shell” planet, presumably because the pull from whichever area of the shell is close to you is offset by there being more shell pulling you away.
Or how long the living guy would have to be free falling to catch up with the person who’s a dessicated corpse?
Far longer than his lifetime, I’m sure.
Let’s say, for argument’s sake, that they are falling in “ideal conditions” and it takes the person 2 days to die (they had the shits when they jumped) and a further two days to dry out. With a parachute open they could be falling at about 10mph (or possibly even slower as they lose further moisture!). 4 days at 10mph is 960 miles
The live person is the best person at skydiving to have ever lived, and spends most of the time not in the panels at 350mph (almost at the speed record). 960 miles at 350mph only takes 2.7 hours.
Maybe not so long after all?
My maths could be completely off though - haven’t used it much in years.
That body’s skeletized, which would take a lot longer than 2 days. Would being constantly falling slow down decomposition? Maybe.
You can use the math below and correct the years to be close to 5. But we would end up with a mummy because of the conditions (wind leading to dessication).
Assuming you don’t bring any food, the usual survival times: 3 days without water, 3 weeks without food. So a minimum 3 days… on the other hand, the time to turn into a skeleton would be much, much longer.
Edit: Since I wanted to do some math, it looks like skydiving is about 120mph in free fall and then 20mph with the parachute open. Let’s say you got scared/bored of free falling after an hour and open your chute, that would be 71 hours before dying. So you would have traveled 1,540 miles (assuming earth gravity, wind resistance, etc). Someone who hasn’t pulled their cord would catch up to you after 12 hours, so very much within the “alive” window.
I think it’s literally not possible to fall that long in one direction in an atmosphere. You could do it in space, though.
You could if it’s bottomless!
You would end up coming to a stop and falling in the other direction.
No, then it would have a bottom. For this pit to be truly bottomless (and considering someone died before hitting anything, it appears to be) it has to go on forever in a supernatural way.
I think you can also have a bottomless pit by simply having a large hole that goes all the way through a planet, directly through its center. But then you’d just go back and forth until wind resistance stops you.
I suppose you’re technically correct, as it has two tops, but no bottom. But the positioning of the corpse doesn’t make sense for a body that’s been going back and forth rather than just one direction the whole time.