Hello Steemians, As you read the title you might be wondering how much time it will take to travel from pole to pole. before we start we have to take some assumptions.
let start with simplification, that earth has a perfect symmetric sphere and has the same density everywhere and the hole has no air in it because otherwise, the air resistance will cause you to reach terminal velocity which implies to eventually plateau. So putting these assumptions away we can proceed.
Letâs suppose youâre standing next to the super dangerous hole and fall in, so your starting speed is zero meter per second . And like youâd normally experience if you fell into any hole, youâre going to accelerate down. But your acceleration depends on how far you are inside the earth.
See, when you are at the top of the hole, the entire Earth is below you, so youâll experience the same gravitational acceleration as you normally would, 9.8 meters per second squared and youâll start to speed up as you fall. But then, things change. Now, you are inside the hole, so some of the Earth is above you and some of it is below you. And this means that gravitational force pulling you up and down as well at the same time. So your acceleration is going to change. fortunately, we have a different trick that we can use to figure out this easily. Letâs pretend that you are inside a spherical shell with a uniform density. In here, no matter where you are, the gravitational forces from every part of that shell will cancel out.
To actually prove this, youâd need to know a super cool thing called calculus and add up the forces from every single tiny portion of the shell. But to keep this blog from getting too math-heavy, just trust me that this works. Now, as you are falling toward the center, the parts further from the center than you form a spherical shell. And we just said that all of the gravitational forces from that shell will cancel out. So, this means that we can simply pretend that that part of the Earth isnât there, and, instead, youâre standing on the surface of a smaller Earth.
So, as you fall, the Earth basically gets smaller and smaller and your downward acceleration decreases. And once you reach the center, and you wonât experience any acceleration at all. But remember: you are still falling down pretty quickly, so youâll zoom right past the center towards the other side. And from here, instead of the Earth shrinking, itâs getting larger and larger as you fall down, since you are now moving away from the Earthâs center.
And with all that Earth above you, the acceleration will flip directions and will now be pointing up. But since you are still traveling down, this means your velocity will start to slow, eventually reaching zero when you get to the other side of the hole. And if you donât jump out, youâll fall right back in and oscillate back and forth in the hole ... forever. I donât know about you, but I definitely have better things to do with my time. But assuming you only travel through the hole once, using some physics, weâll find that this whole trip will take you around 42 minutes. Not too shabby! How would you want to travel across the world? Leave me a comment to let me know. What did you think of that incredible experience? As always, Donât forget to keep on thinking!đ
