*Clarification 1:* Some of you seem to be confusing weight with _apparent_ weight. This is understandable since apparent weight is often referred to as just "weight," especially in engineering. Astronauts in space are not weightless. Objects in free fall are not weightless. They just don't have _apparent_ weight. *Clarification 2:* The two sections of the Earth at 7:14 cancel each other's effects because of a balance between mass and distance. The bottom section might be more massive, but it's _also_ farther away from my clone. The top section is less massive, but closer to my clone. It's just the right amount to make the forces the same no matter how deep the hole is. Kind of cool, huh?

@jamesweeks9583

4 жыл бұрын

So, those two clones in space... if they were completely without motion, is there any movement they could make to start moving? Basically if you were still in space is there any arm or leg movement that could get you moving?

@ScienceAsylum

4 жыл бұрын

@@jamesweeks9583 No. They can twist and contort their bodies, but the best they'll ever be able to do is turn. The only way their _center of mass_ will ever move is from an external force (a force from outside them)... like the gravity exerted by the other clone. Without that external force, they're stuck in place forever. Other examples of external forces would be some kind of rocket pack or simply throwing something opposite the direction you want to move.

@Alexagrigorieff

4 жыл бұрын

Did you mean to pin this comment? Also, Einstein's General Relativity says that it's not possible to distinguish what you call "apparent weight" from just "weight".

@TiagoTiagoT

4 жыл бұрын

@@jamesweeks9583 They could throw their clothes away, or maybe spit (or other forms of ejection of bodily waste)

@ScienceAsylum

4 жыл бұрын

@@Alexagrigorieff I did. KZread has been randomly _unpinning_ my comments. I don't know why. It's happened on several other videos over the last couple days.

The image of the Earth red shifted while morphing into a tiny black hole... crazy attention to details 👏

@meestyouyouestme3753

2 жыл бұрын

You have the crazy “attention” to details… Nick has the crazy details.

I laughed at the clone repeatedly catching fire while falling because I am a terrible person.

@PhilipSmolen

4 жыл бұрын

I laughed as he kept throwing clones in holes.

@thenasadude6878

4 жыл бұрын

6371 km in 20 minutes of acceleration means a top speed of 40250 km per hour, or 25000 mph You can bet he's on fire

@AlleyKatt

4 жыл бұрын

The clone in the hole burnt to ash. So I guess that was the ash hole clone.

@captainobvious.29yearsago70

4 жыл бұрын

@@AlleyKatt I know that guy sucks

@burnerjack01

4 жыл бұрын

You are a wonderful person. Anton Petrov says so.

"There is an art, it says, or rather, a knack to flying. The knack lies in learning how to throw yourself at the ground and miss."

@Ciekawostkioporanku

4 жыл бұрын

42.

@johnclark8359

4 жыл бұрын

What if the tunnel isn't straight but is a cycloid?

@tom_something

4 жыл бұрын

@@johnclark8359 then you have to say "Weeee!" the whole time. State law.

@tom_something

4 жыл бұрын

@@johnclark8359 I think you're asking if the trip time is still the same. I only know one very blunt approach to that question, and it's not a very good one, so hopefully a more mathy person can do the real work. That doesn't mean we can't have fun. According to one video I just looked up, the arc length of a cycloid is equal to eight times its radius. So to make things more fun, let's say we're not even limited to a cycloid that is entirely underground. So we increase its radius so much that its path takes us away from the surface of Earth and then hopefully back. I guess at that point our tunnel is more of a pipe. Two facts arise from this: 1. If the tunnel leads away from the surface of the planet, gravity will not compel us to move in the correct direction from our starting point. 2. If there is no limit to the radius, there is no limit to the length of the tunnel, since it's just 8 times the radius. So that's the distance, right? Or maybe two of those are the distance, since we have to get back to our starting point. What happens if we take "distance equals rate multiplied by time", plug a really really high number in for distance, and hold time at 40 minutes? Eventually, your average speed would be greater than the speed of light. But even before that, your peak speed reaches the speed of light. Since that can't happen, it must not be true that my really long tunnel you weren't asking about anyway could get you to the other side in just 40 minutes. At least not if you're being observed by someone who is standing on the surface of Earth watching this happen. But perhaps you, the traveler, would observe the trip to only take 40 minutes. Relativity and stuff. Maybe that's the 40 minute figure. It's for the traveler. Unlikely, though, as my really long pipe takes you super far from Earth for a while, and it's a highly eccentric orbit, meaning at some point you're out really far and barely moving at all. It would be hard to make up for that.

@dinamosflams

4 жыл бұрын

2:00 kudos to science asylum for trying to solve the equation symbolically for 4 hours 👏

@crouchingtigerhiddenadam1352

4 жыл бұрын

I also use computers to do my calculations. Elsie, Sally, Gladis and Mavis have been doing it for many years! They also make a good cup of tea and bake nice cakes.

@oniruddhoalam2039

4 жыл бұрын

@@crouchingtigerhiddenadam1352 Who are they?

@TheReligiousAtheists

4 жыл бұрын

It's a really easy one to solve, actually. You can just write d²r/dt² as v•dv/dr (where v = dr/dt) and then solve for v wrt r. Once you do that, you have a 1st order differential equation for r wrt t, and it's easily solvable by simply seperating the variables.

@noether9447

4 жыл бұрын

@@TheReligiousAtheists the thing is that is just a trick. You have to solve a similar d.e. before to know to use it(unless you are a genius). Computers don't need to do the same.

@TheReligiousAtheists

4 жыл бұрын

@@noether9447 It's actually a pretty standard trick in solving higher order DEs. The harmonic oscillator equation comes by solving a similar DE using the same trick, so it should be pretty well-known to a professional physicist like Nick

"It's the ability to imagine one type of problem as a completely different problem." Oh cool I'm really good at that! "An easier problem." Aww nuts.

@ScienceAsylum

4 жыл бұрын

😂

@tom_something

4 жыл бұрын

@Phoenix I think it's reasonable to assume that air resistance is not part of this theoretical exercise. Because the other issue is, unless it's a diameter tunnel (straight line through the core), gravity is going to pull the falling body against the wall of the tunnel, and we'd have to factor in the friction from that. Plus, he's using the same model for the Earth tunnel as for bodies in the vacuum of space.

@tom_something

4 жыл бұрын

@Phoenix maybe if you're tossed imperfectly down a tunnel that goes straight though the core. But if the tunnel is off-center, you'd roll instead. It would feel like the tunnel is at an incline, because from a flatworld perspective, it is. That means your acceleration due to gravity would be attenuated by your moment of inertia.

@tom_something

4 жыл бұрын

@Phoenix another point for "no air resistance". It only holds us back.

@tom_something

4 жыл бұрын

@Phoenix I can see the argument for that, but at the same time, does anyone really ever want to have a discussion on semantics? It seems like one of those things that a conversation _accidentally_ turns into, with no one actually intending it to happen. All we'd have to say is that the tunnel is frictionless and evacuated of all air, and other gasses and perfectly sealed off from any other materials that may turn into gasses at low enough pressure, and it's a physics problem again.

"In Physics, sometimes it's helpful to imagine one problem as a completely different problem." And you say _mathematicians_ are the ones who like to generalize things to death? 😁

So the answer is 42? Where have I heard that before?😉

@steveschumann4329

4 жыл бұрын

CG Account so deepthought was right!

@danbhakta

4 жыл бұрын

It should be 42 on all the planets.

@hit3894

4 жыл бұрын

Hitchhikers guide to Galaxy

@hannabaal150

4 жыл бұрын

@@hit3894 Finally! Thanks for all the fish!

@theundead1600

4 жыл бұрын

Pangalatic gargleblaster anyone?

LOl. Clone bursting into flames every time he passes through the core. Nice touch!

Hey Nick, 1) Thank you for still giving us content during the rest of the insanity of the outside world 2) At each step in my path as a physics student, I keep learning news ways of "we can't solve this, so we approximate it or use a nifty trick". It was nice to see this one.

@ScienceAsylum

4 жыл бұрын

Happy to help 😊

9:35 I appreciate that idea the most from studying physics. That there are so many phenomena in physics that mathematically are described in exactly the same way. Like voltage and pressure. Flow and current. Etc. Really helps me to understand physics.

@noether9447

4 жыл бұрын

Flow and current have such similar behaviour because they are described by the same piece of mathematics. Statistics.

@XEinstein

4 жыл бұрын

@@noether9447 I think it's the other way around the physical phenomenon of current on a macro scale is the same as flow on a macro scale and because of that described by the same mathematics. Supper zoom 😉 to microscopic level though and the behavior of an electron in a wire is very different than the behavior of a molecule in a pipe. For example electrons don't experience turbulence, so the analogy flow and current only works on macro level.

@flamencoprof

4 жыл бұрын

@@noether9447 Don't forget Traffic :-)

@kenlogsdon7095

3 жыл бұрын

@@noether9447 Flow and current have such similar behavior because they both amount to the same underlying phenomenon: electrostatic repulsion.

@BigPerm6999

2 жыл бұрын

dependant on mathematics but has systems that are mathematically impossible! We do ok at describing things and making predictions but we cant explain nothing and have no clue whats going on! :D

a great explanation for a tough problem

@8600esemusa

3 жыл бұрын

If a hole is drilled through the earth which on its own is impossible ,, objects or mass cannot pass through it period dumb guy .

@solapowsj25

3 жыл бұрын

Yup😊

@RealZynexx

2 жыл бұрын

@@8600esemusa speak English buddy

Your idea of rethinking a problem as a different, easier problem really resonates with me. I’ve written computer software for many years, and taught many people how to do it. I tell everyone that one sure sign of a great software developer is judicious laziness. Thanks for your excellent videos 🙏

@adreanmarantz2103

2 жыл бұрын

I've often said 'you want to find the easiest way to do something? Get a lazy person'

@ChrisLee-yr7tz

Жыл бұрын

@@adreanmarantz2103 "I choose a lazy person to do a hard job. Because a lazy person will find an easy way to do it." - Bill Gates

8:16 I loved that: some constant stuff multiplied by... Physics teachers should use that sentence all the time.

the more i watch your videos, the more i get into phyiscs, this is my first time visualizing a 2 particle attraction as a ellipitical orbit problem and later using the earlier one as the special case of 2nd...that was awesome, love your videos, great work sir

I'm an out of the box thinker and sometimes I completely forget about the box, this might be a problem. Great video! This is an amazing way to visualize the falling through earth problem.

That orbital one is really a great idea I have generally used the SHM method for periodic motion under gravity Great video as always Please continue making more

Man, I find your show amazing! The presentation style, the depth and the imagination are all really well balanced. Thanks for making us smarter ya crazy. And lot's of luck on your journey through space.

I am a highschool science student, here we are asked these kind of questions very frequently and the spring system helps reimagine countless situations which would otherwise be unsolvable, maybe you can make a video about simple harmonic motion and its practical applications!

@dboy6400

3 жыл бұрын

Eddie Van Halen got famous by using harmonic motion.

@geraldfrost4710

2 жыл бұрын

Simple harmonic oskalator. Often studied as a free-body.

Glad I found this channel! I'm wandering through the old material, and really enjoying it!

Great explnations, that's why I like you videos so much. In many cases, I know the physics beforehand but still get a lot by the way you explain and give the physics better context. Thanks man! 👌

This is the best KZread channel that explains physics from very basic level.

During my EM lectures our lecturer told us to not think outside the box. That's too hard to solve. Think outside the sphere!

@Lucky10279

4 жыл бұрын

😆

And this is exactly why I love this channel, all about change of perspective in physics!

I've been watching these videos for a couple of years, now; and, this is my favorite, so far.

Hey, Can you please do videos on the following topics 1. Temperatures below absolute zero 2. Gravitational waves property. If they travel at light speed, do they have other similar properties like reflection, refraction, diffraction, doppler shift polarization. What is their wavelength range? does special relativity apply to it? 3. Collapsing an air bubble with sound underneath a liquid surface 4. Doppler Shift on a single photon

@rbkstudios2923

4 жыл бұрын

I knew that But I wrote it because I have seen it on the Internet Don't believe me, Google It

@rbkstudios2923

4 жыл бұрын

Seriously Nick😒 Why didn't you heart my comment? I think you should make a hearty clone for that one

Clone catching fire near centre of earth, Earth turning into a black hole when it is imagined a point mass, there little details are so cool!

I have thought of this falling through the Earth problem abt 10 years ago as a kind of simple harmonic motion, I'm glad today 10yrs later someone confirmed it.

Congratulations man, this is your best video so far, very professional stuff. I start to believe you it's really OK to be a little crazy.

I've always called that the fundamental trick of Mathematics. If you have a problem that you don't know the solution to, just make it look like a problem that you do know how to solve :)

All your videos are excellent, but this one is the best I've seen so far.

This video went way more into depth of gravity from your comment on my question in your last video comments. Greatly appreciated!!!

I just realised I was smiling like a idiot while watching all the details and funny animations in this video.... They are great Nick. Can't even imagine the efforts you put into them.

Disclaimer : No clone has been harmed for the making of this video.

@wrOngplan3t

3 жыл бұрын

How do you know though? They're clones after all :P

Excellent video Nick. You produce outstanding videos.

I had to solve this tunnel problems for preparing my competitive exams ! It was in second year of "classe préparatoire aux grandes écoles", two difficult quite general years (I wanted to enter vet school and had to do physics, maths, chemistry, litterature etc...). We had oral mock exams that were called "colles" (or "khôlles" as the litterary classes prépa jokingly wrote to seem more greek), which were kind of conversations with the teacher. For this one, we spent about an hour and a half solving it, and I was very surprised when I found out that only the Earth's density mattered, not the actual distance to travel ! It was four years ago and I'm almost a vet now, I'm happy you brought this back to my memories ;)

Gotta admit, that's really genius.

@ScienceCommunicator2001

Жыл бұрын

Newton was the man!

Well, I haven't gone thru the Earth, but in 1996 I got a yachting friend to bring his fancy new GPS device to my house, added 180 degrees to both co-ordinates and got somewhere in Southern Spain. This was because I was planning a trip to Europe, in which I subsequently drove as near to that point as I could without intruding on private property. Thus, in a cabinet next to my dining table is a rock I can point to and tell a guest it is literally from "the other side of the world". I later learned of the "Earth Sandwich" concept while Blogging the 20th anniversary of the trip:- In 2006, the Internet comedian Ze Frank called for the preparation of an “Earth sandwich”-the simultaneous dropping of two pieces of bread on the ground at a pair of land antipodes, making the Earth into sandwich filling for the first time in history. Two of Frank’s fans responded to the call, one laying down bread in Spain, and the other in Auckland, New Zealand. I could have been there, dammit!

Nice video , thanks !!

I really liked this video. I've been using it as an example for my algebra student of why its useful to learn how to write mathematical expressions in lots of different forms and recognize their equivalence -- depending on what you want to know, one form might make you spend _hours_ to get a messy answer (like your ODE) while form (similar to how you reframed the problem in this video) might let you solve it in minutes. The difference isn't usually _that_ stark, at least not at her level, but it's a good example. It also helps that she loves your channel, so anything I mention is related to one of your videos tends to be a good motivator.

I'm still inside the box. I'm not sure if I'm dead or alive. Probably both.

-"Reimagining it is the ultimate physics trick!" yes!

Great video ! You explained it very well with the graphics Well done. Take a medal out the bucket !

Nice "outside the box" solution. Usually solving a more general case is more difficult than solving a special case and thus not an effective type of outside the box thinking , but this is an example where it's easier and thus effective. The type of outside the box thinking that works most often for me is to begin by trying to identify unstated assumptions, so they can be scrutinized too, and possibly discarded or relaxed.

Am I the only one who has a problem with "falling through the Earth" sideways? (42 minutes or not...)

@nibblrrr7124

4 жыл бұрын

It was bugging me too. But I guess it works if you ignore any friction when you bump into the tunnel walls & slide along them? The counterintuitive thing is that if you dig a straight tunnel parallel to a tangent to Earth's circumference, it looks as if every point was "level" - but "down" is always pointing to center of Earth - so the "straight" tunnel is actually "sloping inward", like a valley (in terms of gravity). You'd still fall/roll/slide through.

@Gary4DLC

4 жыл бұрын

I didn't get your question

@ScienceAsylum

4 жыл бұрын

Yes. We're ignoring friction in the shorter tunnels.

@QDWhite

4 жыл бұрын

Imagine a train on a frictionless track. In fact, people have proposed designs for just such a method of travel. Look up "gravity train" on Wikipedia.

@SquirrelASMR

4 жыл бұрын

Just bring some rollerblades

saw the notification and clicked with lightning speed. still watching and marvelled already

@Starkl3t

4 жыл бұрын

NEXT PLEASE

This question appeared in my physics prospectus twice, once while I was a second-year undergraduate in a mathematical physics course, and I was impressed at the derivation and homework set about. I remembered the drawing about how gravity decreased 1/r2 in space but 1/r in earth to the centre, a line. And in graduate school years later on the comprehensive exam (e.g., comps). I really like what you said in 9:05 about the Coriolis force and not drilling into the center; because during my MS exam the committee drilled the hole at one side, away from the poles, and I mathematically showed it would NOT descend. It would immediately hit the side (a friend of mind questioned me interrogatively) After I answered, I rewrote the problem, drilling the hole through the center and proceeded to derive, from first principles, and delivered a closed form solution, modeling it as a pendulum using classical dynamics. Frequency of small oscillations. My friend, mentioned above, said it would be interpreted as me being disrespectful at the committee the way I answered the question. I think they put the problem in like that on purpose! Nevertheless, I scored well on the exam and I know I answered that problem correct, and I got my vindication. Never looked back since.

Cool video as always!

I watched this video after 3 people, after completing it. I got curious then I refreshed and there is 1157 views!!!!

Great animation, and lots of laughs. When nerd clone showed up and mentioned the earth's rotation I was busting a gut at *sigh* "he's right... "🤣 Cuz dat shit is a lot more work! Great to see your thoroughness in the coverage. Most channels would gloss over that point but no sir not here! ^_^

@ScienceAsylum

4 жыл бұрын

I worked for 12 hours straight yesterday trying to get this video finished by today. Thanks for appreciating the work.

@peterfred445

4 жыл бұрын

@@ScienceAsylum How do you explain human levitation and the observed levitation of ufos where there appears to be no prop wash? There are some good, believable youtube videos on human levitation. Then there's Crookes et al 19th century account of human levitation.

@Richard-bq3ni

4 жыл бұрын

@@peterfred445 I can levitate for a brief moment, but I required a lot of beans to be consumed.

@TiagoTiagoT

4 жыл бұрын

@@peterfred445 Given that they traveled thru space to get here, one would assume they got technology we don't, so anything we say would be just speculation. Maybe they're using the same kind of space warping that could be used for faster-than-light interstellar travel; maybe we're not seeing them, but a side-effect of their cloaking technology; maybe they were not really there in the first place and our memories and recording devices have been tampered with; maybe it's just rockets but using dark matter as propellant etc. There is no way to know without actually studying an alien craft directly.

thanks for uploading this video

Awesome video!

"Unfortunately we can't make a whole through the poles. There is no land on both sides." The 5000K-hot Earth's Core: Am I joke to you?

Flying = falling and missing. -Douglas Adams

@glarynth

4 жыл бұрын

Uncontrolled crash = ablative lithobraking -Kerbal Space Program

Great vid. Thanks

Brilliant again (without the ™) the second part of the video also touches on why the principle of equivalence isn’t quite equivalent, which ought to be a nice stimulus to someone figuring out the implications for GR (as “an exercise for the reader”). Such excellent physics teaching here! Thank you!

I think I'm a "lost in the box" thinker...!

@08:24 "And 42 minutes would still have been our answer." Are you kidding ? Everybody knows that "42 IS THE MEANING OF LIFE, THE UNIVERSE AND EVERYTHING". ! So long and thanks for all the fish !

@carultch

Жыл бұрын

That's just a coincidence of what our planet's properties happen to be, and how we define the minute. Try this calculation with data for a different planet, and you'll get a completely different number. This isn't like the fine structure constant, where it is a very specific rational number that shows up in a surprising place, in a way that is independent from any physical object we inherited, or any manmade unit definition.

@nonothebot

Жыл бұрын

@@carultch Please watch (or read) H2G2 : "The HitchHiker Guide to the Galaxy."

Great video !!

This is not only interresting and usefull, this is totally genius! Again a pleasure to learn this wat, i really love this channel.

Can't imagine how you filmed the clone template...

This channel is such a gem, it is like a running commentary of melvin the mad's diary. This might pose a risk to the dangers of combining the batsuit with a white coat. Daily disclaimer: melvin the mage did not self levitate.

Excellent lesson. About the thinking out of the box... For the tunnel through the center of the earth, the brute force method quickly gives you an equation that looks just like a spring problem. We'd probably all come up with that idea. But the orbit idea IS out of the box thinking. I've worked that problem several times and not once did I consider changing it to a special case orbiting problem. I like!!

great as always

"I spent like four hours trying to solve that thing symbolically before I gave up" ... Spoken by me about every undergraduate physics homework assignment ever!

This reminded me of a similar and more general trick I sometimes use when trying to figure out a "what will happen" physics question. First assume linearity (ie. nothing whacky happening somewhere in the middle of the thought process) and then take it to its limit which is often obvious. That gives you a trend which points to the answer. It's a bit like differential calculus which also looks at where things are headed as you approach infinity.

Well done explanation! And plz make a video of explaining how to imagine this tunnel problem as just moving through geodesics which converges at poles...i.e. according to General relativity... Thanks for all Nick!

brilliant video as always nick, now i really want a video on Gauss' law alone, solving ellipse is easier than free fall who could have guess that(now i don't have any excuses to learn conic sections).

Mind blown, subscribed.

Great vid 👍

This video helped me get some extra credit in my university physics class. Thank you very much :)

This is unbelievably interesting and educational.

this trick of imagining one physics problem as another will totally help me a lot in my future studies. Thanks for the help crazy!!!👍😁

Good one ! ThE most interesting thing about this imo is not just that the time is the same for ALL straight line tunnels but rather that the size of the planet doesn't even matter ! Of course there are several real word issues that you mentioned but all rocky planets being about the same density is a pretty fair assumption for an ideal case. Brachistochrone tunnels are a very interesting extension to this imo.

Telling you man, the Nerd clone is my spirit animal :P Awesome video just like always! I loved the part at 7:48 were the falling clone comes from the other side of the Earth, but inhabitands of that part will see him coming upside down or... he will see them upside down... you know what I mean! That would be pretty cool lol!

Excellent video as always! I always feel a bit smarter after watching one if your videos in that I learn something new, and a bit dumber as well in that they typically show (only too well) how much more there is to learn on any given subject and as such how little I know about things that I previous thought I knew more.

@ScienceAsylum

4 жыл бұрын

If you know "how much more there is to learn on any given subject," then you are in fact smarter now 👍

@RonLWilson

4 жыл бұрын

@@ScienceAsylum Good point!

Elegant. Has been appreciated, the concept of the ISS in a state of continual free fall. See marbles transfer momentum when struck, extend this to free space where mass is fixed in by quark-antimatter-graviton into an absolute location. All photons and graviton interact by transfer of moment.

Excellent sir.

Thanks for confirming what happens when you fall through the earth, (I was guessing that gravity is effectively zero at the centre). I guess once you consider losses due to air resistance, then you wouldn't actually make it out the other side and would oscillate up and down until eventually stopping at the centre. Don't know computational / numerical methods, they are the only solution for those who can't remember all the formulas and rules in maths that solve stuff elegantly.

I've seen this equation before but i thought the symbol a was acceleration, now it was clear, Thanks.

@The Science Asylum thanks this works for Electromagnetic attraction too & force carriers btn 2 charged particles basically explains the Feynman Diagrams

great video!

While solving a problem in which two similar situations are presented and knowing the data and result for the first situation, I have to calculate the result for the second situation for which new data is given, I think of the data of the second situation as some error has occured while measuring it and use the concept of calculation of experimental error in an result. The math still works! It's really all about our thinking. Kind of also verifies that math is made by "us"(and not the universe).

Outstanding as always - in form and in content. How do you do your graphics and -- how did you master that skill?

@ScienceAsylum

3 жыл бұрын

It's a mix between After Effects and Python. Like anything, it took a lot of practice. I've been making videos for 7 years and I was making animations for my university physics teaching before that.

one of your best and craziest segments

This was amazing squared!

That redshift at 6:27 was a nice touch

I love your videos

Most of the time I can’t even find the box, but that’s why I’m here. You’re showing me the box and then how it works. Thanks.

Subbed 👍 First time I’ve seen your channel.

This was supercool!

Its a simple harmonic motion problem. So you can find the period by using eom or considering it as a circular motions problem. Just need to find the angular frequency.

I love that you consider all the things that I always forget about lol

Thanks bro

You're one of those people I love

Excellent video, Nick! You are getting more ambitious all the time, and it is resulting in amazing stuff! Throughout this video, I kept saying to myself "yeah, ok...but what about...". Before I could finish forming the question, you would jump in and answer it! The only thing I left puzzled by is the math that explains how the mass of the portion of a sphere above you is always offset by the mass beneath you. I'm guessing this has something to do with the geometry of asphere, but I really struggle envisioning the intuition behind why that works!,

@ScienceAsylum

4 жыл бұрын

Those two portions of the Earth are different masses, but they’re also different distances from the clone. The bigger part is farther away by just the right amount for the forces to be the same.

Another thing to consider would be the location of the moon during your free fall through the earth. Just as it effects water/tides it will effect your fall depending on its orientation to the axis of your tunnel and will change as it’s relative location changes during the fall. Interestingly the presence and location of the moon also means free falling objects near earth don’t all fall at 9.8 or straight down. The same considerations and more have to be made in orbital mechanics, which this problem is a type of as discussed in the beginning of the video. Great video! I think I just found a lesson plan.

Hi Nick ! As per Einstein can i say that at centre of earth there is no space curvature/ "space pressure" /flat space and at surface on earth there is curved space /"space presure" ??

Reminds me of my JEE days. Really love your videos.

Yeah. That's really nice trick. We have been using it for a long time.