hey smart people what's going on my name is dylan dance i'm a physicist from the land down under
today we're going to be watching some doctor who we'll see if we can find any physics math and
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comment down under so let's get into the video let's watch some doctor who and this
this is home
we're standing under a black hole in orbit you can see yourself we will hold it
but we can't be this lump of rock is suspended in perpetual geostationary orbit
around that black hole without falling in disgust and that's bad yeah okay so we're going to discuss
well how about we do a calculation and we can see whether or not it's possible to orbit a
black hole i reckon we could do some black hole physics some relativity uh and we can
see for ourselves so let's see what we can work out it's time to calculate mathematical so here
we have it here are my calculations i'll put it up there in case anyone wants to follow it
because we're not going to go through it it's a bit intense and i will definitely
bore you and you'll be clicking off as stephen hawking used to say you know you show one equation
and you're half your audience so i'm hoping i'm left with some people after showing this so what
i've pretty much done is derived what the closest stable circular orbit would be uh of a black hole
about the same mass as sagittarius a star which is the supermassive big old black hole in the
center of our milky way galaxy so doing that and then i also calculated the angular momentum
that this planet would require to stay in this stable orbit so it is important
to say i have assumed that the black hole is perfectly spherically symmetrical uncharged
non-rotating and in empty space so you can see there's a few assumptions there but let's run
with it so the curvature of space time due to the black hole can be described by the schwarzschild
metric as you can see here and schwarzschild just a fun little fact his name actually means black
shield which is bizarrely appropriate because it's it's a physicist's name a very famous physicist
so that's really bizarrely appropriate you know because it's describing black holes
um so i've used that and then you've got the lagrangian over here and then you've got the
euler lagrange differential equation and then as you can see down here i've done some jedi tricks
some wizardry and you eventually arrive over here at the radius and the angular momentum
and after all that you can see down here i've worked out that this planet could orbit this
black hole with the same mass as the one in the middle of our galaxy of a distance of about 35
billion meters without falling inwards any closer and it's getting devoured but
the tiniest of alterations or perturbations and this planet is going to get crushed
so i did make a lot of assumptions as well so if you factor in things like the black hole rotating
it's much messier charged all sorts of other stuff that i've just completely ignored it's gonna get
messy so there you go you can orbit a black hole and in fact if you replace the sun with a black
hole of the same mass all the planets would continue on in their exact same orbits though
things would get a bit cold i don't even just get pulled inside and crushed so they can't be enough
you should be pulled right in we should be dead and yet here we are beyond the laws of physics
so not quite like we just showed not beyond the laws of physics until you go inside until you
cross the event horizon at that point we're pretty sure you go you've gone beyond the laws of physics
um we re you lose all predictability our equations blow up general relativity's equations that is
and we can't make sense of it so it's a very interesting area and we really have no idea what's
inside a black hole you know if there is a center or not or if there's a planck star at the center
there's a lot of ideas out there maybe we'll talk about it in a future video because we've
already talked about black holes enough i think in this one so let's keep watching
until we crash into the sun
bit of a situation so this is a pretty interesting situation this thing has 42 minutes before it
crashes into the sun which i'm sure you all get the reference there you know the answer to the
life the death the universe and everything or whatever it is and it pops up everywhere and
i remember actually doing this calculation if you cut a hole through the planet earth
and you you know made it a vacuum in there how long would it take for a human or anything
to fall from one side to the other well it's exactly 42 minutes how cool is that jettisoning
pod
sorry
we'll fall into the sun way before he has a chance to do anything if i can boost the magnetic lock
on the ship's exterior as she re-magnifies the pot now while i'm out there you've got
we can calculate how strong this magnet essentially needs to be we'll calculate the
magnetic field strength required to get that pod back when the doctor activates this clamp thing
that saves the day so let's calculate mathematical so here we are we've done the calculation as you
can see there's not it's not very long but i'm not going to say it's simple because
one of my pet peeves in physics or math i hate it when you're watching someone do a calculation
you know whether it's a physics professor or math guy and uh you know they'll do the
calculation and then at the end they'll say it's trivial or they'll say very simple calculation
shout out bro like you know it might be simple to you because you've been doing it for years but
it's generally not the case for people watching and i'm sure some of you will think this looks
very simple and some of you are going to think that looks really really complicated so i'm
never going to say that because i remember what it was like when i was first starting
and it always looked complicated to me it looks interesting and some of the math when you get into
the deep end looks beautiful but it almost always looks scary and complicated so don't worry it's
meant to look like that even if you know it's not that much to it so we've made a couple assumptions
of course and we've approximated the speed of this thing to be the same speed as nasa's fastest space
probe the parker solar mission and that thing is traveling at about 430 000 miles per hour crikey
that actually reminds me i need to come up with some sort of catchphrase like the crocodile hunter
another great aussie so if you've got any ideas let me know down under um i can't just copy other
people's stuff like i love mathematical but that's adventure times thing or maybe i can
just steal it but let me know if you have any good ideas down under and maybe i'll use it so
that i mean even saying down under the comment section i got that from someone's comment so
i do go through them and read them so if there's a good suggestion i will definitely use it
back to what i was talking about it is moving this thing and we made a couple of other assumptions
it has about the same mass as a small car about 1 000 kilograms and down here you get
the magnetic field strength to be 0.46 tesla this is actually pretty reasonable because that is
pretty similar to a small electromagnet but this would only get the escape pod to stop this is the
minimum you'd have to you need a stronger magnet if you want to retrieve it and there's a lot of
assumptions here like we assumed a constant velocity but the thing is getting closer to
the sun so there should be some acceleration which we didn't factor in we could have if we have known
more of this you know information but it's a show it didn't tell us anyway yeah so pretty
reasonable situation good stuff doctor who let's keep watching ah there we go universal roaming
never have to worry about signal again no way there's too mad you're telling me i can phone
anyone anywhere in space and time on the mobile how long do you know the area code
frequent flyers privilege so their physics is almost as bad as their accent i can't stand
the british accent now you might say but you guys down in australia just british convicts
yeah we are but uh i just can't do their accent just can't
but i hope you guys know about relativity and the speed of light so that kind of um
makes something like this phone just not possible you won't be out of phone just anywhere
around the universe you won't even be able to talk to mars or even the moon lifetime
unfortunately but that's as far as we can tell you know there's always the possibility that we have
some things incorrect or there could be some loopholes and wormholes who knows
that'll do it for today's video guys make sure you like and subscribe and if you want to win that 500
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