How do we know how long the Sun has left to live? | 7 things we need to know

they often hear people say that the Sun is about halfway through its life and then it's got maybe 5 billion years or so left to live before it runs out of fuel where does that number come from though because the calculation itself is actually not that difficult but we have to know so many things that layer on top of each other before we can even hope to get at that number so what I'm gonna do is I'm gonna go through the calculation back of the envelope calculation nice and simple for how we get that rough estimate of the fact that the Sun has about five or so billion years left to live every time I say something that you're gonna be like wait a minute how do we even know that I'm gonna raise a little flag I'm gonna make a list of all the things that we need to know in order to work out how long my son has left to live and I'm gonna come back and explain how we even know that in the first place okay so to work out how long the Sun has left to live we first of all need two things we need to know how massive the Sun is and how bright the Sun is something we call it's the luminosity how much energy is it giving off per second now the sun's mass is 2 times 10 to the 30 kilograms or 2 with 30 zeros after it its luminosity is 3 point 8 times 10 to the 26 watts or joules per second energy given off by the Sun per second and with these two numbers we can use one of the most famous equations in the entirety of physics I'm talking about Einsteins e equals mc-squared mass and energy are equivalent so if you have something with mass M then you can turn it into energy E so assuming that the Sun powers itself with fuel that it has inside of it we can assume that the sun's mass is its fuel for its energy and so with e equals mc-squared we can work out the total energy that the Sun would have plugging in those numbers we can then divide that by the amount of energy it's giving off per second to get how long the Sun will live in total in seconds then we can convert that to years and we get an answer that is far far too big now the reason it's too big is because that calculation has assumed that the sun's entire mass ie all the stuff that in the Sun will be available to use as fuel for it to burn to give off light and heat and energy which we love because it allows us to have fun days at the seaside but that's not the case the way the Sun powers itself is by nuclear fusion it takes atoms of hydrogen and fuses them together to make helium and in that reaction energy is given out and that's the energy that we then receive on earth the thing is it's only hot enough in the very center of the Sun for those reactions to take place you need to tremendous amount of to force four hydrogen atoms together so actually nuclear reactions are only taking place in the core of the Sun which is about ten percent of its mass if we use ten percent of two times ten to the 30 kilograms we still get too big of a number out from our calculation but some of you might have picked up already on the reason for that is that the hydrogen in the Sun that it's using as fuel isn't purely converted to energy like e equals mc-squared assumes some of it turns into helium need four hydrogen atoms to make one of helium and a helium atom is actually ninety-nine point seven percent of the mass of four hydrogen atoms so actually only ten percent of the total mass is useful for nuclear fusion and you'll only get point zero zero three but if that mass converted to energy and if we use those numbers then we get out that the Sun has about ten point five billion years worth of hydrogen fuel available to it but that's the total lifetime of the Sun not how long the Sun had left to live to work out that you have to know how old the Sun is already and we know that that is 4.5 billion years old so if you take one from the other you get about six billion years old which for a back-of-the-envelope calculation is not bad if you do it properly with all of the modeling then you come at the sort of more green value of say like five billion years or so but you know what's one billion years between astrophysicists and friends so back-of-the-envelope calculation done here's our list of seven things that got flagged that I said that we needed to know in order to be able to do that calculation and I think you'll agree it's quite a long and interesting looking list and probably a lot of you will be wondering yeah how did we work those things out so first up the mass of the Sun how do you calculate how much stuff is in this when we're stuck on the fact of the earth is in orbit around the Sun though means that the gravitational force pulling the earth inwards towards the Sun is perfectly balanced by the centrifugal force pushing outwards on the ear so just like you do when you get on a merry-go-round and if you've been on a merry-go-round you know that you feel that force pushing you off the merry-go-round as you go faster and faster and so by balancing those equations we can see that we can measure the mass of the Sun if we know how fast the earth is moving and but what distance it is from the Sun and then also this gravitational constant which was the first sort of accurately measured properly in a lab by Henry Cavendish now we obviously don't know the speed the earth is moving around the Sun but speed equals distance over time and the time that the earth travels around the Sun is well a year 365 days or 365.25 days anyway we know that the distance it travels is just the circumference of its orbit which if we assume is circular and you remember your high school math is just 2 pi R of course actually the orbit of the earth is sort of more elliptical shape but let's go with circles right now because it's just a little bit easier in terms of the math and so then we can cancel out that speed that the earth goes round the Sun just to get an expression in terms of the distance of the Earth from the Sun and then also the time it takes to go around and this gravitational constant again so okay we only need to find the distance from the earth to the Sun to measure how massive the Sun is how do you get the distance from the earth to the Sun though is there for the next question measuring the distance to objects that aren't solid is very difficult but solid things we can do that dead easy right we do it all the time with air traffic control that use radar radar takes radio waves and it bounces it off the solid object comes back you know the speed that the waves have traveled at so the time delay gives you the distance but the Sun is not solid it's a plasma which basically means that it's like a gas but the electrons found in orbit around the atoms anymore they're just like freely roaming so you've got sort of like a charged soup of particles basically so we can't use radar to measure the to the Sun but we could use radar to measure the distance to solid objects in the solar system like other planets for example and if we think about the setup of earth going around the Sun and say Venus or mercury going around the Sun then there's a special place in Venus's and Earth's orbits where they make a right angle triangle with the Sun so if you wait for Venus to get to that point and it makes this perfect right-angled triangle you can measure the distance between Earth and Venus easily because it's a solid and it will bounce the radio wave back off nice and easy you can then measure the angle between Venus and the Sun in the sky at that point and then it's just trigonometry to work out that distance between the Earth and the Sun so all you haters on trigonometry out there that's like trigonometry is not useful outside of school well it's to me anyway next up the luminosity of the Sun and you think this would be an easy thing to measure because you're just measuring the amount of energy you get from the Sun per second which you can do if maybe you say leave a part of water out in the Sun and see how quickly it heats up for example you could measure the amount of energy you're getting the thing is you're only measuring the amount of energy that reaches us on earth so the total output from the Sun will go out into a sphere and then we'll only measure that tiny cross-section that intersects with your pan of water or your solar panel to measure the amount of energy we're getting that's something called the flux rather than the luminosity flux is proportional to the luminosity divided by the distance to that object squared now we just talked about how we get the distance from the earth to the Sun so if we just measure the flux of energy you receive on earth we can then easily get back to the luminosity of 3.8 times 10 to the 26 joules per second next up e equals mc-squared Einstein's most famous equation in fact probably the most famous equation in the world but how do we know that energy mass or equivalent and how do we know that you happen to times the mass by C squared it all comes from a consideration of how much energy things at rest compared to things that are moving have so you'll have learned at school that kinetic energy things that are moving have an energy of 1/2 MV squared so their mass times by their velocity squared but photons don't have mass and yet when they're moving at this incredible speed they still have energy and momentum so that kinetic energy formula doesn't really work so if you work through all of the maths of what the energies of different particles with mass and without mass have which is actually just high school that's it's not overly difficult then you actually come down to the conclusion that an object completely at rest will have the energy equal to its mass times by C squared now I'm not gonna go through the math here because that is probably a whole video by itself but if you are super interested in that Ethan Siegel from starts on the bank has a fantastic article on it and I will link it down below so number four on our list that the Sun is powered by nuclear fusion is kind of intrinsically linked to number six on our list but a helium atom is 99.7 percent of the mass of four hydrogen atoms kind of needed one to figure out the other but it's a little bit of a long story how that was actually figured out and it starts about 1904 when Ernest Rutherford discovered the enormous amount of energy released by radioactivity specifically alpha decay when an atom of an element can essentially decay into a lower mass element and it does that by giving off what we call an alpha particles I mean it's two protons and two neutrons just like in a helium atom and the fact that so much energy could be given off by a nuclear process made people think well perhaps that's what's powering the Sun this thing that's giving it off an enormous amount of energy but it was only very heavy elements that underwent this radioactive decay things like uranium plutonium the elements that there are so chock-full of protons and neutrons that it's just really difficult to hold them all there now if that was the case if the Sun was powered by these very heavy elements then we should be able to detect the presence of those elements in the light we get from the Sun because all elements sort of leave a quantum fingerprint on light because either they absorb a specific wavelength of light and that's very obvious when we take the light from the Sun and we split it through a prism through a spectrum this is exactly what happens when you get a rainy day or a waterfall and the light is split through those little water droplets and forms of rainbow what you don't see though are the very very specific wavelengths of light that are actually missing because in a rainbow they all sort of blur into one but if you can get the resolution to see it you see that that rainbow actually has gaps in it dark bits where we don't see that very specific color and it's because an atom of a specific element that's in the Sun has absorbed it but when you look at those specific wavelengths and you correlate them with the wavelengths of absorption of light we see on earth when we look in the lab you find that it's mostly hydrogen and some helium and so people quickly realize that actually those heavy elements aren't present in the Sun at all and that the Sun therefore couldn't be powered by radioactivity it was then in 1920 that a British physicist called Aston actually managed to measure the masses of individual atoms of elements so he managed to very very precisely measure the mass of a hydrogen atom helium atom and so on and so on through the periodic table and he did that using a really clever device called a mass spectrometer and a mass spectrometer is sort of like a chemists best friend I have already thought about them since ailable so this was fun doing this research for this video but essentially what happens is you first of all take out an electron from around an atom and by removing an electron you remove some negative charge so you've positively charged the atom that you then have you then fire that item through the mass spectrometer instrument where you set up a magnetic field now electric charges moving in magnetic fields they have their paths deflected they have their paths curved but the amount that it's curved depends on how heavy the thing is that's moving so if you send a hydrogen atom down a low curve much more than say a helium atom would that is heavier than a hydrogen atom even though they've got the exact same charge by just removing one electron and with this you can measure incredibly precise masses over the elements what was surprising to chemists at the time though is that the elements atoms weren't just pure multiples of each other but it took Arthur Eddington making the connection between that mass difference an e equals mc-squared to realize that if you could take four atoms of hydrogen and somehow fuse them together so that they became an atom of helium then you would give out that tiny difference in energy but if you had enough hydrogen then you could get out an enormous amount of energy by doing that now that's great but it really was only a hypothesis there was no way that you could actually therefore test the fact that that was going on in the Sun except for the fact that you saw that the Sun was mostly made of hydrogen and some helium now through the 20th century many physicists worked on the actual theory of what would physically happen in that process of taking four hydrogen atoms and making into one helium atoms it's not necessarily as simple as it sounds so that included gamau Atkinson kutiman and vice occur in the process yes you formed the helium but you also released two electrons two electron neutrinos and then some energy now the hydrogen helium we can't detect but what about the neutrinos neutrinos are incredibly incredibly tiny very small mass particles in the standard model of particle physics and they're not really impeded by anything they can just go through everything in their path and so getting out of the Sun is actually relatively easy for them they literally stream out of the Sun from these nuclear reactions we only know that because people eventually detect it those neutrinos on earth from the Sun then men all the evidence pointed towards nuclear fusion as the process powering the Sun so I guess we skipped number five on the list there that the inner 10 ish percent of the Sun is actually hot and dense enough for these nuclear reactions to occur forcing these hydrogen atoms together to become helium now how we figured that out kind of all falls under the umbrella of helioseismology so Helio meaning the Sun was in Helios the Sun God in Greek or is it Latin I think it's Greek and then seismology which might be a word you recognize from people studying earthquakes and it's using those earthquakes that we've been able to figure out what the interior of the earth is like so what about sun quakes as waves propagating through it all the time and the closest sort of analogy really is a sound way of propagating through the Sun we like to say the Sun rings and you can listen to it and by listening to all the different frequencies that you get as all those waves ping around the interior of the Sun interfere with themselves and set up this weird pattern that we can then unravel with some really clever maths you can then figure out what's going on in the interior because the pattern depends on how fast the waves are moving and what they're moving through and they speed up and slow down depending on the temperature and pressure of the stuff that they're moving through so by producing that map and I'm rambling all the frequencies that we hear from the Sun we can get an idea of what the temperature and pressure is actually like inside the Sun using that map we can work out that only the inner 10% ish is hot enough and has a high enough pressure to be able to force atoms together and knowing what that temperature and pressure has to be your comes from quantum physics and understanding the behavior of atoms on the very very tiny scales again that wouldn't even just be a single video like if you want to understand quantum physics I'd recommend doing an undergraduate degree in physics but maybe one day I'll tackle a video on that and so with all that information and assuming that the Sun will start off as a pure ball of hydrogen and be able to use all that to convert it to energy in its lifetime we get the total lifetime of the Sun but that's not how long the Sun has left to live for that we need to know the last thing on our list which is the age that the Sun is now it's not something we can really get from studying the Sun you know it's not like a tree that we can cut down and count the Rings but what we can assume from other sort of planetary systems and new stars forming in the rest of our galaxy in the Milky Way we can assume that the Sun and the planets and everything else in the solar system all formed at the same time so if you can measure the age of another object in the solar system then you can get at the age of the Sun now we could try and find some the oldest rocks on earth but most of the rocks on earth will have been pre processed because the fact that well we have you know volcanoes and plate tectonics that sort of like melt down rocks and reform them so really what we need is a relic from the very early days of the solar system that sort of been left alone pristine from it very first formation and luckily we have those in the form of asteroids that then fall to earth is meteorites now in those meteorites and asteroids are those very heavy elements like uranium and plutonium that undergo this radioactive decay so for example uranium decays into lead so if you know the rate at which that happens and you can measure how much lead there is then you should be able to work out how old it is except for the fact that you don't know how much uranium you started with but what if we had two different types of uranium that decayed at two different rates into two different types of lead then what we'd end up with is two different amounts of lead that have arrived at that point at two different rates and that would allow you to get it how old that object is they probably thinking how can you have a different type of uranium Becky it's an element it's the same thing it's just uranium right but if you add extra neutrons to an atom you make something which is called an isotope it's the same element it's just a little bit heavier with those extra neutrons and so that's what makes it decay at that different rate because you've actually got a more unstable atom by adding those extra neutrons so by working out the ratio of the two different lead isotopes you'd get in the end products you can get how old the asteroid and therefore the solar system and therefore the Sun is which you find is about four and a half billion years old yeah so that was all the information we needed to answer that one question how long does the Sun have left to live it's incredible when you think about it like how many results and even different areas of science had to come together for us over centuries of research for us to be able to answer that question so next time you hear someone say the Sun is halfway through its life or has five ish billion years to live I hope you think about all the human effort and centuries of work that went into producing just that one number I know I wore this jumper like really recently to film another video but it's just so soft and cozy I'm tripping over wires again Oh still not used to this weird new arrangement don't know how I feel about it it was then in 1920 that a British physicist called Aston managed to measure the very specific it was then in 1920 that a British British furnish I've got American British it's not actually different is it now meteorites there are those incredibly heavy elements elements I can think Elmen meteorites have ailments then what we'd end up with is the ratio between two different types of red red LED then what we'd end up with would God so that was my water bottles been on this side the entire time they take one sip and then I get the whole the whole car the Sun was a hot dense place and then 4.5 billion years ago nuclear fusion started wait you

Channel: Dr. Becky

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Keywords: dr becky, astronomy, astrophysics, science, physics, space, big questions, the sun, solar physics, helioseismology, nuclear fusion, nuclear fission, radioactivity, einstein, e=mc2, mass of the sun, speed of light, becky smethurst, rebecca smethurst, dr becky smethurst, radio waves, radar, venus, solar system, astronomical unit, distance from earth to sun, vacuum, how old is the sun, earthquakes, interior of the sun, interior of the earth, sunquakes, luminosity, flux, isotopes

Id: IMogF5W7Pbw

Length: 23min 46sec (1426 seconds)

Published: Wed Feb 05 2020