How does Mercury's orbit prove General Relativity?

you know what we do not talk about mercury enough like I know it's not as cool as like Venus or Mars or in any of the gas giants either because it's pretty small and it's so hot everything's so arid there but if it wasn't for mercury we would not understand general relativity half as well as we do and Mercury's orbit was actually the very first proof of Einstein's theory of general relativity that we ever had so when Einstein came up with his new theory of gravity in 1916 his theory of general relativity he did that through saying if we can imagine gravity as curved space-time any object that has mass will curve space-time and the bigger the object the more it will curb the space around it so that objects also traveling along that space will travel along that curved path and get their trajectories changed then he said we could think of planetary orbits just like that and when he did that he came up with a whole new suite of equations to describe his theory of general relativity now that was all well and good but it was just the erratically it's one thing to actually just say mass bend space-time but you actually also have to prove that as well and so Einstein came up with three tests that you could do to confirm whether this was the case the first one he said would be that stars positions would change during a solar eclipse and that was because we were blocking out the light of the Sun we could see the stars behind it and we could see that the light from them has been bent around the Sun on their way to earth now he had to wait about four years to actually get that proof from Eddington in the 1919 solar eclipse so we couldn't use that at the time in 1916 to prove it the second test that he came up with was this idea of gravitational redshift so a redshift is when light has its wavelength stretched out to longer wavelengths or lower energies or redder colors why we call it a red shift and that happens because of the expansion of the universe as well mainly because when we observe it but it can happen if light is also being dragged backwards by the gravitational pull of something as it tries to travel up and out of that curved space-time unfortunately in 1916 Einstein didn't have any way of proving whether that was right either in fact we had to wait till 1954 when a chap called popper finally proved it was happening around Stars and the third test that Einstein came up with was whether it could predict planetary orbits so having observed a planet in a specific position one night could you predict where it was gonna be in a month's time from the equations that he derived and in particular he wanted to try and explain the orbit of mercury because it had been long been known that Mercury's orbit was a little bit dodgy so Newton's equations of gravity that had been sort of the leading theory of gravity since 1713 when he published Principia and he took catalyst laws of planetary motion and how the planets go around the Sun and generalized it into this big theory of gravity and so while those equations gave really good predictions for where the rest of the planets and the sky would be after observing them you know for a month later for Mercury it always gave slightly the wrong answer and no one knew why that was for a very long time until 1859 when the very a published a huge long list of the position of mercury over a number of years and found that what was actually happening was that its perihelion was processing planets don't actually orbit in perfect circles actually ellipses and so at some points it's a bit further away and some points it's closer and the point at which it's closest is its perihelion it comes from the latin peri meaning closing Helion meeting sun and what the varier found was that that wasn't always in the exact same place in mercury orbit it was actually moving with mercury if you were actually to plot Mercury's orbit out what it will look like it's kind of like a spirograph pattern to people remember that game I absolutely loved that game as a kid I usually find me just think of a time with like lots of different colored pens anyway that is what Mercury's orbit would look like if you saw it over centuries now that diagram I just showed is a huge exaggerated what this effect actually looks like a single orbit of mercury only takes something like 88 Earth days and so you can't see it over a single orbit you have to wait many many orbits for this effect to sort of stack up for you to be able to see it in fact when the very a actually measured how much it processed each year in the sky he found that it was something like one and a half degrees per century essentially or if you want to use a different unit it's 5,600 arc seconds a century so an arc minute is when you take a degree and split it into 60 and then if you take an arc minute and split it into 60 again you get an arc second which is a tiny tiny unit but sometimes movements on the sky are that tiny and we do need to measure things in arc seconds now this wasn't that much of a surprise that this was actually happening because in Newtonian gravity it was expected when there's something that is quite close to a massive object but is also being perturbed slightly by all the other objects in the system so the main reason why Mercury's orbit does this is because it's not just interacting with the Sun but it's also feeling the pull of all the other seven planets that are also orbiting the Sun at the same time the thing is if you use the equations in Newton's theory of gravity to predict how much Mercury's orbit should process per century you only get something like five thousand five hundred and fifty seven arc seconds per century not five thousand six hundred arc seconds per century so there's 43 arc seconds of precession that unaccounted for by Newton's laws of gravity no nice 59 when the Varia announced this he said that 43 arc seconds unaccounted for could be due to the fact that the Sun isn't perfectly round it could be an oblate spheroid which means it's kind of squashed at the poles just like what Saturn is because it's rotating very quickly and it did turn out that that plays a small part but it's not enough to account for 43 arc seconds per century or Lavar EA said there must be another planet inside the orbit of mercury orbiting the Sun could explain the fact that we're getting this extra 43 arc seconds and if we put that into the equations it should all come out with 5600 arc seconds per century now at the time in 1859 that was the most favored hypothesis because 13 years earlier in 1846 lavare ei himself and Johann Galle had actually found nephew they discovered Neptune through a motivated search for another planet because of the weird orbit of Uranus that couldn't be explained and was suggested the only reason that it was like that was because there was another planet beyond it that was Puteri yet slightly and pulling on it more so as odd is an extra planet inside the orbit of mercury - you and me sounds like then it wasn't such an outlandish idea because well they'd only just discover Neptune it was that feeling that there could be something else out there that had never been spotted and so this hypothetical planet inside of Mercury was dubbed Vulcan after the Roman god of volcanoes and fire and forges now through the rest of the 19th century confirming that this hypothetical planet Vulcan existed was peoples top priority and obviously people wanted to be the person who discovered it and there was a lot of false claims throughout most of the 19th century including people that were adamant that they'd seen something transiting across the face of the Sun despite the fact that someone who was observing the other side of the world at the exact same time didn't see anything there were people that claimed they'd spotted a planet during the solar eclipse very close to the Sun in a position where no known star was thought to be but really highlighted the fact that these were all false claims though was there every single observation gave us a different answer for the properties of Vulcan and Vulcans orbit so some would claim that it was further in towards the Sun some claim that it was further out some more massive and some less massive if they'd all agreed then that would have probably been quite a convincing hypothesis but it became pretty clear pretty quickly that this hypothetical planet wasn't actually there and couldn't explain the strange precession of Mercury's perihelion as it orbited the Sun now this is where Einstein comes in in 1915 with his theory of general relativity that said that masses curved space-time and all other objects travel along that curved space-time and the equations that he came up with essentially described that curved surface or geodesics as he referred with the mass that all the masses would then be traveling along and so from that general equation of curved surfaces he managed to apply it to the solar system and get equations for what the orbits of the planets would be like given the fact that they were traveling on the curved space-time created by the Sun and he found that his general equation for the planets reduced down to exactly Newton's equations just plus one extra term and that extra term was two G M over C squared R cubed so G is the big gravitational constant that tells us sort of how strong gravity generally is in the universe M is the mass of the Sun C being the speed of light and our being the distance of the planet ie mercury in this case from the Sun so it wasn't that Newton's equations were wrong at all it was just that that term disappears when you have either very small masses so like the things that we experienced on earth when we throw balls in the air or projectiles or very large distances between objects like with the majority of the planets in the solar system it's just that for mercury which is much closer to the Sun and so has a much smaller value of R ie distance from the Sun that term no longer tends to zero if you divide by a small number you get a much larger number and so that term is much more important for Mercury's orbit than it is for any other planet in the solar system so what Newton's laws really were were an approximation that just didn't happen to hold for mercury it's also worth noting here that you Hannes Kepler who came up with the laws of planetary motion that Newton took to apply to his theory of gravity in progeria they were written down in the early 1600s and that was back in a time when people including Kepler thought the speed of light was infinite now in Einstein's extra term you divide by the speed of light squared so you're dividing by infinity squared which is infinity and if you divided by infinity then you're gonna get essentially zero mathematicians won't like me say not that dividing by infinity gives you zero it tends to zero is what you should technically say it's a singularity but I'm happy with just saying that it divides by zero sorry I feel like all of the numberphile professors are gonna descend on me saying essentially it gives you something incredibly incredibly small and so that extra term of Einstein's would always have disappeared back in the 1600s when they thought that the speed of light was infinite but we now know through many many different painstaking ways of measuring it that the speed of light is not infinite it actually has a finite speed of about 300 million meters per second which incidentally you couldn't measure in a microwave with some marshmallows which is a super-fun experiment for a Sunday afternoon and would highly recommend it you won't get the most precise answer but you will get something in the right ballpark which is pretty damn cool for a microwave and some marshmallows so what Einstein did next with his extra term was work out how much of an effect it would have on the predicted position of a planet and in particular how much extra precession of the perihelion of mercury did it give you and when he plugged in the numbers he found it gave you an extra forty three arc seconds per century on that procession the estimate at the time of the amount of precession that was unaccounted for was 45 plus or minus five arc seconds per century and so Einstein rather anticlimactically at the end of his paper sort of announcing general activity and giving this proof of it through Mercury's orbit stated that it showed full compatibility ie it proved his completely groundbreaking theory it's worth stating here actually that to do this Einstein actually made a massive approximation when he went from his big general theory of geodesics and curved space-time to giving the equations for the planets around the Sun it actually took Schwarz Shields a couple of months later having looked at Einsteins work and going yes this is great to actually come up with the non approximated solution to all of these equations but with the advancement of telescopes and radar throughout the 20th century we've actually been able to confirm that the same thing happens for the other planets all the other planets perihelion processes as well just by a tiny tiny amount that is also predicted by general relativity so for Earth our perihelion processes 3.84 arcseconds per century because of this effect venus 8.6 two arc seconds per century it's so small that back then people would never have actually been able to observe it and realize that there was actually a problem I mean this is really cool but I bet a lot of you are thinking why should we care [Applause] [Music] like yeah we have a better theory of gravity now and we can explain how the orbits of the planets move but that doesn't really change things down here on earth and we're working with the small masses the Newton's equations just give a good enough approximation to it's why we still all learn them in school well it's actually our understanding of general relativity that allows us to actually have a global positioning service so the satellites that go around the earth that essentially every time you want to know your position on your phone from maps or weather or whatever it is they send a pin to the satellite and they triangulate between two or three different satellites where you are on earth down to you know meters precision and that's only possible through our knowledge of general relativity because the satellites as they're moving around the earth they're moving in the curved space-time that the presence of Earth gives us and so they're actually affected by this idea of gravitational redshift all of those pings of communications they send down to earth and back up the satellites are affected by this gravitational redshift and so if we don't correct for the fact that the timing between them will be slightly off each time they would be out by something like ten kilometers per day so the next time you pull out your phone to use maps or to look at the weather for your exact location and get minute by minute when it's gonna rain and when it's gonna stop raining or you use the Sat Nav in your car just think of mercury and of Einstein and a spark shield and just say a little thank you in general to physics and that's only possible because we were founded and that's only two G M over C squared R cubed then connected with gravity and Principia in 15 whatever it was when was pretty apparent Tippie uplink you see I think appear kepler actually thought listen perfect my Amazon parcel that you tell me to if you need you need me to be with you I will where you lead [Music]

Channel: Dr. Becky

Views: 211,585

Rating: 4.92452 out of 5

Keywords: general relativity, mercury, einstein, gravity, relativity, planets, orbits, sun, solar system, gravitational redshift, eddington, schwarzschild, precession, perihelion, newton, kepler, dr becky, astrophysics, science, astronomy, rebecca smethurst, becky smethurst, physics, universe

Id: 8Sm99OVG5A8

Length: 16min 42sec (1002 seconds)

Published: Wed Nov 06 2019