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# Parsec definition

## Video transcript

you've probably heard the word parsec before and science fiction movies or maybe even in some things dealing with astronomy and what what I want to do in this video is really just tell you where this where the where the word and and the definition of the word really come from and just to kind of cut to the chase it's just a unit of distance it's just about three point two six three point two six lightyears but what I want to do is just think about where did this weird distance come from this distance that is roughly three point two six lightyears it comes from it comes from the distance the distance of something of something probably a star but let me say something because there are no stars exactly this far away from us the distance of something whose parallax or let me say that that has that has a parallax parallax angle of one arc one arc second and the word comes from the pair in peril x and ii in arc second so it's literally par let me do this in a different color it's literally parsec you could think of as kind of a parallax parallax arcsecond how far would this thing be it turns out it's three point two six light-years and we can actually calculate that and that's actually what I'm going to do in this video so let's say there is something let's say so this is the Sun this is the earth at some point in time this is the earth six months later at the opposite end of the orbit and we are looking at some distance we're looking at some object some distance away we know that this distance right here is one astronomical unit and what we want to do is figure out the distance of this object and all we know is that it has a parallax angle of one arcsecond so let's remind ourselves what this means if we're looking right at right at remember we're looking from above the solar system so the earth is rotating in this direction either case and so in in this point in the year we don't know when this is depends on what star that is at this point in the year right at sunrise right when we first catch the first glimpses of the sun's light if we look straight up if we look straight up the angle the angle between that object in the night sky and straight up is going to be the parallax angle so this is going to be one this is going to be one arc arc second and just to make it consistent with the last few videos we did on parallax let's just visualize that how that would look in the night sky so let me draw the night sky over here let me do that in purple maybe let me draw the night sky over here this is looking straight up this is north south west and east and so you can imagine in this situation the Sun is just rising on the east the Sun is just rising on the east let me make it the color of the Sun the Sun is just rising on the east and so this will be towards the direction of the Sun you can imagine that to some degree well this is north north as the top of the earth right here kind of pointed towards us out of the screen south is going into the screen hopefully that helps the visualization or another way to think about it the Sun is rising in the east this is going to be towards the direction of the Sun of a certain angle from the centre in this case it's one arcsecond so it's going to be right over here so this this angle right over here is going to be one arcsecond and then if we were to see where that object is six months later it'll be the opposite we're going to be looking we're going to be looking in the st. this the centre of the universe or I should say the center of the night sky at that point the same direction of the universe the universe actually has no center we've talked about that many times if we look at the same direction the night sky will be looking six months later and instead of it being at dawn it will now be at sunset we'll be just getting the last glimpses of the Sun and so the Sun will be setting the Sun will be setting in the West the Sun will be setting in the West and so this angle this angle right here which is also the same thing as the parallax angle it'll be this will also be one arcsecond so this will also be one arc second one arc second so let's figure out how far this object is what is what is an actual parsec in terms of astronomical units or light-years so if this is one arc second this is going to be and remember one arc second is equal to one 3600 one thirty six hundredths of a degree one thirty six hundred of agree so this angle right over here is going to be 90 minus one over 3600 and we just use a little bit of trigonometry the tangent of this angle the tangent of 90 minus one over 3600 is going to be this distance in astronomical units divided by one well you divide anything by one it's just going to be that distance so that's the distance right over there so we get our calculator out and we want to find the tangent the tangent of 90 minus one divided by 3600 and we will get our distance in astronomical units two hundred six thousand 264 I'm going to say two hundred sixty-five so this is going to be equal to this distance over here is going to be equal to 206,265 I'm just rounding astronomical units and if we want to convert that into lightyears we just divide so there are 63 thousand one hundred and fifteen lightyears per astronomical unit I'm sorry astronomical units per Lightyear so this is let me actually write it down just so you make it I don't want to confuse you with the unit cancellation so we're dealing with 206,265 astronomical units and we want to multiply that times one light-year is equal to sixty three thousand one hundred and fifteen astronomical units and we want this in the numerator and the denominator to cancel out and so if you divide 206,265 this number up here divided by 63 1 1 5 the number of astronomical units in a light here 63 1 1 5 let me delete that right over there we get 3.2 all the way the way the math worked out here round into three point two seven light years so this is equal to this is equal to roughly three point two seven light years so I should just show its approximate right over there but that's where the parts that come from so hopefully now you just realize it is just a distance but even more you actually understand where it comes from it's the it's the distance that an object needs to be from Earth in order for it to have a parallax angle of one arc second and that's where the word came from parallax arc second