all right next is it problem number 17 on homework for chapter 17 and this is the one that deals with the parallaxing distance of a star and the diagram that is shown to you in this problem looks like this and it's the geometry for parallax Earth orbits the Sun its distance away from the Sun on the averages one astronomical unit one point four nine six times 10 to the 11th meters and if you can measure the shift in the angle of a star tells you that it's a fairly nearby star then we can actually calculate its distance from the Sun to That star based upon using right angled trigonometry they get a trigonometry is not your finger that's just a foreign language to you then please don't panic it's not important at this point I'll never make you do trigonometry as part of an exam question for instance but the relationship here is that the tangent of this angle P and you learn this in trigonometry class is just a definition thing the tangent of an angle in a in a right triangle is always equivalent to the opposite side of the triangle which in this case is the value of our opposite side of the triangle from the angle divided by the adjacent side to the angle and there are two sides to this angles so you say which one's the adjacent it's the shorter of the two yes the longest this side is called the hypotenuse so the adjacent side is the value D right here so okay you know that's just the using the definition of tangent that angle in trigonometry well you're being told the problem that you have a parallax angle and of course R is a well-known value the earth-sun distance now thanks to the last chapter so I should be able to solve this just for a d schat night to get the star son distance and that works out to be you know deep students of algebra here is equal to switch the two are divided by the tangent of P now Tina tchen is just a number you know you punch in a value for the angle in your calculator you have ten and it spits out a number doesn't it and that value is too constant at that point is just going to be you know the value that you divide R by now somebody realize that when the value of P the tangent of the P angle is very small then we don't even need to take a tangent anymore it just becomes the angle itself P in units of radians which we talked about once before but it's a little bit confusing especially if you've never had to economically before but here's the cool part somebody figured out that if the angle P is equal to one arc st. never arc second an arc second is equal to 160 if an arc minute that's a degrees right of an arc minute and that's equal to one 3600 of a degree so the point is an arc second is incredibly tiny smug from the width of a hair you literally need a microscope to see something that's small but for the nearest stars to us the Alpha Centauri is the series's the proceeds of the world are the universe they have angles that are even smaller than that shift over a six-month period as earth goes around the Sun so you know we don't need bigger angles than that so somebody said well if you had a parallax angle of one arc second which is bigger than all the others they've been all of it then what would the value of DB and the calculate vet in meters using are meters or some distance and I realized that if you can put it into the light-years that distance becomes about three point two six light-years well-fed number rings a bell three point two six lightyears is something called a parsec and a distance to a star having a parallax angle of one arc second is called a parsec even sounds like it parallax of one arc second Parr sick so forget trigonometry stuff what we're going to use for this point forward is that the dis is to any star measured in pcs yeah which stands for parsec is equal to one y is R equal to one because that's one astronomical unit if you use this set these units parsecs for D astronomical units for R and arc seconds for P then all we need is the angle let's say P measured in arc seconds and this will be the formula that we kind of apply from this point forward I can get the distance to a star in parsecs if I know that its parallax angle is in arc seconds so back to the problem number 17 it says you know hypothetically if you had a start with a parallax angle of one thousandth of an arc second 0.001 then what would the distance to that object be all you're doing is plugging in the value of the parallax angle in arc seconds so 0.001 and then when I divide this by this or this by this I'll get a distance that's in parsecs well what's one divided by one one thousand how many times has a thousand fit into one a thousand times one thousand what one thousand parsecs now measuring angle is this tiny you know one arc second is hard to do and we can deal with earth-based telescopes if you want to start detecting ales down to 1/100 are thousands of an arc second you need of course Earth orbiting satellites that have incredible resolution above the Earth's atmosphere like the guy yes I like that we talked about earlier in this chapter okay