 So, let us take up numerical excel write down the moon is observed from two diametrically opposite points a and b on the earth. So, here is the earth draw the earth like this from two diametrically opposite points a and b you are observing the moon we are treating moon as a point object let us say moon is here you are observing from two diametrically opposite points the moon how it will be you are observing like this from point a and then from point b till like that that is how you are observing the angle subtended by the moon by two directions of observation one direction is this first observation direction this is the second observation direction ok the angle subtended this angle which is subtended do not use calipers ok do not use it otherwise later on you will have yourself to blame you are not able to calculate anything in the exam last year also it was very calculation intensive j in x and 2,014 also it was very calculation intensive. So, if you are not if you are not able if you do not have practice to calculate you are gone ok and being good with number is an art ok it is something which is which does not come to everyone ok it is an art do not think that it is a donkey's job there are so many donkey's job but calculation calculating being good with number is not a donkey's job it is something which will really help you lot later on also some of the highest paying jobs are for people who are good with numbers ok. So, this angle is 1 degree 54 minutes the diameter of earth is the diameter of earth is 1.2 7 6 into 10 is to power 7 meters this is the diameter of earth ok you need to calculate the distance of moon from the earth understood the question first thing is you have to convert the angle in radiance then only you can say that is equal to argl and divided by radius that theta is 1 degree 54 minutes how to convert this in radiance 1 degree is 1.745 minus 2 then. 54 by 64 plus 54 by 2.9 you can say 54 by 60 into this or if you know what is 1 minute in terms of radiance which is what 2.91 into 10 is to power minus 4 you can get this in terms of radiance all of you understood this one how many radiance you will get here how many radiance. So, it is a radiance is 0.336 see you are not able to calculate you are not able to calculate and get and arrive at the distance. So, it is 0.3155 into 10 to the power minus 4 3.3155 10 is to power minus 4 you said it cannot be. Look at this this itself is 10 to the power minus 3 or the order. No sir it is 0.03306. So, it is sad that you think that calculation is something which is very boring or it is a donkey's job you are not able to put a donkey in job. So, donkey will be proud 0.0336 sir 3.365 to 10 to the power minus 2 ok I will tell you the correct one. It is 3.32 into 10 to the power minus 2 yeah we just calculated it further yeah yeah. You have this American accent. So, it is pi and take pi is 3.14 into next. What? So, can we take the degrees in terms of pi and take that pi is 3.14 by doing the calculation. Yeah pi is 3.14 you can do that, but y 2 you know complicated I mean y 2 increase the calculation you should if you remember what is 1 degree what is 1 minute you can just use it otherwise you are telling me you will first derive what is 1 degree in terms of radians what is 1 second in terms of radians and then you will do that definitely ok. We did just that to find out how much is 1 degree and how much is 1 minute all right. Now, you have the angle in terms of radians can you calculate the distance of moon from the earth by the way these are the true values. So, if the distance 3.8 4 into 10 to the power of 8 meter yeah. So, let us say this is the distance this distance is small d. So, what can I say capital D divided by small d is what arc length divided by radius this should be equal to this angle. So, how much you got small d as. Sir I am get 3.84 3.84 into 10 to the power 8 10 to the power 8 it is actually around 20 times the diameter of the earth a distance of moon from the earth ok. Let us do one more numerical all of you get it right only mistake you can make is calculation error, but if nobody gives a damn whether you make calculation error or some other error conceptual error it should get minus 1 only understood. It is the exam you are writing they do not care how you getting the answer ok. They just care about the final answer nothing else and understood all of you ok next question all right write down suns angular diameter suns angular diameter is 1920 minutes ok. The distance of sun from the earth distance of sun from the earth is 1.496 oh you remember these values this is the distance of earth from the sun ok how far the Jupiter is from the mass further than that not from the sun no yes yes it is further than this. You need to find diameter of the sun how much is the diameter of this sun. So, what is the angular diameter? It is basic angle subtended by the diameter of this sun the most obvious thing. So, but a subtended where? On earth. On earth it should be where are the humans. Sun is bigger I understand what you are saying. So, but then treat earth as a point and sun as a bigger object see it is a suns diameter that is making angle and it will be making angle at a vertical location of the earth. There are some approximations. So, you might be wondering it is from the bottom surface of the sun or from the center of the sun more or less they are same because the distance of earth from the sun is much larger than any dimension of earth or sun. How much are you after approximate like 1 or 2 decimal points that is it do not be like you know 2.3679532. Stop at 1 or 2 decimal points because these values are approximate only we are not the exact value. So, why you are calculating up to 10 decimal places that is approximate value itself anybody got the answer before 8.4. So, first step is to draw the diagram itself. That is wrong which you got. So, it is 8.89 into 10 to the power 11. Oh wait I am sorry about it in the question it is written minutes, but actually it is in the solution they are treating it seconds. So, it is seconds 1, 9, 2, 0 seconds. Sorry about that. Can we just keep it as. As if all of you are getting right answers oh my god what. You get this I mean there is a multiplicative factor right. So, just ok now that you know it is correct all of you should get the right answer. So, this is the diagram this is the sun this is let us say earth the diameter of the sun makes 1, 9, 2, 0 seconds the angle this is diameter d and this is the distance of the sun from the earth. So, how we will go about this capital D divided by small d should be equal to what? 1, 9, 2, 0 into. Into 4, 4, 3, 4, 5, 6. That is a minus 6 of 4. So, 6. I got this divided by 6. So, you know the small d value you can find the capital D ok and it is 1.39 into 10 is upon 9 diameter of the sun is 1.39 into 10 is upon 9 meters which is around 100 times the diameter of the earth. Then you have to convert minutes into radiance also ok you have to use SI units. I got 1.39, but not a little 10 power 9. I know. So, we know that. I got this. All right. Yeah, I got this. Good. Ok. So, all of you understood how we can use the property of angle to determine the large distances ok. So, this is the calculation of large distances. We are indirectly calculating the distance large distances by just using the definition of angles ok. Now, stop talking. Now, we have to also come up with a method to calculate the small sizes, small lengths because the lengths we are dealing in physics they are like this you know. For example, size of a proton is 10 is minus 15 meters and distance of the diameter of observable universe is 10 is power 26 meters. So, we are dealing from 10 is power minus 15 to 10 is power 26 meters and we as humans can calculate only let us say from 10 is power minus 5 meters or 10 is power minus directly I am saying directly using a scale or something. We can only calculate from 10 is power minus 4 times 4 minus 5 meters using screw gauge or things like that. To let us say directly if you want to calculate let us take 1 kilometer which is 10 is power 3. So, the range is from 10 is power minus 5 to 10 is power 3 meters for direct measurement using scale or whatever. But the range we are dealing with in physics is 10 is power minus 15 to 10 is power 26. So, there are indirect methods to determine the large distances. There should be indirect method to determine the small distance also. You cannot put a scale to measure the distance of electron from the nucleus. There should be some indirect method like these. This method is for estimation of large distances. Now, there are various indirect method. This is just one of the method to find the large distances. Similarly, we are now talking about indirect method to measure the small distances. Small distances as in size of a proton or let us say size of an atom things like that. So, one particular method is in our syllabus because you can practically do that.