 That is one what is coal attitude coal attitude same attitude first do this coal attitude is something else it is a complementary angle of a given attitude 90 minus latitude angle did you get this Latitude is a complementary angle of, sorry, coal attitude is a complementary angle of the latitude, 90 minus latitude angle, a line, a earth and a satellite are. So, basically this angle is a coal attitude angle. This is the equilateral plane, this is the latitude angle. First one, how many you got it? First one, only 2, 3, did you get this? Don't forget about that, first focus here. The radius of a planet is r1 and satellite revolves around it in a circle of radius r2. The revolution is t. I think this is simple. So, mass of the satellite v square by r2 is equal to g mass of the planet m divided by r2 square. So, you will get velocity to be equal to root over gm by r2, 2 pi r2 by v is the time period. Basically mass of the planet is not given to us. Accessing due to gravity for the planet just like earth will be gm divided by r1 square. So, get the mass of planet by substituting value of velocity over here. In terms of t, you get m and then substitute here. You get the value of g. Same thing you guys have done? There is a 40 by t square into r2 cube by r1 square. 4 pi square? Yes, and I have looked to make it pi square equal to 10. 4 pi square r2 cube divided by t square r1 square. So, the next one sin was 0.15. But you just put like the height of the geostation. See guys, listen here, all of you. Geostationary satellite, geostationary satellite will be where? Will be somewhere here, right? It will be in the plane of the rotation that you have discussed. It will rotate like that. Are you getting it? Once it gives out signal, it will only give out signal here and there. It can't give signal beyond this. It can't give signal from here till there. Yes or no? It can give signal only from here till there. Signals can't cross the earth and reach here. So, there is a significance to this angle and this angle is called co-lattitude angle. It is co-sealing though. And this angle is latitude angle, lambda it is. And this is 90 degree. So, lambda plus c is 90 degree. Now, what do you say? So, for the geostationary satellite, why can't it go about a different diameter? We discussed it. Last class we have discussed it. So, we discussed why it has to be about the diameter, but not why it has to be perpendicular to the rotation axis of earth. We discussed that also. It has to be along this plane. If it has to be, if you are telling me like this here, it can't rotate like this. No sir, but why can't it rotate from that point about? Like this? Yeah. But earth is rotating like this, no? Why will that change like this? Why not? Earth is rotating like this and your satellite is rotating like that. So, how can you be about the same point? You have to rotate with the earth. Okay sir, but it will still work. No, it won't work. No sir, it won't be geostationary, but that satellite can still exist. Hi, it can exist. You can throw an object and rotate like that. No problem, but geostationary satellite will only lie in the plane of the equatorial like that. Getting it? So, we need to find this angle basically. How will you find that angle? Radius of earth is given. What else is given? We know the height of the geostationary satellites. This h is given and this is r anyways. So, hypothesis is given, r is given. So, sine of co-latitude is r divided by r plus h. Do you know what is h? 35,800. So, you can find out. Sine of critical comes out to be 0.15, sine of co-latitude. Okay, I am giving you 15 minutes to complete both of them. Get the answer, okay? Can you get the answer? Sir, is that? I am not asking you to speak. Please solve quickly and keep quiet once you are done. All of you attempt it? 8 kilometers per second. All of you should get the answer. Sir, it is equal to 3.8. See, if you remember a few things like escape velocity 2GRE is 11.2 kilometers per second. You can use this expression directly. You can compare whatever you have with these values and get the answer. You do not have to substitute G and M again. No, it is 5.6. Take that. Sir, it is the first one kilometer per second and the second one 10 kilometers per second. All of you do this. All of you should get the answer. 6,040 kilometers is the radius also. Okay, so it goes the maximum height of the radius of the earth. So, U1 plus K1 is equal to U2 plus K2. U1 is what? Stop talking. GMM by, this is U1 at the earth surface plus kinetic energy half M into V square. This is equal to U2 minus of GMM by what? 2R plus 0, small and get cancelled away. So, velocity will come out to be how much? Formula here, what are you getting here? Root over GM by R. 2GM by R is 11.2. So, answer is 11.2 divided by root 2, which is roughly 7.9 kilometers per second. 11.2 divided by root 2. You do not have to substitute what is G, what is ME and all that. You already know this value, escape velocity. The value of G is GMM by RE square, this is 9.8. You have to use these values. Okay, usually you never have to substitute what is capital G and mass of earth. You can always use the already known values to get the answer. So, the second one is approximately 10 kilometers per second. 10? Yes. 10 approximately. Industrial space. Yes, 10. Okay, it is fired with 15 kilometers per second, which is higher than the escape velocity. So, it will go to infinity and still have some kinetic energy. If you fire with the escape velocity at infinity, its kinetic energy becomes 0. That is how we derived it. Okay. So, U1 plus K1, where K1 is half MV square plus U1 GMM by RE. This is equal to potential G is 0 at infinity plus kinetic energy half MV1 square. So, V1 will come out to be root over V square minus 2 GMM by RE. Now, how you proceed with this? I know that V square is how much? 15 square. This is 15 square and this is how much? 11.2 square. And this is what? A plus B and A minus B. 15 minus 11.2 into 15 plus 11.2. Yes, you look at roughly, this is 100, root over 100 is roughly 10. So, you need to understand these tricks. Don't be like a fool, start substituting GMM and RE here and... Should be K per second. What? K per second. Oh man, I am used to writing KM per hour. Okay, last question of HC-Rama. We have done entire HC-Rama sitting here in just 3 hours. So, it is not that you have lack of time. Less than 3 hours, 2 and half hours. It is not lack of time which is stopping you. It is your attention which is focus attention which is lacking. Not lack of time. Entire HC-Rama. Solid? This is far-side radius. Yes, this far-side radius. Joby radius is equal to midnight. So, it is a black hole. Even light can't escape. This is the last question. Don't make silly room in the last question. So, is it 8,004 centimeters? Kilometers. So, is it 14.3 to 10 to the power minus 10? So, is it 8.8 to 10 to the power minus 3? Yes, I got that. So, it is 8, right? Yes, it is 8.8. So, earth has to get compressed to 9 mm. That is like 0.1 centimeter radius sphere. To become a black hole. Same mass should be condensed to 0.1 centimeter radius sphere. Are you able to get it? Yes. Get the answer. Not only earth. All the people living in and all the plants and animal everybody should get compressed. Do you think as people are getting born the mass of earth is increasing? Yes. It is a big concern. It is all the redistribution of the mass that is happening. So, all the elements from one place, whatever people eat, all that get transformed into a life, a person get born, died, against all the minerals get dissolved in the 5 elements. Then again they will recombine to create a human. So, most of you have not got it. How many of you got it? So, SK philosophy formula is what root 2 g m divided by the radius. This has to be equal to 3 into 10 is for it. Right now if you put r is radius of earth it was 11.2. So, you can say that 2 g m e divided by radius of earth it was 11.2 kilometers per second. So, 1.1 into 10 is per 4. So, now divide it. So, root over r e by r is equal to 3 divided by 1.1 into 10 is power 4. 3 divided by 1.1 think. So, r by r e 1.1 this 10 is power minus 4 minus 4. This much meters. Oh, I have to multiply the radius of earth with r. Yes, I am correct. So, r is 1.21 by 9 into 10 is power minus 8. 6.4 into 10 is power 6. Okay, you do not have to put the value of g and m e. Again we can avoid that. But if there is lack of problem practice you will put it. Fine, so these are the questions from this chapter. They are all mains level. So, advanced level we could not do.