 Hello everyone. I am Mr. Praveen Ellapa Kumbar. Today we want to see numerical on the orbital parameters. The learning outcome of this topic is at the end of the session student will be able to illustrate the concept of orbital parameters. The contents of these topics are here we want to see two numerical problems. So we will start the first problem. So the first example is a satellite is orbiting in a circular orbit which is 1000 kemi away from the surface of the earth. Then how many times in a day the satellite will be overhead from a particular location on the earth. So in this given data I want to draw one diagram. This is a center of the earth. Now this is the position of the satellite. Suppose we consider this is a satellite. So we know that this will be the radius of the satellite and this will be the height from the surface of the earth. That is we know that that is 1000 km away from the surface of the earth. And we know the radius of the earth is 6378 km. So the total distance of the center of the earth here is so the total distance. So I want to calculate here distance from the center of the earth is 1000 plus 6378 that is 7378 km. So according to the Kepler's law the formula of the time that is the time we calculate the time here 4 pi square r cube divided by mu. Where mu is the Kepler's constant. So mu is equal to everyone remember the mu value. So mu value is 3.986 into 10 raised to 5 km cube per second square. This is the value of the mu. So we want to put this value into this equation what we get? We get t is equal to 4 pi square into r cube. r is what 7378 km 7378 bracket cube divided by mu. What is mu? 3.986 into 10 raised to 5. So after this multiplication what we get? After this numerator multiplication we get as 1.5 into 10 raised to 13 divided by 3.986 into 10 raised to 5. So after this solving or after the simplification of this one we get square root of we get 39.77 into 10 raised to 6. So this is the answer. After this solving the square root of this one we get what is the answer? We get 6306.94 second. So this is what calculation of the time. Now here what we want to calculate? Here we want to calculate how many times a satellite in a day will be overhead. So the third point I want to solve here because for the understanding purpose. So third point how many seconds in a one day? So time in a one day I want to convert that into the second that is second is equal to 24 hours into 60 into 60. We want to convert into the second that will become as 86400 second. This we get this one. So what we calculate? Here we calculate therefore the number of times the satellite will be overhead is I want to divide that things. So this one 86400 divided by this 6306.94 so it nearly approximately after division you get the answer is 13 times. This answer is 13. So answer is what? 13. So I want to write how many times? 13 times. So in a one day the satellite will be overhead how many times? 13 times. The satellite will be third the satellite will be the 13 times. So now we want to consider the second example. Let us see the second example. So now let us see the second example. The determine the orbital height in kilometer of a satellite orbiting in a circular orbit with orbital period of a sideral day. So we want to calculate the orbital height for the sideral day. So first of all for the calculation of these things we want to know the concept of the sideral day. For the sideral day what is the time period? So for the sideral day the time period is 23 hours 56 minutes and 4.091 second. But our task is we want to convert this thing into the second. So for the conversion of this into the second. So first of all I want to convert 23 hours. So how we convert the 23 hours? 23 into seconds for the multiplication 3600. So we get 82800 second. So now I want to convert second thing what? Second thing I want to convert 56 minutes into the second. So 56 into multiply by 60 I want to convert minute into the second. So what we get? 33600 second. So the next thing is 4.091 second. So I don't no need to convert that in second because that already present in second. So I want to add these things. So after the addition of these things what we get? 86164.09 second. So I get this is a time for the sideral period. So now I want to calculate the height for the calculation of height means what? R I want to first calculate. For that purpose I want to apply again the K plus law. What is that K plus law? So the K plus law is according to the K plus law. What is that? R is equal to T square mu where mu is a K plus constant. T square mu is divided by 4 pi square raise to 1 by 3. So this is the formula. So I want to put the values. So we know that T is what? T is we calculated that 86164.09 bracket square. Mu value we know that that is a K plus constant. We put the values into this equation what we get? Mu is a 3.986 into 10 raise to 5. So divided by 4 pi square raise to 1 by 3. So after the numerator solving what we get? 2.959 into 10 raise to 15 divided by 4 pi square divided by 4 pi square raise to 1 by 3 raise to 1 by 3. So this after division of these things we get 7.49 into 10 raise to 13 raise to 1 by 3. So we get this is R. So after the simplification we want to again we want to do the simplification. So after this one I will get 42164.12 kilometer. So this is what I want to calculate the R. I want to calculate the here R. So I want to calculate the orbital height for that one I for the calculation here what you want to calculate orbital height. I want to calculate the orbital height for the calculation of orbital height. So given distance R minus the radius of the earth you get the orbital height therefore orbital height is equal to R minus this R is what? 42164.12 minus radius of the earth. What is the radius of the earth? 6378 is the radius of the earth. So after the subtraction of that what we get? 35786 kilometer you get the orbital height. So everyone remember for the orbital height. So orbital height means what? I want this suppose this is the earth okay this is what this is earth and here is a satellite position exactly. So I want to calculate what? I want to calculate this much height only. This is called as a orbital height. Okay this is called as a orbital height. So whatever this R I calculated this R I calculated this is a total R. This is a total R. So I want this one much. So from this R if you subtract this radius. If you subtract this radius you get this orbital height. So the orbital height is what? Orbital height is equal to total radius. Total radius that is R minus earth radius. So that R is calculated this equation number one. R is calculated from the equation number one. If you put this value that is 42164.12 minus what is the earth of radius of the earth? 6378 after subtraction you get 35786 kilometer. The references for these topics is thank you.