 I am Mr Praveen Yalapa Kumbar. Today we want to see numerical sun orbital parameters. The learning outcome of this topic is at the end of the session student will be able to illustrate the concept of the orbital parameters. The contents of these topics are here we want to see to now the first problem is a satellite is orbiting in an elliptical orbit with apogee height at a 20,000 kilometer and the perigee height at a 400 kilometer. So, we want to calculate here the ratio of velocity at perigee to that of apogee will be. So, before solving this problem first of all we want to try to understand the concept of apogee and the perigee. So, basically what will happen my friends this is a earth. Suppose this is earth that I want to write this is earth and satellite is orbiting the satellite is orbiting in a elliptical orbit satellite is orbiting in elliptical orbit. Suppose the satellite is at a point here. So, this is satellite. Now, this we called as a satellite. Now my friends the perigee and apogee the perigee means nearest distance. So, if in this diagram if you observe the perigee is this one this one is called as a perigee. The perigee means what nearest distance and the apogee will be the farthest distance longest distance that is called as apogee this is called as apogee and this is called as a perigee. So, now for solving this type of a problem first of all you write down given data. So, what is a given data the apogee height. So, I will write given data here given data. So, I will write here given data that is what the first of all the apogee height what is the apogee height apogee height is equal to 20,000 kilometer and what is the perigee height perigee height will be 400 kilometer and what we find out the ratio of velocity at perigee to that of velocity at apogee. So, I will find out this one. So, first of all you calculate the velocity of perigee then you calculate the velocity of apogee and take the ratio of that one you get the answer of velocity at perigee and the velocity of apogee. So, before solving this type of a problem you know the what is the radius of the earth. So, the radius of the earth is so radius of earth is equal to 6378 kilometer that that we want to know these things this is we know radius of the earth is 6378 kilometer. So, after that one I want to calculate I want to write down distance of distance of apogee distance of apogee from I want to calculate now distance of apogee from where from the center of the earth from the center of the earth. So, I want to calculate now distance of apogee from the from center of earth. So, what is what we come that one that is called as apogee that is distance that we treated as RA. So, how we calculate? So, we made the addition of 6 this is a radius of the earth is what radius of the earth is 6378 plus what is the apogee height 20000. So, what what we get 6378 plus 20000 we get 26378 kilometer. So, we get the distance of apogee from the center of the earth. Now, after that one we calculate the same distance of apogee distance of apogee from where from again we calculate from center of earth from the center of earth. So, distance of apogee I treated as that is RP. So, what we get 6378 is the radius of the earth plus 400 kilometer. So, what we get 6378 plus 400 we get 6778 kilometer. So, this is the distance of perigee from the center of the earth now after that one. So, what is our we want to calculate velocity of perigee and velocity of apogee. So, what is the formula of okay. So, before that one we want to calculate we want to calculate the semi major axis we want to calculate the semi major axis. So, semi major axis is equal to the semi major axis is equal to distance of apogee from the center of earth that is we call as RA plus distance of perigee from the center of earth that is RP divided by 2. So, we want to put the value of RA and RP into this equation that is 26378 plus what is RP that is 6778 divided by 2. So, after this solving this one you get. So, after the addition you get 33156 divided by 2. So, after solving you get 16578 kilometer 16578 kilometer is velocity at perigee to the velocity of apogee. So, I want to write here velocity of perigee divided by velocity at apogee. So, what is the formula for that one the formula is. So, I will write velocity as BP divided by velocity at VA. So, what is the formula the formula is 2 by RP minus 1 by r divided by. So, I will write here for this one again 2 by RA divided by minus 1 by r this is the formula for the velocity of perigee and velocity of apogee. So, now we want to put the values into this equation. So, what we get? So, we know that RP means what my friends RP means perigee from the center of the earth RA is a what the apogee from the center of the earth that we know the put the values there and r means semi major axis. So, the simply we want to put this values into this equation what we well first of all we calculate the VP. So, what is a VP? VP is under square root of 2 divided by RP minus 1 by r. So, we put the values what is a RP? RP is a 2 divided by 2 divided by 6778 minus 1 by r 1 by r means what 1 by 16578. So, after the solving this equation we get 2.34 into 10 raise to minus 4 2.34 into 10 raise to minus 4 after solving this get. So, after the square root of this one we get 0.01532 is a VP that is velocity at the perigee the same we want to calculate for the velocity at the apogee. So, I will write down this is equation number 1. I want to calculate the velocity that is at VA that is at VA. So, for the VA what is a formula? The formula is 2 by RA minus 1 by r. So, we want to put these values into this above equation what we get? We get 2 by what is the RA? RA is a 26378 minus 1 by r. What is a r that we know 16578? So, after you want to solve this one. So, after the solving this one we get 1.54 into 10 raise to minus 5. So, square root of this one we get 3.93 into 10 raise to minus 3. Okay, this is a what VA? This is a what VA? So, this is a equation number 2. What will come? Therefore, I want to write velocity of velocity of perigee divided by velocity at apogee. So, put the equation number 1 and 2 here what we get? So, 0 velocity at perigee what 0.01532 divided by 3.93 into 10 raise to minus 3. So, after the solving this one we get 3.89. So, answer is what? 3.89. So, the ratio of the velocity at perigee to that apogee will be 3.89. So, this will be the answer. Now, we want to consider the second problem. The second problem is the difference between the farthest and closest point in a satellite elliptical orbit from the surface of the earth is 30000 kilometer and sum of distance is 50000 kilometer. If the mean radius of the earth is considered to be 6400 kilometer, determine the eccentricity and the length of the semi major axis of the orbit. So, here I want to write down first given data from this example apogee minus perigee equal to 30000. Why? Because when we made a subtraction between this apogee and the perigee what will happen due to the subtraction the radius of each is cancelled. The radius is cancelled in the subtraction. Therefore, this apogee minus perigee is 30000. So, this is a given point first. Now, second point I want to calculate the apogee plus perigee. So, for that apogee plus perigee is apogee plus perigee is equal to there is a formula. We want to put that formula. So, after that putting the formula what we get 50000 plus 2 into 6400 kilometer. So, after the putting these values and after solving this what we get? We get 62800 kilometer. Now, we want to calculate what I want to calculate. So, what we want to calculate? We want to calculate eccentricity. We want to calculate the eccentricity. The second thing I want to calculate the length of the semi major axis. So, what is the formula for the eccentricity? So, eccentricity is equal to apogee minus perigee divided by apogee plus perigee. So, apogee plus perigee. So, this is a formula. We want to put these values into this above equation what we get? 30000 divided by 30000 divided by 62800. So, after the division of the equation what we get? Of these things we get 0.47 is the eccentricity 0.47 is the eccentricity of this equation. So, now I want to calculate what? Now I want to calculate the semi major axis. So, for the calculation of a semi major axis. So, we know that in the previous problem we solve that the semi major axis is equal to apogee plus perigee divided by 2. So, I want to write semi major axis is equal to apogee plus perigee divided by 2. So, we want to put these values into this equation. So, what we get? Apogee plus perigee that is we want to calculate here apogee plus perigee is what? 62800 divided by 2. So, after the solving this one what we get? 31400 kilometer. The references for this topic is thank you.