 Hello, everyone. Welcome to a video lecture on Arbital Parameters. Myself, K. R. Biradar, assistant professor, department of electronics and telecommunication engineering, Walsh and the Institute of Technology, Solapur. Let us start with the learning outcomes first. At the end of this session, you will be able to illustrate orbital parameters with their expressions. First one is apogee. Apogee is the point on the satellite orbit that is at the furthest distance from the center of the earth and it is denoted by A and it is given by capital A which is equal to small a into 1 plus e, where small a is the semi major axis e is the eccentricity. You can see this diagram there is at earth. So, satellite is revolving around this in an elliptical path. The point from the earth on the orbit which is furthest or longest path is called apogee. So, you can find it is revolving in this elliptical path when it reaches at this place. This is a furthest distance from this satellite to the earth center that is represented as apogee. Then what is semi major axis? When you have a ellipse in it consists of two focuses. This is focus 1 and focus 2 and it is a center of the ellipse. Satellite is revolving in the elliptical path. The distance or furthest distance from one point on the orbit to the another point on the orbit and crosses at the center of the ellipse. From this distance to this distance this is called major axis. When you want to divide r by 2 then it is semi major axis and so, shortest distance of 2 points in orbit that is this point and this point when you join these 2 that is called minor axis. Half of this will be semi minor axis. Perigee is the point on the orbit that is nearest to the center of the earth and it is denoted by capital P and it is given by capital P is equal to small a into 1 minus e. Same diagram you can see here from the center of the earth and the point on the orbit which is closest to the center of the earth. These two distances is called the perigee. So, you can find when satellite comes at this point which is a closest distance from the earth center that is the perigee. Next we will define semi major axis and semi minor axis. These are the geometrical parameters of an elliptical orbit and these are calculated from the known values of apogee and perigee. If I know apogee and perigee I can calculate semi major axis and semi minor axis. Again you see this diagram. Here sun and the planets are considered. This is an elliptical shape. The planets are evolving in this elliptical path and so this ellipse forms two focuses F1 and F2. Sun is at one of the focus sun is at F1 now. When you form a distance or furthest distance on this elliptical path we need to consider two points point 1 and point 2. This distance is called major axis. Half of it will be it is semi major axis and with respect to minor axis. So, shortest distance between two points and crossing to the center of the ellipse that is called the minor axis. So, half of it will be considered semi minor axis. Semi major axis is represented by A and major axis is equal to 2A and semi minor axis is represented by small b and minor axis will be equal to 2B and semi major axis that is A is equal to capital A plus capital P divided by 2. Capital A is apogee and capital P is the perigee. Similarly, semi minor axis can be calculated A minus P divided by 2. From the basics of mathematics we can define what is the eccentricity of ellipse E? Pass the video and think and write your answer. I think you might have written the answer. The eccentricity E of an ellipse is defined as the ratio of the distance between the center of the ellipse and the focus C to the semi major axis. You can see here this ellipse has a one focus and it has center the distance between these two is C and semi major axis is A. So, the ratio of these two C divided by A gives the eccentricity. E eccentricity can be calculated E is equal to square root of small s square minus small b square divided by A. In this slide we shall see about ascending and descending nodes. How do you define the ascending and descending nodes? The satellite orbit cuts the equatorial plane at two points. First one is at ascending node and second one is at descending node. How do you define it ascending node? The point where the orbit crosses the equatorial plane going from south to north. So, satellite is revolving in this direction. It is moving from south to north and it crosses at cuts the equatorial plane at particular point. This point is called ascending node. What about descending node? The point where the orbit crosses the equatorial plane going from north to south. Satellite is moving from north to south even it cuts at equatorial plane that is called the descending node. You can see this diagram. So, these are the two parameters and that first one is period. This is also called orbital period. Period is a time it takes for a satellite to complete one orbit. This time is also called as site real time. So, satellite to complete one path how much time it takes that is called the period of a satellite. Height of a satellite it is height or altitude from satellite to earth surface. Now, we need to consider here this point from the surface of the earth to the satellite distance that is called the height of the satellite. What about radius of orbit? Is the sum of satellite height and the radius of earth. Here the height of the satellite plus radius of the earth from the earth center to the satellite that distance is called radius of orbit. Inclineation angle the angle between orbital plane and earth's equatorial plane. Line of nodes the line joining the ascending and descending nodes through the center of the earth which is going to join the line from ascending and descending nodes through the center of the earth. Sub-satellite point this is the path traced out on the earth surface directly below the satellite. Now, you can see this is my earth satellite is revolving in this path ok. When it traced the on the surface of the earth this path where it form a traced path that is called the sub-satellite path line of upsides which denotes the distance of the line that joins the nearest and furthest points across an orbit passing through the center. It also refers simply to the extreme range of an object orbiting a host body. When I draw a line from the furthest point to the nearest point on the orbit from this earth's center and also it passes at center of the earth that refers to the line of upsides. You can see this diagram this is furthest distance from the center of the earth and this is the closest or nearest distance from the center of the earth. Join these two points by passing through center of there that is called the line of upsides prograde and retrograde orbit an orbit in which the satellite moves in the same direction as the earth's direction. You can see this diagram this is an orbit where the satellite moves in the same direction of the earth that is called the prograde orbit. Otherwise an orbit in which the satellite moves in a direction counter to the earth's rotation. Please note most satellite are launched in a prograde orbit because the earth's rotational velocity provides part of the orbital velocity with a consequent saving in launch energy. These are the references used to prepare the above PPT. Thank you.