noc19-ae08-lec24

Let us start this lecture with a thought process from Mahatma Gandhi, the father of our nation. He says what is really needed to make democracy function is not knowledge of facts, but the right education. This is really a very important statement as we are living in a democratic country and to make our democracy vibrant we need to have a right education. Unfortunately we are not imparting that kind of education at this moment. So we need to improve upon it. So let us recall in the last lecture what we learnt about, we have basically looked at the space flights and its orbit and we derived relationship for time period and then angular velocity and orbital velocity for a circular orbit when the satellite is moving in a circular orbit. And then we use the Kepler law and also basically discuss about relationship for orbital velocity around an elliptical orbit. And later on we looked at various types of orbits what we can and today we will be discussing more about earth reference orbit. So there are several types of earth reference orbits have been devised by various scientists, but we will be discussing only five of them and which are being used and one of them is your equatorial orbit as its name indicates that if we it will be basically moving around the equator. So if you look at this is your earth and there will be the north pole and this is your equator, I can say this is your equator and this is your north pole and south pole and this is the west and this is your east direction. Of course keep in mind that the earth will be moving around something around this axis will be some rotation omega which will be moving and making certain angle and keep in mind that this is your equator and if that orbit is moving around this equator we call an equator. Keep in mind that the earth is always moves from west to east direction that is the way it will be moving and so if this plane the an orbit which is around the equator and the satellite is moving along the direction of the earth as the earth is moving from west to east then we call as a equatorial orbit. Keep in mind that this is being used for look at the weather conditions and communication also in the equatorial region and it cannot really see the polar regions in the north and south poles like these are poles basically north pole and south pole and it is easier to really launch the satellite or the rocket vehicle from the nearer to the equator. It is advantageous for India to have this equatorial orbit or to place the satellite on the equatorial orbit and but the disadvantage with this equatorial orbit is that it can see only the regions around this and then as I told earlier the polar regions and other places where it is having importance it cannot really scan. Therefore and in this equatorial orbit keep in mind that along with the equator this angle the inclination angle of the orbit with the equator is zero and when this inclination angle of the orbit with the equator is 90 degree we call it as a polar orbit and polar orbit can cover a larger distance because of fact that this earth will be rotated around that. So, it will be scanning over the larger regions and so therefore it is being used and it will be remaining something around 11 hours on this polar regions that is why polar it is being used very much and but in order to have a larger surface area being scanned by the satellite which is moving in the orbit the people have developed a another highly elliptical orbits that we will be discussing later on. And if this inclination angle becomes 180 degree then it become a equatorial orbit but we call it as a retrograde equatorial orbit because of fact that it will be moving the satellite will be moving in the opposite direction to the rotation of the earth. But the advantages of this is that it can scan very quickly because it is moving in the opposite direction but however it is very difficult to put the satellite in the retrograde equatorial orbit because of fact that you need to have a higher amount of energy and to put that way. So therefore it is not being very much used but however one can think of doing that. As I told earlier that to get a little more scanner as compared to the polar orbit which will be discussing little later on there is a orbit which is known as the Molniya orbit which was devised by Russian scientist and is being used by Russian people earlier days. It is a highly elliptical orbit with half major axis of around something 46000 kilometer and minor axis around 6800 kilometer with a inclination angle of 63.46 degree. So that means this will be in this case it will be like that somewhere 60 degree. It is very useful because of fact that it can provide a wider coverage area over the high altitudes as it remains in north hemisphere around 11 hours. So that is why it is being used. So we will be now discussing another very important and profusely used orbit is known as the geostationary orbit. And let us take this is our earth planet and this is our orbit and in which the satellite is moving. And keep in mind that the beauty of this geostationary orbit is that when it is moving let us say this is moving with certain velocities, orbital velocities and such that it will be moving around earth in around something 24 hours. Exactly if you look at it will be moving for a time period of 23 hours 56 minutes and 4 second which is same as that of the earth. Therefore it will be looking as if it is a stationary if you are observing this satellite from the same space and throughout the day. That is the beauty of this geostationary orbit and which is being used and provided the height here altitude is something around 35,786 kilometer. And of course this we will calculate how you can get this little later on and keep in mind that geostationary orbit is very important and this is also moves around the equator. And it moves along with the direction of the earth motion or the movement. So we will be discussing more about that now we will discuss about the polar orbit. So polar orbit as I told the inclination angle between the equator and the orbit is around is equal to the 90 degrees. And this shows the images of that and let us say this satellite is around here in this location it is moving around it is revolving around this directions. And this is your earth and when the earth is rotating in this direction from west to east it will be scanning all the places from the top to bottom as it is moving around. So it will be scanning entire range. So that is the good part of that and if this polar orbit can be precessed at the same period during which the earth precesses the solar orbit then it is known as the sun synchronous orbit. That means it is synchronized with the sun such that the satellite will be looking at the earth when it is illumined with the sun rays all the time. To explain it further let us look at what is happening the sun is here and the let us say this is your satellite orbits and the satellite orbit surface over here and this is your north side and if it is moving then it could see that this is illuminated and the satellite can see this portion. So of course as it is moving along the earth so this is the winter season this may be spring season but again the satellite will be looking at the earth here and it is illumined by the sun and all other throughout the year it will be like that. So that whenever the satellite is looking at the earth and the earth is illumined by the sun. So that is the beauty of sun synchronous as a result it can provide continuous illumination from the sun on the earth viewed from the sun synchronous polar satellite. This is special sun synchronous satellite is basically special kind of polar satellite and sun synchronous satellite orbit is located about something around 715 kilometer from the surface of the earth. So this can monitor strong storms that move across the poles whereas the geostationary satellite cannot view the things whatever is happening around the poles and that is the limitation of the geostationary orbit and whenever you want to have certain things in the near the polar region nowadays it is very important because of your ice being melting out due to the global warming. So therefore you will have to keep track of it and polar satellite is very important and so on. The beauty of sun synchronous satellite is that it can be used for imaging for weather predictions and other things as you need not to have a extra care to take the photographs and then these things. Of course for the geostationary orbits can be used for communications and other purposes. So now let us look at geostationary orbit and as I told earlier this is let us say planet here and we call it basically earth and this is your satellite which is moving at a orbital velocity of V naught and when you look at it basically it is geostationary satellite orbits around the earth as fast as the earth spins in the circular orbit in the planet of the earth equator with a radius of something 42,164 kilometer. That means from this to that center to center this distance will be r and that is equal to if you look at this is your r and r is equal to 42,164 kilometer. But if you look at this altitude this is your altitude right this is your h and keep in mind that this is your r p r e I can say the radius of the earth of earth right and that is h in this case this h will be this is your h, h will be equal to 35,786 kilometer. When the satellite will be placed at an altitude of 35,786 kilometer from the surface of the earth right in a circular orbit around the equator we call it as a geostationary orbit and this orbit allow the satellite to continuously look at the same spot on the earth because whenever you are looking at this earth surface and you will be looking at the same spot because as it you are moving with the same angular velocity with which earth is also moving. So, that is the beauty of stationary in other words if one could see a satellite in geostationary orbit it would appear to over at the same point in the sky. That means if you could look at good telescope the satellite and then you will find as if it is there in the same space same point in the sky. So, but the problem with this satellite as I told earlier that is basically that it can see around this equator equatorial region and it will be also cannot see the other portion of the polar and the other portions cannot scan the entire globe. So, for that people devise another orbit which is similar to the geostationary orbit and the only difference is the angle of inclination is not 0 it is different and generally geostationary orbit around the equator inclination angle is 0, but this geosynchronous orbit it can be of any angle and of various geosynchronous orbits are being devised and used by the people. So, lot of satellite you can put it. So, the geosynchronous orbit is very useful for locating the position of hurricanes monitoring the developing the CVS terms in around the globe and the various regions depending on what is your interest and therefore, geosynchronous orbit is being used profusely and keep in mind that all geostationary orbits are also geosynchronous. But not all geosynchronous orbits are geostationary that you should keep in mind and now we will be looking at basically little bit more about geostationary orbit and keep in mind that this geostationary orbit was basically proposed first by the George O. Smith in one of his scientific friction book which is known as Venus equilateral. Later on it was also used by the Arthur Clark in 1945 and of course, the George O. Smith proposed this thing in a very crude manner in his scientific friction book, but not really had given any detail about it. Whereas, the Clark Arthur Clark had given little detail about it one of the scientific magazines and if you keep in mind that it basically if the satellite is placed in the equatorial orbit moves at the same orbital velocity in the same direction of that of the earth, it appears to be stationary to an observer on the earth. Therefore, that we call it as a geostationary orbit and keep in mind that we need to now find out what will be the radius or the distance between the satellite and the center of the earth. So, for that as I told like the angular velocity of the satellite around the satellite moving on this orbit is same as that of the earth. That means omega e is equal to omega of the satellite and we know that this omega of the e is equal to root over g and m e. This is basically mass of the earth and divided by this r g q because if this is being orbiting around this earth like if this is your earth and let us say this is your satellite which is having here then this distance is r geosynchronous orbit or geostationary orbit. So, this is your r. So, from this you can get very easily I can get from here this is your r g is nothing but your g m e by omega square and that is q. So, if I know this omega of the earth here and we know the gravitational constant, we know the mass of the earth. So, we can find out what is the r g. So, that is angular velocity of the earth if you look at that is basically 2 pi into your time. Time if you look at this is as I told 23 hours 56 minutes and 4 second, but if you take 24 hours the number what we will be getting is would not be right. So, therefore, you will take 2 pi into 23.9344 hours into 3600 that is your second. You can convert and that happens to be 7.292 into 10 power minus 5 radian per second and keep in mind that this r g which happens to be the radius of geosynchronous orbit r g. We can find out r g by just substituting these values root over 1 by 3 and that is g. g is if you look at it is 6.67 10 power to minus 11 and m e earth. We already know that is 5.97 into 10 power 24 divided by 7.292 into 10 power to minus 5 into whole square right into whole square. You will get it is something around 42164 kilo meter and keep in mind that this is your h as I told earlier this is h will be r g minus r p and r p is this one or r p. I can write down this is your r p or r e rather it is not p. It is basically e r e radius of earth this is your satellite and this is your earth and that is happens to be 42164 minus 6378 which is equal to 35786 kilo meter. So, if you look at I mean we got this that is the altitude which is required to have a geostationary orbit. In other words you will have to place a satellite in the orbit on the altitude of 35786 kilo meter from the surface of the earth. Then only it will be geostationary and it will be with the same direction of that of the earth and it is in the equatorial region or the equator. So, which we will be looking at in the next lecture. We will be discussing about what will be the requisite velocity to reach an orbit because that is very important. So, for the rocket propulsion is concerned and the rocket vehicle should provide that kind of velocity. So, that it can reach an orbit and particularly you know any orbit whatever you do. Thank you very much we will discuss in the next class.