 Hello everyone, welcome back to the next lecture. We are discussing about the topics platform used for remote sensing in which we are specifically talking about the near polar sun synchronous orbits. In the last lecture, I told you concepts related to the overpass, equatorial overpass time, overpass time or over like different, different latitudes and what is like the typical inclination angles all these things were near polar sun synchronous orbits. Also we started discussing about like the repeating nature of orbital cycle. I told you that after every given number of days the ground track at which the satellite overpass will repeat say every 16 days once or every 24 days once and this is actually in order to produce like a global coverage with like meaningful high spatial resolution. This orbital repeativity will be achieved under certain conditions or a certain criteria. So the criteria is given in this particular slide. s is equal to 360 n by L where s is the longitudinal gap between two orbits say this is orbit 1 and orbit 2 on any given day. I told you that when a satellite completes one orbit and when it is going to start its second orbit it will start from a point that is west of its starting point. It will always happen. So there is like a shift in the longitude at which the satellite is starting its new orbit that longitudinal shift should be equal to 360 degrees. This is like one full rotation around the earth into n by L where n is the number of days and L is the number of orbits. That is say take for example for like older Landsat series of satellites the n was around like 16 days and L was around like 233 orbits. That is this is day 1 let us say this is first orbits satellite is starting from equator. Satellite will start moving orbit 1 it will come to like a new location orbit 2 again in of it will come to a new location like this this will be keep on proceeding day 2 again it will start from a new point like this this will be keep on going. After 16 days satellite would have made 233 orbits then when it is starting its 234th orbit it will start from the same ground point A. So this is like a general condition in order to achieve orbital repeativity 360 into n by L where n is the number of days L is the number of rotations the or the number of orbits the satellite should make. Both of them must be integers n is also an integer L is also an integer they cannot be like kind of like fractions and they should be represented in like the smallest forms that is without like a common factor say 16 by 233 you cannot like have like a common factor between them. Some satellites may have like 18 to 55 something like that there should not be like any common factors between them the number should be represented in kind of like a lowest possible form. When that achieves the numerator will tell what is like the number of days once the satellite cycle will repeat say 16 or 18 24 something like that and the denominator L represents the number of orbits the satellite should make after doing this. Now we have seen for a satellite to be launched in like sun synchronous orbit naturally we always have like a limitation in orbital height normally whenever a satellite is launched in sun synchronous orbit near polar orbits we try to keep it between this the range of say 500 to 1000 kilometers in order to achieve our like other mission objectives that is like the normal range and also the period of rotation also will be around in the range of say 90 to 110 minutes. So, the range is actually pretty short for us in order to achieve this. So, let us like maybe like take few example in the last lecture I told you in a given day the satellite will not make an exact number of integer orbits it will always have 14 points some orbits 15 points some orbits like that based on its orbital height it will not be 14 orbits exactly in a day 15 orbits exactly in a day. The reason is if it makes integer number of orbits in a given day then that means the orbital track repeats every day that is let us say the orbit can be placed like that but normally it would not be. So, what I told you is like say here the n is 1 every day the orbital track should repeat. So, normally what will happen is for the typical height orbital height in which like a near polar sun synchronous orbit will be placed l will be 14 or 15 or 16 it can be in this particular range that is satellite can make like 14 orbits or 15 orbits or 16 orbits. If this has to be like kind of like what to say if n is equal to 1 which means the satellite should complete like exact integer number of orbits around the earth. When n is equal to 1 the satellite will make exact integer number of orbits. When that happens the satellite will overpass the same location on the earth like this is orbit 1 orbit 2 everything I am talking about day 1 ok day 1 orbit 1 day 1 orbit 2 day 1 orbit 3 etc. In day 2 orbit 1 will again start here in the same point we can make the orbit to work like that like every day we can make the orbit 2 go over like a same track again and again. That will be achieved when a satellite is made to have like an exact integer number of orbits in one day. Day means like side detail day 8000 164 seconds, but normally we will not do that we means like the scientist will not do that because let us say this is like the entire globe equator say this is orbit 1 day 1 orbit 2 or like I draw out in kind of like a map it will be easy to represent ok this is equator say this is like orbit 1 day 1 orbit 1 day 2 like this it will be keep on moving. Say if n is equal to 1 we want the orbit to repeat every day means again the same starting orbit 1 in day 1 will be achieved in day 2, but just see the distance between them. Normally for the time period of our satellites near Polar Sun-Slinger's orbit satellite which will be roughly around 90 to 110 minutes to complete one full orbit earth would have moved at the equator earth would have moved by a distance of around like 2000 to 2500 kilometers that is let us say this is like orbit 1 day 1 when it completes one orbit and comes to its orbit 2 day 1 the shift in the distance or the distance in the between its starting point a to b along the equator will be in the range of 2000 to 3000 kilometers. This is like a large gap actually. So, what will happen a satellite will have like a definite swath width of coverage the gap in the equator is something around like 2000 to 3000 kilometers. So, whatever the satellite can cover that is let us say this is like the orbit like the swath width the satellite can cover ok what I am drawing in green color with the swath width. So, from one overpass a satellite can cover only like a definite swath width that is fixed by like the sensor parameters the scan angle or like the push broom geometry whatever. So, this is limited by the sensor characteristics. Now, if I want like everyday repeat cycle then let us say the satellite is making like 15 number of orbits every day then after making 15 orbits in day 1 in day 2 the first orbit will be exactly over at the first orbit in day 1 that is possible. But because of the swath width constraint the central portion here will not actually be imaged that is this particular zone where I am like kind of scratching will not be imaged ok. Similarly, between orbit 2 and orbit 3 there will be like a gap which will not be imaged. There is always like a limitation normally satellites will not have very wide swath normally because very wide swath in order to achieve like a very wide swath what we should do we should make like the sensor to scan like if it is like a visc broom sensor it has to scan widely like the scan angle should be very wide. So, that the swath width will be around like 3000, 2500 or 3000 kilometers. When that happens already we have discussed that if the scan angle is too wide or too away from the nadir the GAFOV size will increase the GSI size will increase everything which will lead to image distortions. So, normally we will not prefer that we will try to keep the swath width nominal. Even if you want to put like a push broom type of like very long array of sensors again it will be difficult to cover like that much swath. So, except very few satellites like MODIS or VARS most of the earth observing satellites in near polar sun synchronous orbit will have like a smaller swath in the order of like few hundreds of kilometers not in thousands of kilometers. So, that will actually make orbital gaps if you want like a everyday overpass. That is why I said in the last lecture that scientists will always make sure and the starting point on every day of the like the starting point of the orbit every day will have will be at different different ground points. Say here today let it be like point A like orbit 1 day 1 is over point A. Orbit 1 on day 2 will be at some other point say point B which may be between somewhere here in between location. Those things are made sure orbit are designed in such a manner that is these kind of gaps will not occur. Then by adjusting this N by L parameter scientist will make sure the satellite again come to its original track again once after say 16 days 18 days 24 days and so on. So, normally a satellite in sun synchronous near polar orbit will not have repeativity of one day such orbits are called resonant orbits like N is equal to 1 there which will everyday repeativity will not be provided because it will it will leave us with like a very wide gap especially at the equator. From the given orbit we will not be able to cover all the regions on the earth surface definitely there will be like a gap which will stop us or which will prevent us from achieving a global coverage. But still we can put like a satellite with 3000 kilometer swath it is possible, but normally we would not do it again in order to maintain like the geometrical consistency of the image except like very few sensors like modus avhra virs most of the satellites in near polar sun synchronous orbit has a swath width of only hundreds of kilometers. So, this is again to drive home the point like the longitudinal shift is given by 360 N by L. This is also equal to this thing P N into omega e minus omega s where P N is the period of rotation of the satellite. Omega e is the angular velocity of earth and omega s is the angular velocity of the orbit orbital plane that is when satellite is completing one orbit earth is moving and that is why the ground track or the nadir trace of the satellite comes to a new point that we know, but satellite orbit is also processing in the same direction as that of earth. So, there will be like a slight shift of the orbit to the west to the east actually earth is moving similarly the orbit track also will move orbital plane itself will process that is the nature of sun synchronous orbit. So, the net effect is what we are calculating here. So, this is again like representing the longitudinal shift in another form this condition should again be satisfied where instead of writing in 360 degrees I have written it in 2 pi radiance. Now, I told you the repeat cycle is actually designed or kind of like planned by the scientist and engineers taking care of the mission. It can actually be planned in several ways a few examples given here. Say a same satellite with 16-day repeat cycle we are going to discuss as an example. So, this satellite will repeat its ground track again once every 16 days. Let us say the satellite is placed in orbit of altitude 542 kilometers above the earth surface. For such a satellite this will be like orbit 1 in day 1 this will be like orbit 1 in orbit 2 in day 1 like this is like the S longitudinal shift within a day this is how it will look orbit 1 day 1 orbit 2 day 1 this is like the longitudinal shift. Here like for diagrammatic sake they have put it in this direction from left to right. Now the same it can be now again and let us say now it has completed one full day it is going to start day 2. Say the first orbit in day 2 can be just adjacent to the first orbit in day 1 it can be here somewhere. So, this is orbit 1 day 1. The next day third day the first orbit can be just next of orbit 1 day 3 it can be shifted like this. So, what it means is the huge gap between orbit 1 and orbit 2 on day 1 every day like on day 1 this is like orbit 1 on day 2 sorry on day 1 this is orbit 2 this is like the in between gap ok. Every day the orbital starting will be so planned such that it fills the in between gap between them. So, this is orbit 1 day 1 orbit 1 day 2 orbit 1 day 3 orbit 1 day 4 like this everything will be kind of like filling the gap in between. So, after this after it completes 16 days it will start repeating. So, this is one way in which we can achieve this. At the same time let us say now the satellite is put in like a 700 kilometer altitude again with the same 16 day repeat cycle. Now how it will be this will be like orbit 1 day 1 orbit 2 day 1, but in second day satellite may be somewhere in between on third day satellite may be here on fourth day the satellite may be here that is the first orbit in the successive days can be planned in many different ways that is what like I am trying to convey. It is not as we change the orbital height we have like a certain range right we can play with this 500,000 kilometer orbital height 90 to 110 minutes of like orbital period which will which are like interrelated. When we play with it the repeat cycle can be arranged like every day you can like play in between or you can have like what is known as like a sub cycle that is orbit 1 here orbit 2 you can like move the satellite orbits in different different manners. All these things are planned by mission scientists in order to maximize the ground coverage. Normally we want to get as much as coverage of earth as possible and based on the spatial resolution characteristics of the sensor the swath width of the sensor and everything and the repeated nature that is required for the mission objectives and all these things the satellite planners will decide in which orbit we should put it. There is always like a small leverage or small range of altitude heights in which we can play. So, essentially the orbit in which the satellite is put like the 360 N by L I told that N by L can be played with within like a definite range it can the values can be varied by varying that values between in order to like a certain number of degrees we can try to achieve the repeat cycle we want. Say certain satellites will have like a 16-day repeat cycle certain satellites will have like a satellite called ISAT 2 has a repeat cycle close to 90 days. So, the orbit track will repeat only once every 90 days because of its very small swath width. If you want like extremely narrow swath width what will happen you should plan your orbit such that they all fall very close to each other that is the L should be extremely large 360 N by L the L should be kind of like extremely large then only you will get like a global coverage. If you make like the swaths orbits wide enough you can like what to say reduce N or have N as kind of like a small number all fixed by this orbital height the range what we have we can play around with the N by L. So, what is like the final take home messages the repeat cycle is one at what day the orbit will repeat itself within the repeat cycle itself there can be several strategies of making the satellite cover the earth in its entirety. So, normally scientists will try to maximize the ground coverage based on the swath width. Let us say orbit 1 is here on day 1 on day 2 orbit is here. Let us say the swath is wide enough to cover 2 orbits say it is in the order of say thousands of kilometers. So, from day 1 also a ground point will be imaged on day 2 also the same ground point can be imaged because of its very wide swath width. So, that is possible. So, normally such tactics will be employed by scientists in order to maximize the ground coverage and a same repeat cycle can be achieved from different, different orbital heights by playing with this numbers. Now, this is like example for like orbit track of Landsat 1, 2, 1, 3. So, this is how it is say day 1 the orbit is starting like this orbit 1 day 1 day 2 it is like this. So, this is like the S I was talking about the launch journal shift like the entire thing. So, day orbit 3 will be like this orbit 4 will be here like this it will be rotating. So, orbit 15 like it will complete 14 points of orbit in a day. So, when it comes to like second day orbit number 15 will be just next to its orbit number 1. So, on third day the orbit number 29 will be somewhere here just next to its orbit 15. So, this is how the orbit track was planned. For some other satellites it can be like in a definite manner. So, all these things combined together will define the ground coverage of the satellite. Normally for Landsat series of satellites the distance between orbit 1 and day 1 orbit 2 and day 2 will be less than the swath width. So, that we will get some sort of like side-lab between 2 orbits. Say swath width will be around say 180 kilometers, orbital gap may be in the order of say 130 150 kilometers. So, that will achieve there will be like a small side-lab between 2 orbits every day. So, that common in between portion will be imaged both in day 1 and on day 2. This is to enhance like the ground coverage. See this is again an example with Landsat 1, 2, 3 the orbital period is 103.34 minutes, repeat cycle it has 18 days, longitudinal difference between 2 consecutive orbits along the equator 25.8 degrees, orbital cycle repeats after 251. Maybe with all the data we can check if this is kind of like achieved okay. So, n is 18 days, this is 251 orbits. So, the s is 25.8. So, we can actually check it. We can play with this in order to arrange this. Everything is kind of like interrelated, but the same number the orbital the s or the longitudinal difference between the 2 orbits orbit 1 and orbit 2 on the same day. We can achieve this by playing with this particular number based on our project needs. See this is how it is. This is like orbit 1 day 1, orbit 2 day 1 distances 2800 kilometers at the equator. So, orbit 1 on day 2 that is labeled here as orbit 15 it is shifted by 159 kilometers where the swath width will be around the range of like 180 kilometers. So, this suggests there is some amount of like overlap around like 25 26 kilometer overlap is there between the 2 orbits. So, that small portion in between will be covered on both the days. This is to further ensure everything is every part on the globe is covered continuously. So, with all these long discussions you would have realized that there is like a relationship between the temporal resolution of the satellite and the orbital characteristics. Yes, the temporal resolution is the time period or the time gap between 2 images that we acquire for a same spot right. So, the temporal resolution is governed by the orbital characteristics at what repeat cycle the orbit will come, what is like the ground track that is being planned. With this the swath width both of them combined together will define temporal resolution. Say, Landsat satellite like Landsat 7 and Landsat 8 has like a repeat cycle of 16 days, swath width of 185 kilometers. So, that means, the satellite can see only like a small region of earth near its nader, it is not like a full scanner. It will just scan like a small area. So, unless a satellite comes over at the orbit it will not cover in like a very large area. So, we have to the temporal resolution is also 16 days, only when it comes over it we will get an image ok, the swath width is very narrow. Take an example of modus sensor or VAR sensor. For modus sensor the swath width is around 2300 kilometers. That means, from this particular location on orbit it can cover a very wide swath. So, what it will means? It will mean that from different different orbits it can image the same point on the earth due to its very wide scan angle. Similarly, VARS has a swath width around 3000 kilometers. Again it can cover the same point on earth from different different orbits. From this orbit it can cover overhead. From the next orbit it can during the scan it can cover. All these things will help us to achieve higher temporal resolution. So, the temporal resolution at what or the time between the coverage of the same ground point on the earth depends on the orbital characteristics and the swath width. They are related but they are not the same temporal resolution and the repeat cycle of the orbit. So, remember very fine some of the fine details we have to remember in all these things. Like some satellites will have the capacity to see only like nadir and like very small part. That is like Landsat series of satellites. Some satellites has very wide scanning capacity like modus VARS. Let us think in terms of like the overpass time of such satellites. Normally in sun synchronous orbits what we think we can calculate the satellite overpass time at our particular latitude or longitude. We can do that. If a satellite cannot it has only like a very narrow swath that means the overpass time whatever is there for the orbit we can assume it to be like the overpass time for the entire swath width. Like this is like the swath width. The center line is like the nadir trace of the satellite. This is the exact line over with the satellite is overpassing. This is like the swath width. If it is say this is very narrow in the order of 200 kilometers we can achieve like the same time. Say here the time let us assume it is like 10 a.m. Here also we can achieve assume it to be like 10 a.m. Let us take example of modus. This is the nadir trace of the satellite orbit. Swath width will be something like this in the range of 2300 kilometers. So, here the overpass time only we will calculate. Let us say this is 10 a.m. But due to the very wide scan it will cover several degrees of longitude on either side such that the local mean solar time here and here will be totally different from here. Like in the last lecture I told you about like this time equation. I just wanted to highlight it again here because whatever the time we calculated is only for the exact ground point over nadir, ground point at nadir not at any other locations. This is we should always keep in mind. So, for sensors such as modus and all with its very wide scan angle we cannot think all the points in the image in a given latitude or covered where at the same local mean solar time. No, they will be at like different local mean solar time because of its very wide swath width a point on exactly on the nadir track will be having the overpass time what we calculated. Whereas if a point is on the extreme of the scan line it will be at a completely different overpass time. This we have to keep in mind. And finally, apart from all these orbits like we discussed in detail about two kinds of orbits geostationary orbit and near polar sun synchronous orbits. There are other types of orbits to mole knee orbits with there which we are not like going to discuss. But there are certain satellites which are put in asynchronous orbits. Asynchronous orbits means they will not maintain like the same overpass time they will overpass a same location at different different time interval when the sun angle is at different different angles. Say a very good example was there was a satellite called TRMM primarily for measuring rainfall in the tropics with the inclination of 35 degrees and 400 kilometer orbital height. It was a asynchronous satellite. Similarly, international space station which is now a house of like several remote sensing sensors, JDI, EcoStress and all. And they are all like that particular ISS that itself is like a satellite platform now. It is in an asynchronous orbit say today it may overpass over Mumbai at say in the morning. After few days it may overpass at like evening time and so on. Such orbits are also possible. But normally for what to say normal for the day to day remote sensing images what we see all the images all the satellites will be mostly placed in sun synchronous orbits. But I am just telling you it need not be satellites can also be placed in asynchronous orbits. With this we end this particular topic. Thank you very much.