 Hello everyone, welcome to the next lecture in the course remote sensing principles and applications. In the last lecture, we started discussing about the various platforms that we use in remote sensing. We discussed about ground based platforms and aerial platforms. Today we are going to start the main discussion topic of these lecture series. Like lecture series in this particular team of what we are going to discuss is space based satellite platforms. Like even in the introductory lectures, I told you that we will concentrate more on satellite based remote sensing because that is one of the most widely used data collection platform for remote sensing activities. Any user across the globe has the capacity to download the data acquired from a satellite and use it for their applications like civilian satellites. Whereas aircraft observed data or ground observed data most of them if not all are still treated confidentially or not available in public domain. But relatively if you compare with this satellite observed data are available relatively easy in a easy more easy manner. We can just download almost any data we want acquired from a satellite over any region of our interest across the globe. So, that is why satellite remote sensing is one of the most widely used technology when you compare with other platforms. The principles are the same like the remote sensing principles are more or less the same. But we have to understand the platform to some more extent like how the data is being collected from satellites, how the characteristics of the satellite orbits will affect the way we collect the data all these things we should get an idea in order for us to appreciate this in a better way. How satellites collect data? Each satellite that is observing the earth from space will revolve around the earth in a particular orbit. So, a satellite orbit is kind of like you can think it of like a path in which the satellite will be constantly moving. Say in the earlier classes I discussed about geostationary orbits and near polar orbits when I discussed about the like the data collection when we just before we discussed this broom push broom and all. I told you briefly about near polar orbits geostationary satellites and all. So, basically each satellite will be in its own orbit. So, that is we can think it of its define a predefined path in which the satellite has to move perfectly. If the satellite comes out of its path normally the engineer sitting from ground will try to bring it back to its designated orbit to achieve like the required project goals. So, what exactly an orbit? An orbit is like a predefined path in which the satellite moves around the earth. So, if this is the earth if the satellite moves around the earth like this it is an orbit or if this is the earth satellite can move around like this. Any different orbit it can take and the satellite will be in that orbit for that particular mission it has to be in that orbit in order to achieve the mission goals. If the satellite comes out of it definitely has to be brought back to its orbit. So, it is kind of like a predefined path in which a satellite revolves around it. And for earth observing satellites all the orbits will have what to say will revolve around the earth with earth center as also the what to say. Like for circular orbits I am talking about it will be kind of centered in the earth. Earth center and the orbit center will most likely match. So, for remote sensing applications we can think of orbits as circular orbits like whatever discussions we are going to do we will assume those orbits are circular because most of them are near circular if not perfectly circular. There are special cases in which the orbits are elliptical like the way earth revolves around the sun like sun is here earth revolves in an elliptical orbit. Similarly, satellites also will revolve around the earth in elliptical orbits but we will not discuss that we will confine our discussions to circular or near circular orbits because most of the commonly used remote sensing satellites revolve in near circular orbits. So, a satellite has to be launched from ground. So, once the satellite is carried by a rocket the satellite will be placed in its orbit some sort of like orbital some sort of maneuvers will be carried out by the ground based controls in order to put the satellite in its designated orbit. Once the satellite reaches its orbit it will self sustain for a certain period like without requiring any sort of like ground based control. How the satellite sustains itself in an orbit with very minimal support from the ground? First thing is there are like two forces majorly will be acting on the satellite which is in an orbit. First thing is earth's gravity. If a satellite is moving around the earth earth's gravity will try to pull it downwards that is the first force. Second force is due to the circular motion of the satellite. There will be like a centrifugal force which will try to take the satellite in the opposite direction like in our school physics we learned about centripetal force and centrifugal force right. So, the effect of centrifugal force is to take us away from the circular motion. If you are like moving in kind of like a merry-go-round the speed of the velocity at which you are like rotating will try to push you away from that merry-go-round. If the merry-go-round is rotated very fast by the shopkeeper or someone we will be feeling as if you are like flying like this. So, we will be like moving and rotating in like a slightly inclined manner right that is because of the centrifugal force it pulls us away from the circular motion. Same thing the centrifugal force will be acting on the satellite trying to move it away from a circular orbit. So, these two forces will balance out each other in order to maintain the satellite in its orbit. The Earth's gravitational force will be balanced out by the centrifugal force due to the rotation or revolution of the satellite around the Earth's surface. So, simply put the force due to gravity can be written like this. So, here I am writing it in form of f is equal to ma ok. So, m is the mass, a is acceleration. Since we are talking about gravity we use the acceleration due to gravity gs. So, the gs value we know 9.81 meter per second square on the surface of the Earth ok. So, if we use that say this is like Earth center, this is like surface of the Earth the satellite will be still at a certain height away from the Earth's surface. So, this force due to gravity we have to balance it for this particular orbital height. So, that is why we are using this kind of like an inverse square law kind of relationship r by small r the whole square. So, capital R is the radius of Earth. The small r is summation of radius of Earth plus the orbital height say 700 kilometers away from the Earth's surface, 1000 kilometers away from the Earth's surface and so on. So, this particular equation basically gives you the force due to gravity. This force is balanced by the centrifugal force that formula is m v square by r. m is the mass of the body, v is the velocity with which it is moving and r again the radius at which the object is moving from the center of Earth ok. I also already told you like the orbits in which the satellite is moving the center will center of the orbit and the Earth center will match with each other like they will be placed like this right. So, this small r is the distance of the orbit from the center of the Earth that is nothing but the radius of Earth r plus the orbital height h ok. So, this is like centrifugal force both of them will balance out each other equate both of them. So, that is I just erase this m gs r by r the whole square you can equate to m v square by r. From this you can calculate the velocity by this equation you can cancel out the terms and you can get the velocity of the platform that is or the satellite that is moving around. See this formula gives you the velocity at which the satellite will be moving the velocity will be is equal to square root of acceleration due to gravity multiplied by radius of Earth square divided by radius of the orbit from the Earth center ok. So, this is like a very simple formula which we can use to calculate the velocity at which a satellite is moving around the Earth. If we know the velocity we can calculate the time taken by a satellite to complete one full orbit around the Earth like say if there is sun if there is Earth we all know the Earth takes one full year to complete one full circle around the Sun right. Similarly, each satellite will take certain amount of time to complete one full circle around the Earth. We call it as the orbital period of the satellite that orbital period of the satellite also we can calculate. So, the formula is here it is like derived in a pretty simple way. So, the time taken like when the satellite completes one say this is Earth this is the orbit in which the satellite is moving say the satellite is here. Let us say the satellite starts from point A it will revolve Earth something like this it will again come back to the same point A. So, the time elapsed between for the satellite to complete one full circle we call it as the orbital period. And within that orbital period the satellite completes this one full circle the circumference it completes the circumference is given by 2 pi small r that is the radius of this circle which is a combination of radius of Earth plus orbital height h. So, this is 2 pi r it completes one full circle and it moves with a velocity of v like we all know that what to say distance is equal to velocity into time we know we know the velocity now using the previous formula. So, the time taken to complete is distance by velocity and the distance we know the circumference of the orbit which is 2 pi r and then v we can calculate from the formula. So, using this we can calculate the time taken for the satellite to complete one full revolution around the Earth surface. So, if you look at this particular slide we can understand that there is a relationship between the altitude of the platform the velocity of the platform and the orbital period of the satellite. Say altitude if the altitude increases that velocity will decrease say altitude is given x axis. So, velocity is given in this particular axis. So, the velocity decreases as the altitude increases similarly the time period taken to complete one full circle around the Earth surface increases as the orbital height increases. So, most of the satellites in the near polar orbit will be around this range 400 to 800 kilometer range typically. So, you can see what to say the period in which the orbit. So, the period which the orbit lies something around here to here roughly they may take something around like what to say 2 hours or so if it is like in an 800 kilometer orbit they may take anywhere between like above 1 and half hours to 2 hours kind of to complete like one full rotation revolution around the Earth surface like Earth observation satellite in this 400 to 800 kilometer band where most of the near polar satellites are located. So, based on the orbital height the velocity of the platform will be fixed we need not do it like once it is put into orbit the satellite has to move in that particular velocity it will automatically start moving then only it will be balanced out. If it moves any faster or any slower the orbit is going to change actually. So, say for example the orbit satellite is going to be is slowing down when it is slowing down due to some effect then the Earth gravity will try to start pulling it down easily. So, this is called like orbital perturbations this can happen. So, unless the velocity is maintained the orbit cannot be maintained the velocity will be there it is defined by this law gravitational force has to be balanced out by centrifugal force only if this happens satellite will be in its orbit. So, the velocity is kind of like predetermined also the time period is also determined with respect to orbital height. So, the mission planners when they plan for a mission they will try to analyze what orbital height we should achieve in order to achieve the mission goals. We can be put the satellite in 700 kilometers orbit or we can put it in 400 kilometers orbit all these things people will do based on they will take into account all the factors and decide the orbital height based on the orbital height the orbital period and also the coverage around the Earth surface will vary. So, in order for us to further discuss orbits we need to know two important variables or parameters related to orbit. Actually in order to locate a satellite in space we need like six different elements to know we call it as like Keplerian elements but in order to keep the discussion simple we will just try to learn about like two important parameters about orbits which we should understand. The first thing what we call it as orbital inclination and second thing what we call it as ran or write ascension of the ascending node. So, these two parameters we will learn before we move ahead. So, what exactly is an orbital inclination? Inclination means the angle made by the orbital plane with respect to Earth's equatorial plane. So, here in this particular diagram this is Earth's surface this is the Earth's equator. So, each satellite will have its own orbit defined. Say when you look at it from any one particular angle it will be appearing in form of like a line. In fact, it is like a two dimensional plane. Like if it is Earth is like this the orbit will be like kind of like this. It is like a plane, orbital plane. So, the angle made by the orbital plane and the equator we call it as orbital inclination simply put. Here I am not going like in a complex way I am defining it in a as simple way as possible. So, this orbital plane or this inclination can vary between 0 to 180 degrees. So, 0 means orbit is placed along the equator Earth's equator. Satellite is moving in the same direction as that of Earth's surface. Then 180 degrees this way around orbit is still in equator but the satellite is moving in direction opposite to that of Earth. Say Earth is rotating like this satellite may be moving like this. Some satellites may be having inclination something around this 90 to 100 degrees. That means Earth is here satellite will move around like this from pole to pole we can say or near pole to near pole near north pole to near south pole the orbital plane will be oriented like this. So, this angle is what we call the orbital inclination. So, typically for satellites which is in this kind of like a near polar orbits the general convention to measure inclination is say this is Earth, this is Earth, this is the Earth's equator. Let us say there is some orbit something like this. So, we measure the angle inclination angle that is like kind of like a convention. We will measure the inclination angle when the satellite is moving like this towards north and then we will measure angle in anticlockwise rotation that is we will see in that particular direction in which the satellite appears as if it is moving from south to north. Then at that particular direction we will measure the angle between Earth's equator and the orbital plane in anticlockwise direction. So, this is like a convention for measuring inclination for satellites that are moving from pole to pole. Similarly, if the satellite has I0 or 180 based on the direction in which it moves normally say if it moves in direction same that of Earth say Earth is moving like this if the satellite is also moving like this we call it as like 0 degrees inclination if it is at the equator or if it is at the equator but if it moves in opposite direction we call it having an inclination of 180 degrees. These are basically the conventions. So, normally a satellite with inclination angle 0 to 90 degrees will be understood to move in the direction same that of Earth. Say if Earth is rotating like this satellite will be moving like this we call it as prograde motion. So, in the same direction as it of Earth's surface the inclination will be from 0 to 90 degrees. These are like small conventions people follow that is why I am telling it repeatedly. So, for certain satellites inclination will be more than 90 degrees under certain circumstances we have to understand the satellite moves in a direction opposite to that of Earth's motion say Earth is moving like this satellite will be moving like in some other plane like this either along the equator or along the pole to pole that is fine but still the net resultant direction will be say Earth moves from west to east the satellite will be moving from east to west. So, this is regards to orbital inclination. Then comes right ascension of the ascending node or simply put we will call it as orbital longitude just for the sake of our simplicity while talking. So, what exactly this orbital longitude is? Let us say we have Sun. Earth revolves around the Sun again in an elliptical orbit but here we have put it in kind of like a circular orbit for simplicity sake it is true it is not really it is not circular it is elliptical we all know. So, in this orbit there will be like say Earth is tilted in its axis Earth is tilted 23 and a half degrees in its axis. So, due to this Earth's tilt and due to the Earth's and this is Sun this is Earth and due to Earth's revolution around the Sun over a period of year the Sun will appear as if it is moving from 23 and a half degrees north to 23 and a half degrees south and then come back. So, it is say Earth is tilted like this Sun is here due to Earth's rotation around the Sun and changing this elliptical orbit and all Sun will appear to move from 23 and a half degree north to 23 and a half degrees south we know this. During March Earth the Sun will be around the near the equator it will slowly move towards 23 and a half degree north latitude we call it summer for the northern hemisphere then again it slowly moved towards the equator go towards southern hemisphere 23 and a half degrees south then again it will come to equator it will complete one full cycle equator to 23 and a half degree north again come to equator go to 23 and a half degrees south again come to equator one full circle it will complete in one year. So, you can see the Sun moves from equator to north 23 and a half degree in tropic of cancer and tropic of Capricorn repeatedly within a year. So, you can think of the Sun moves in one particular direction right. So, there is a particular day in which Sun will be exactly over at the equator in its way to the northern hemisphere like say now the Sun is at southern hemisphere 23 and a half degrees south here then while moving towards northern hemisphere it will cross the equator once during that particular day that will happen during like March every year we call it as vernal equinox where the day daylight period will be most likely equal to the length of night day time is equal to night time duration. So, during summer we have longer days during winter we have longer nights on equinox or around equinox the length of day will be exactly equal. So, on the day of equinox there will be like a we can draw a line joining earth center and the Sun say earth is moving around in its orbit this is the position in the earth orbit in which the earth achieves on the day of vernal equinox. On the day of vernal equinox you draw a line connecting Sun and the earth and fix this line wherever the earth moves let us say we are like able to somehow fix this line. So, the angle between this particular line and our orbital plane in which direction is oriented we call that as orbital longitude. So, this is like again like a very simplified definition here also there is kind of one thing we have to remember like vernal equinox we defined earth is moving from southern hemisphere to northern hemisphere on that particular day it will cross the equator. So, it is kind of like coming from bottom of earth to top we can think it of like if you orient north upwards you can think it of it is coming from here to here there it is crossing the equator that day is vernal equinox. Similarly, satellite also especially if it is moving from like pole to poles it will have it will move from southern hemisphere to northern hemisphere, northern hemisphere to southern hemisphere like this. Then also even satellites around the earth will cross the equator from south to north once from north to south once in every orbit in every single rotation around the earth it will cross the equator from moving from south to north and then similarly from moving from north to south. So, this motion when a satellite moves from southern hemisphere to northern hemisphere we call it as ascending pass. So, these are some terminologies we use you need to like know them and understand them ascending pass we call when the satellite moves from south to north descending pass we call when a satellite moves from north to south like this. So, there will be like a point in the orbit when the satellite will be exactly over the equator moving from south to north say this is earth satellite is moving like this says from south to north when it is moving at a given point of time it will cross the equator hold let us say we are able to hold the satellite at that particular point. At that particular point if you hold it the orbital plane will be in kind of like a certain angle. So, the angle made by the orbital plane and this line joining the sun and the earth on the day of vernal equinox we call it as orbital longitude or technically we called as right ascension of the ascending node. The angle made by this ascending node point like the orbital plane where the ascending node is let us say the ascending node is here in the orbit. So, the angle made between this and the line joining sun and the earth we call it as right ascension of the ascending node. So, these two things are like orbital inclination and this right ascending of the ascending node are two important things we should know and based on this we will discuss further actually there are like plenty of other elements we should know in order to define like a satellite in its orbit like if it is a circular orbit we need to know this H basically like the orbital height above the earth's surface or if it is like a elliptical orbit instead of this orbital height H we should know what is known as the semi-major axis and semi-minor axis like if you have an ellipse elliptical orbit we will always have something kind of like a semi-major axis A semi-minor axis B we do not have like one single radius we have this A B we have learned it in the school geometry right if it is an elliptical orbit we should know this if it is a circular orbit we should know the orbital height H or the distance from distance of the orbit from the center of the earth. So, these things we should know similarly we should know the what to say the angle between perigee positions and all. So, just for simplicity I am not going into the details only two parameters we are defining one is inclination another one is simply put orbital longitude or right assumption of the ascending node. So, in this lecture as a summary we started discussing about the satellite based orbits we just got introduced to how like satellites maintain its orbit and the relationship between the orbital height velocity and the time period of the orbit to complete one full revolution assuming circular orbits whatever we are discussing we assume the orbit is a circle and also we got introduced to two important concepts the orbital inclination of the orbital plane and the orbital longitude or right ascension of the ascending node. With this we end this lecture. Thank you very much.