 Hello everyone, welcome to this session. I am Mr Praveen Yalapa Kumbar. Today we want to see orbital petrobation. The learning outcome of this topic is at the end of this session student will be able to explain the concept of orbital petrobation. The contents of these topics are first we see the introduction in that one what is the means of the petrobation then we want to see effects of Earth's oblateness and after that one we want to see what will happen if inclination changes. So we want to see one by one the first introduction. Whatever the orbital equation developed by the scientist initially that will assume by the gravitational attraction and that scientist will be known as Keplerian orbit results. So the Keplerian orbit results in an ellipse whose properties are constant with the time in practice the satellite and the earth respond to many other influence including that out of that one first is a symmetry of the earth gravitational field the gravitational fields of the sun and the moon solar radiation pressure and the last one is for the ELIO satellite the atmospheric drag. So all these four contents these things all of these interfacing forces cause the true orbit to be different from a simple Keplerian ellipse. So if unchecked they would cause the sub satellite point of nominally geosynchronous satellite to move the time. Much attention has been given to this technique for incorporating additional petrobation forces into the orbit descriptions. So the petrobations are assumed to cause the orbital elements to vary with the time. The orbits and satellite where that revolve into that orbit and the satellite location at any instant are taken from the oscillating orbit calculated with orbit elements corresponding to that time. So as the petrobated orbit is not an ellipse so whatever the first of all equation that developed with the assumption of that orbit is ellipse but whenever we calculate the petrobation orbit at that time we assume that that orbit is not an ellipse. So some care must be taken in defining the orbital period. Since the satellite does not return to the same point in space once per revolution. So the quantity most frequently specified is called as Atmolistic period. So Atmolistic period is defined as the ellipse time between successive perigee passages. In addition to the orbit not being a perfect Keplerian ellipse there will be other influence that will cause the apparent position of a geostationary satellite to change with time. This can be viewed as those causing mainly longitudinal changes and those that principally affect the orbital inclination. So the first type is called as longitudinal changes that is also called as in-plane changes. So for that longitudinal changes we take an example of effects of the Earth's obliqueness. So second one is known as inclination changes that is also called as out-of-plane changes and here we want to see the example of effects of the sun and the moon. So first we want to see effects of the Earth's obliqueness. So the Earth is neither a perfect sphere or not a perfect ellipse. So it can be better described as a triaxial ellipsoid. So these will be defined by the scientists Gordon and Morgan in 1993. So the Earth is flattened at the poles. The equatorial diameter is about 20 km more than the average polar diameter. In addition to these non-regular features of the Earth there are regions where the average density of the Earth appears to be higher. So these are referred to as regions of mass concentration or mass comms. That is out of that one. First one is the non-spiricity of the Earth. Second one is the non-circularity of the equatoral radius and the mass comms. So these are the lead to a non-uniform gravitational field around the Earth. So therefore due to these reasons we can calculate the perturbations. So the force on an orbiting satellite will therefore vary with the positions. Now we have taken an example for the LEO satellite. For the LEO satellite the rapid change in position of the satellite with respect to the Earth's surface. It will lead to an averaging out of the petro-beating forces in line with the orbital velocity vector. So this is not true for a geostationary satellite. So whatever that we discussed that is related to the LEO satellite. But this will be not true for the geostationary satellite. So a geostationary satellite is a weightless van in an orbit. So the smallest force on the satellite will cause it to accelerate and then drift away from its nominal location. So the satellite is required to maintain a constant longitudinal position over the equator. There will generally be additional forces towards the nearest equilateral bulge in either an eastward or westward direction along the orbit plane. So due to this it leads to a resultant acceleration or de-acceleration component that varies with the longitudinal location of the satellite. So due to this position of the mass combs and equilateral bulges there are four equilibrium points in the geostationary orbit. So out of the four two are called as a stable and the two are the unstable. So these two stable points here we taken an example of a valley and in that valley first of all the valley part first is a stable part and remaining is a deep one. So the stable points are present at the bottom of a valley. The unstable points are the top of the hill. So now we want to take an example from that example we want to see the exactly what is the means of a perturbation. If a ball is per shade on top of a hill a small push will cause it to roll down the slope into a valley where it will roll backward and forward until it gradually comes to a final stop at the lowest point. So the satellite at an unstable orbit location is at the top of a gravity hill. So given a small force it will drift down the gravity slope into the gravity well that is in valley and finally stay there at the stable position. So the stable points are at about the 75 degree east and 252 degree east. The unstable points are at around 162 degree east and 348 degree east. If a satellite is petrobed slightly from one of the stable points then we do not require any thruster. But if suppose it will at the unstable position then we require accelerate its drift towards the nearer stable point and once it reaches this point it will oscillate in longitudinal position about this point until it stabilizes at that point. So that example we apply here for the satellite. So these stable points are sometimes called as graver geosynchronous orbit locations. So now we want to see the second one is known as inclination changes. So this figure one shows the effects of the sun and the moon. So if you observe this is the earth, this is the sun, this is the moon. So earth is rotating around the sun. Now we want to see the description of this diagram. So once again I draw this diagram for understanding purpose. Now the plane of the earth's orbit around the sun the ecliptic is an inclination of 7.3 degree to the equilateral plane of the sun. The earth is tilted about 23 degree away from the normal to the ecliptic. The moon circles the earth with an inclination of around 5 degree to the equilateral plane of the earth. Due to the fact that the various planes the first one is the sun's equator, second one is ecliptic, third one is the earth's geographic equator, fourth one is the moon's orbital plane around the earth. So all these are of the different. So a satellite in orbit around the earth will subject to a variety of out of plane forces. So there will generally be a net acceleration forces that is not in a plane of the satellite's orbit. So this will tend to try to change the inclination of the satellite's orbit from its initial inclination. So under these conditions the orbital will process and its inclination will change. So the mass of the sun is slightly larger than that of the moon but the moon is considerably closer to the earth than the sun. Therefore for this reason the acceleration force induced by the moon on a geostationary satellite is about twice as large of that of the sun. So the net effect of the acceleration forces induced by the moon and the sun on a geostationary satellite is to change the plane of the orbit. So due to that one the initial average rate of change is 0.85 degree per year from the equator plane. Now if suppose that will be the sun and the moon are the same side of the satellite's orbit then the rate of change of the plane of the geostationary satellite orbit will be higher than the average. And in the second case if it is opposite side of the orbit then the rate of change of the plane of the satellite's orbit will be less than the average. So under this normal operations ground controllers commands spacecraft manures to correct. So in plane changes that is called as a longitudinal drifts out of plane changes that is called as inclination changes of a satellite so that it remains in the correct orbit. So some manures are designed to correct for both the inclination in longitudinal drifts simultaneously in both one burn of the manusing rockets on the satellite. In other in others two manures are kept separate that out of the two first one will be the burn will correct for elliptically and longitudinal drift and another will correct for inclination changes. So the references for this topic is thank you.