 I am Mr Praveen Ellapa Kumbar. Today we want to see the numericals on the orbital parameters. The learning outcome of this topic is at the end of the session student will be able to illustrate the concept of orbital parameters. Here in this topic we want to see the two numerical problems. So out of that one we will start the first numerical problem. Now we want to see the first numerical problem that the question is a satellite is orbiting in a geosynchronous orbit of a radius 41,500 km, find the velocity and time of the orbit. So first of all we want to write the given things. So what are the given things? The given things I want to write the given things that is I called given data. So that is first is radius, the first thing is radius of the orbit that is 41,500 km. So I will write here radius of orbit is equal to 41,500 km that is Re plus H that is Re plus H. So the second thing is the geosynchronous gravitational coefficient. So I will write the gravitational coefficient that is gravitational coefficient G0 is equal to the gravitational coefficient G0 is equal to 398600.5 km cube per square. So this is a formula for the second that is a gravitational coefficient G0. So now I want to calculate the what velocity of the orbit. So write down velocity, the A things I want to calculate velocity of orbit. So what is the formula for the velocity of the orbit? So that is Vs is equal to under root G0 by Re plus H. So we know that what is G0 that is called as a gravitational coefficient. So I will write under square G0 is 398600.5 divided by Re plus H that is 41,500 that is 41,500. So after this division we get under square root 9.604831 and solving this we get is equal to 3.099 km per second. So this is a what this is the velocity of the orbit that is Vs. Now we want to calculate the second thing that is V that is time of the orbit that is also called as period of orbit. So I will write period of orbit. So I want to calculate the period of orbit. So for the period of orbit I will write down formula Ts is equal to 2 pi d raised to 3 by 2 divided by G0. Okay that is gravitational coefficient. Now I want to put the values so 2 pi so d d raised to 3 by 2 that is 41,500 raised to 3 by 2 that is the radius of the orbit and divided by G0. So G0 is what G0 is 398600.5. So now we want to solve this mathematical equation. So I want to write after solving this part I will write 2 pi so 41500 raised to 3 by 2 it gives 845492.746 and when you solve this one so square root of 339000 sorry the square root of 398600 and 0.5 that gives the value of 631.348. So after when you multiply this 2 pi into this equation we get as 53092330.44 divided by 631.348. So after this division I will get the answer as 84093.60676067 second. So that is the period of the orbit. So from this examples now we want to calculate the velocity of the orbit that is velocity of the orbit is 3.099 kilometer per second and also we calculate the period of orbit that is 84093.6067 second. So we calculate the velocity and the time of the orbit. So now we want to solve the second example. In the second example we want to calculate what will be the change in velocity if the radius reduced to 36000 kilometer. Now we solve the first example in that in the second example we prefer the given data from the first one and they will ask the what will be the change in velocity if the radius reduced to 36000 kilometer. So first of all we calculate the velocity in this example and after that one we want to know the what is the change in velocity. So in this case now I want to calculate the velocity. So the velocity here the given data first of all I want to write that is Re plus h what is that Re plus h the Re plus h is 36000 kilometer 36000 kilometer Re plus h that is 36000 kilometer. Now what is the now see now the second thing is now I want to calculate the velocity that is Vs what is the formula of Vs Vs is equal to G0 divided by Re plus h. Now put these values into this above equation what we get so we know that G0 G0 from the previous example what is that G0 G0 is a constant. So I want to put this into this equation that is G0 what is that one the G0 is 398600.5 so I want to put this here so I will write here G0 is what 398600.5 and in this second example what is the Re plus h Re plus h is 36000 kilometer. So after this division what we get my friends we get 11.0722 11.0722 so after this square root of 11.0722 we get 3.3274 kilometer per second so but what is our question our question is what will be the change in velocity so I calculate the change in velocity is equal to change in velocity is equal to so whatever the velocity in the first case whatever we calculate what is that one 3.099 kilometer per second so this is what this is equation number one and this is what equation number two now subtract the equation number one from the two so we get change in velocity so we get change in the velocity so change in velocity become as 3.3274 minus what is in this equation it is 3.099 so 3.099 kilometer per second so after this following this one we get 0.2284 kilometer per second so this is what the change in the velocity that is 0.2284 kilometer per second. So in this way we want to solve the two problems so first one we want to calculate here the satellite is orbiting in a geostation orbit and we want to find out the velocity and the period of orbit and in the second example what will be the change in velocity if the radius reduce to 36000 kilometer so after that one the change in velocity is 0.2284 kilometer per second the references for this topic is