 Right, so next let us talk about another very important concept in this chapter that is satellites So today we'll be talking about this as the last topic for today satellites. What are satellites anyone? What are the satellites satellites are the objects or a body that revolves around a planet? Okay, so it's very simple an object revolving around planet you call that as a satellite right and what is planet a planet is an object that revolves around the Sun okay like that you can understand it is and it just a definition of it okay so now let us try to analyze the behavior of satellite okay let's say this is the orbit of the satellite satellite will be moving in a circular orbit okay we are assuming that that it will be moving in a circular orbit if it comes under the influence of neighboring planets that there will be slight distortion in the orbit will be there but more or less it will be circular only so all the motion in this particular chapter we are assuming it to be circular only whether it planet revolving around the Sun or satellite revolving around the planet so we are assuming it to be circular only okay so let's say this is earth okay we are talking about earth satellite let us say okay the the radius of the revolution for the satellite let's say this is my satellite okay this satellite is moving okay this is moving like this with velocity v okay mass of the planet let's say earth is that planet let's say Me and mass of this satellite is small m okay by the way these satellites can be natural can be artificial also for example moon is a natural satellite okay and whatever satellites are launched let's say if ISRO launches a satellite or GPS satellites all those are artificial satellites okay satellites have its own importance so there are different purposes satellites are used because there once you are above the earth surface your field of vision is enlarged you can literally scan through entire earth so it can be used for military purposes or you know there are multiple things like for example you can use it for predicting the weather or movement of the monsoon there are so many things you can do with the satellites okay but we'll not get into the all that right now let let us first try to analyze the motion of a satellite okay let's say its mass is small m the velocity is v okay so can you write down the the force equation first as in the gravity of force is equal to centrifugal force can you write that equation all of you quickly do that okay so toward the center if you see there will be a gravitational force like this okay and then there will be a centrifugal force like that centrifugal force will be equal to mv square by r right and this gravitational force f g will be equal to g mass of earth into mass of planet divided by r square fine so this force should be equal to centrifugal force mv square by r right so this is just force balance this must be happening if a satellite is moving around in a circular orbit okay all right now from here a very interesting thing will come up so you'll see that if r get cancelled off you'll get m into v square is equal to g m m e divided by r all right if you multiply half both sides this is nothing but kinetic energy okay all right and potential energy is what potential g between the satellite and the earth this will be minus of g mass of satellite into mass of earth divided by the distance between them right so this is the potential energy and that is kinetic energy which is equal to this okay so you can see that kinetic energy is nothing but minus two times of the potential energy yes or no all of you able to appreciate okay wait it is minus one by two times minus half times the potential g any doubts please ask quickly okay so you can say potential g is minus of two times of kinetic energy potential g is minus of two times of the kinetic energy so total mechanical energy is what potential g plus kinetic energy okay so when you add it up you will have potential g is minus of two times of kinetic energy right so plus kinetic energy so total energy is negative of kinetic energy this is total energy of the satellite all right so if you know that total energy is t kinetic energy will be negative of t and potential energy will be negative of the two times of the kinetic energy all right or potential g is two times of the total energy so like that you can relate kinetic energy potential g and you can play around with that no doubts right no doubts now let us try to derive the Kepler's law of orbits things are clear now any doubts crystal clear okay now for the satellite and this is treated like a numerical okay for a satellite of mass m revolving around radius of r about a planet of mass capital M all right this these things are given for this you need to find the time period find out draw the draw the diagram okay and then try to find the time period quickly by the way in your ncrt they always have considered distance from the center they write it as re plus height from the surface okay so don't get confused okay we are taking distance from the center so that is why we are writing small r when you read from ncrt or I don't know how they have taught in school they will write radius of earth plus h okay so I have directly taken it as a r but a g is not constant g is a variable yeah so g depends on r now you need to substitute that as well I want only as a function of r small r what is a time period see always guys remember whenever something is moving in a circle okay if any object moves in a circle the first equation you write is the central force the force was the center should be equal to mv square by r okay that equation you should write just close your eyes and write that equation before even thinking of anything okay so central forces gravitational force g m1 m2 by r square should be equal to mv square by r so that is where you start solving the question whenever something is moving in a circle okay all right let me solve this now so this is small m the satellite has mass small m it moves with velocity v okay so I can write here g m into capital M divided by r square this is equal to mv square by r all right so from here I will get velocity or the magnitude of the velocity to be equal to under root of g m by r okay this is the velocity or the speed with which the satellite is revolving around the planet okay time period of this satellite is 2 pi r which is distance divided by the speed v okay so you can see that it will be equal to 2 pi r multiplied by this r divided by g m right so t will be equal to 2 pi root of g m r raise to power 3 by 2 right now square both sides you will get t square is equal to 4 pi square divided by g m into r cube right this which you can say that t square is proportional to r cube all right so although you have derive t square proportional to r cube for the case of satellites but same kind of equations you can write for a planet also planet revolving around the sun exactly same thing will come out okay so you can see that Kepler has arrived at this particular expression without knowing any formula any equations just purely by observation he came up with this particular relation that t square is proportional to r cube okay so I will quickly talk about weightlessness okay just give me one minute I will just quickly talk about it okay so suppose you are orbiting in a spaceship okay or you are inside the satellite this is your satellite okay very small satellite it is okay so here is an object inside okay now we are trying to see what is the force the net force this object inside the spaceship will feel okay now since this object is revolving around the radius of r okay it must be feeling a centrifugal force outward which is m v square by r right and the same object must feel gravitation pull also okay which is equal to g m m by r square okay so the net force net force on the object is what g m and by r square minus m v square by r this is the effective force okay which should be equal to 0 okay which should be equal to 0 so I mean is this thing clear is this thing clear all of you quickly type right so net force is 0 so the object inside will not experience any force I mean the net although individually there are forces this force and that force but they add up to 0 and hence you do not feel any force so even when you place your feet on the floor of this spaceship the spaceship will exert zero normal reaction because net force is anyway balanced so normal reaction is not required fine if normal reaction is 0 it will be like a freefall situation or you can say that weightlessness you will not feel any pull towards the earth clear so this is what the weightlessness is about all right we will meet again soon bye bye