## Satellite Energy

when a satellite is moving around it has

certain energy why it has energy two

reasons number one it has got velocity

it has got mass therefore it has kinetic

energy number two there is always a

force of attraction towards the earth

and against this force there has been a

displacement created from here it should

have been here because of the force of

attraction but there is some energy some

work has been done on it which has

pushed it apart from the earth that

gives it potential energy so a satellite

has got both types of energy potential

as well as kinetic energy now we will

calculate it how much is the potential

energy with satellite potential energy

with satellite

now this is a system which has got mass

M this is a system which has got mass M

there is a distance between the two

equal to R and we know the potential

energy of the system this potential

energy is equal to minus G M upon R this

we have already done so this is

potential energy with the satellite with

respect to but know how much is the

kinetic energy kinetic energy kinetic

energy is half M orbital V Square and

here we put the value of V orbital V

orbital this values there this we can

write as G and me upon R okay so we have

to make the square of it

so this is half and this is G square ne

square upon R square okay it is this way

so no there has to be certain correction

on it it was not like this there was it

root in world yes so if we make square

of it then it is g m-e upon R this way

so this is equal to half g m-e M upon

GME M upon R GME M upon R but this is

minus 1 this is plus off please remember

kinetic energy due to square of velocity

it is always positive kinetic energy is

always positive

but due to force of attraction the

potential energy is negative in this

case now how much is the total energy of

this satellite

total energy is sum of potential energy

and kinetic energy sum of potential

energy and kinetic energy make the sum

of two if you make the sum of two what

you get is minus half G and me ya upon I

so everywhere you find GME M upon R GME

M upon R gme upon r so what you have to

remember is see potential this kinetic

energy make it negative this becomes

total energy and potential energy is

minus one full GMM upon R this is minus

half these are very strange relations

but these are pair additions actual

relation so you have to remember in this

half of the potential energy is equal to

the total energy and this happens

because of sign conventions this is Plus

this is minus this is also minus this is

total energy of a settling okay so this

is about the energy of this satellite

now there is one thing if a satellite

wants to leave its duty of orbiting

around and want to become free why it

cannot answer is it it's velocity should

increase then only it can move and go

out when the velocity increase in other

words its energy

increase how much energy it needs so

that it become free it is short of

certain energy if we give it that energy

it will be free from the binding binding

of what binding is rotating around now

how much is the shortage answer it this

is the shortage if here is earth and

here is a particle moving this way no

connection with this what is their

energy with respect to this earth answer

this has energy zero potential energy

with respect to this or total energy

with respect to this so if we give this

much energy positive energy to a

satellite then it will be free from the

job of rotation energy plus half g m-e M

upon R if given to satellite then its

total energy will be zero

this and FX total energy is zero what

will happen there shouldn't exist if its

total energy is zero answer is it should

exist to the infinity that means it is

no more in the orbit so this is short of

this energy if somebody gives it energy

it will become free then why it is

making orbit now because this energy is

not with him if somebody gives him this

energy then it will become free that is

why we call this energy as binding

energy binding energy is that energy

required by a satellite if that energy

is given to a satellite then it will

leave the job of orbiting and will go

from that space so that is binding

energy and its amount the binding energy

is equal to 1/2 GME M upon R so we have

studied about satellites and all the

quantities related to satellites for the

practical use there are two categories

of satellites geostationary and polar

satellites how they are used what is the

difference between them that we will see

in the next lecture thank you