Keplers 2nd Law - Gravitation, Physics, Class 11 Video Lecture

hello friends this video on gravitation
pac-12 is brought to you by exam feel
calm no more fear from exam please make
sure that you have watched all the
videos from part 1 to 11 before going
ahead with part 12 in law is more
popularly known as law of areas why
because this law stated the line joining
a planet to the Sun sweeps out equal
areas in equal intervals of time what
does that mean that means whenever the
first block clarified the fact that the
planet will revolve in an elliptical
orbit the second law stated that the
area covered by the planet while
revolving around the Sun will be equal
in equal intervals of time that means
the rate of change of area with time
will be constant let us suppose here we
see that this is the Sun located at the
focus and this is a planet which is
revolving around the Sun let us suppose
I consider an instant from where it
starts to volume let us suppose this
position is p1 it reached p2 so when it
traveled from p1 to p2 so what is the
area swept in traveling from p1 to p2
this area right now again the same
planet will keep revolving it will come
to some other point let us say p3 again
it will keep going and it will reach
some points of P three and again it will
go on and on so again in this case fraud
when it traveled from p3 to p4 the area
covered is this area so according to the
second law it says that the area
traveled in moving from p1 to p2 let us
suppose this time taken to go from p1 to
p2
testing again time taken from going from
P to P 4 is again dead shutting so the
area traveled in this case will be equal
to the area traveled from P 3 to P 4
that means in equal intervals of time it
will travel it will cover or it will
sweep out equal areas so that that was
what was proposed in the second law and
that is why this law was known as the
law of areas because this law talked
about the areas covered by the planet
while revolving around the Sun let us
suppose that a position and momentum of
the planet is denoted by R and B
respectively
RS for position and P is for momentum
right now what would be the area covered
by the planet in time delta T as you can
see here I say that the planet moves
from p1 to p2 in time delta T so what
would be the area covered by the planet
in this time that means what is this
area so let us denote that by Delta a so
this area will be half into R where R is
the R denotes the position of this
planet as I already told so half into R
into the distance which it travels here
right now let us say that the planet the
velocity of the planet is V if the
velocity of the planet is V then this
distance which it travels from p2 p1 to
p2 in time delta T will be V into delta
T so this would be V into delta T so we
can say that the area traveled that is
this area would be equal to half into R
into V into delta T so we are using
simple mathematics here so from this we
can say it is a by delta T is equal to
half R cross V
we are dealing with all vectors these
are all vector quantities right now this
we can write as we already know that
momentum momentum is equal to mass into
velocity right so we can say velocity is
nothing but momentum divided by mass so
if you do that with mass being a
constant quantity it will come out so
this would be R cross T now what is R
cross V that is the cross product of
read the position vector and the
momentum vector that is nothing but L
where L is the angular momentum so L is
the angular momentum when I talk of P P
is the linear momentum so this is L by 2
m now L by 2 M is equal to constant for
any central force what is the central
force any force which is directed
towards the center so in this case also
when the planet is moving around the Sun
the force which is acting on the planet
is towards the Sun so that is a central
force so for any central force the total
angular momentum remains constant
angular momentum for any central force
is constant so that is a basic principle
so using that we find that Delta a by
delta T is equal to constant that means
the area covered with time is equal to
is equal to constant that is
equal areas will be covered in equal
intervals of time and that is what the
second law states so we will quickly
review this derivation once again let us
suppose this is the Sun this is the
position of the Sun and let us suppose
any planet was initially at p1 it
travelled a distance and reached p2 in
time detract
so how much distance did it cover along
this path it is V into Delta P if V is
the velocity of the planet let us
suppose the position is denoted by a so
what would be the area covered from p1
to p2 it would be half into R into V
delta T right
we know that linear momentum P is equal
to mass into velocity so we replaced
velocity with peep divided by M so from
there we found that Delta a by delta T
that is rate of change of area with time
is equal to L by 2 m where where L is a
constant for any central force therefore
we observed Delta a by delta T is
constant catters equal areas will be
traversed in equal intervals of time so
we covered Kepler's first law and second
law now we'll go ahead and see what does
Kepler's third law stick thank you
please visit exam vo calm to watch free
educational videos try3 online tests get
the best quality study materials study
from the best tutors and mentors and
much more thank you once again