Good morning. This will be our first class
on rocket propulsion and in this class we
will
look at what is the subject on rocket propulsion;
how it differs from other propulsion
subjects. We will go through the course contents
and then see the books that we must be
referring to. May be the introductory part
will take some something like ten fifteen
minutes and then we will get started with
the course.
Let us first take a look on what this subject
on Rocket 
propulsion is about. The word
propulsion comes from the Greek word pro pellerie.
The word pellerie in Greek means
push, therefore we are talking of something
pushing. Pro as you know mean something
like forward or before, therefore the word
propulsion means push forward and therefore,
whenever we talk of any subject on propulsion,
what we mean pushing forward.
Let us take the simple example of say, a car
which has to claim up a hill, up an inclined
plane. The engine of the car pushes it forward;
and by pushing you are changing the
velocity of the car or you 
are imparting a momentum to the car. What
is momentum?
We say the car has a velocity v, it has the
mass, if you say mass into velocity is what
is
momentum and if you want to change the momentum,
you have to change the velocity of
the car since the mass of the car is about
a constant.
You give some velocity and you have what we
call as change of momentum. Now you
know in space deep space, we do not have something
like atmosphere and therefore, the
act of imparting momentum to the object in
space 
is what we deal with rocket
propulsion. I will again repeat: propulsion
means pushing objects and when we say
rocket propulsion, we are dealing with pushing
objects in space.
Space means anything beyond us, may be up
there. Therefore, may be first we must get
an idea on what space is about. But before
getting more into defining space, let us
quickly get some idea on what this whole course
is on and how we are going to organize
ourselves in the next forty classes.
May be in the first class starting today,
we will look at what we meet by the word space,
what constitutes space, in what way motion
in space is going to be different than motion
on the ground. That means, we talk about motion
in space and once we know how
motion takes place in space may be, we will
able to find out what is the exact
requirements of a rocket.
To be able to make a rocket -- a rocket could
be something very small or it could be
huge -- I must know what is the requirement
of motion of a rocket in space? So the first
chapter will deal with motion in space and
how we go about converting this motion in
space to the requirement of a rocket. Once
the requirement of a rocket is clear to us,
the
second chapter will deal with let us say,
the theory of rockets.
You know, I would like to ask a question:
why should a theory of rocket be different
from a theory of a car or let us say, theory
of a gun? I fire a gun - the bullet leaves
the
gun. In what way is rocket different from
a gun? What is your thinking on it?
You say it is a non air breathing system.
So what, we will get into some details of
air
breathing, non-air breathing later. Let us
say, I have a gun, I fire a bullet from a
gun and
the bullet leaves the gun at high velocity.
Let us assume a rocket is like this. There
is some mass which is available in the rocket.
The mass which is available in a rocket, must
be able to push it forward. That means, it
propels the object 
and what is the object, you have something
like a space capsule which
it pushes forward. The mass in the rocket
is what propels and we call it as a propellant.
By propellant in a rocket, you mean the substance
used for pushing up the rocket or
propelling the rocket. Now in the case of
a rocket, the propellant is continuingly getting
exhausted, it leaves the rocket and therefore,
the weight of the rocket keeps coming
down, and therefore compared to a car in which
I carry something like ten litres of petrol
or something near it, I carry tons and tons
of propellant which is ejected out and
therefore, the theory of a rocket is different
from a car or a bullet.
And therefore, we have to look at the theory
of rockets which will be the second chapter.
After finishing the second chapter, since
we need to give change of momentum and
therefore,
we will go into nozzles which produce high
velocity and help us to achieve a large
change or impart a large change of momentum
to the object in space. You all have
studied nozzles in your gas dynamics course.
If necessary, we will start from the basics,
go through the basics of nozzles, advances
in nozzles but it is an involved chapter.
If you have a rocket something like this:
may be the internal configuration. I have
something like a nozzle here. The flow must
run full otherwise if some portion does not
run full, I could get something like a side
force in addition getting a force in this
direction. Therefore, the theory of nozzles
is quite involved and the third chapter we
should be doing is on nozzles.
In the fourth chapter, we will get back into
the propellants or what is used for propelling.
It could either be a solid propellant, could
be a liquid propellant, could be a gaseous
propellant, could be a hybrid a combination
of these things, could be electricity itself,
could be nuclear, could be anything. And therefore,
in the fourth chapter we will study
about the different propellants.
What are the characteristics required to make
a good rocket and towards this we will
study about propellant solid, liquid, gas,
hybrid, electric may be nuclear propellants.
Once we are clear about the propellants, we
can go into the details of the rockets
The fifth chapter would be solid propellant
rockets. And this type of rockets has been
used very extensively in India both for GSLV,
PSLV and we will have to look at it, look
at the design considerations of a solid propellant
rocket.
The sixth chapter, would be on liquid propellant
rockets. They are more versatile and in
this chapter, we will basically look at what
are the cycles of operation, in what way it
differs from a gas turbine combustor, may
be an IC engine and what are the modelling
features. The liquid propellant rocket is
continuously evolving and when we talk of
cryogenic propellants, it is again a form
of liquid propellant.
Having studied solid and liquid propellant
rockets, in the seventh chapter, we study
about
hybrid rockets and some rockets which use
a single propellant, what we call as mono
propellant rocket. This would finish the different
type of rockets, how to make them,
what are their features and what are the problem
areas in rockets. And once we are clear
about it, we go to an advanced subject which
is combustion instability.
This chapter on unstable combustion on instability
is particularly important for PG and
research students. Since, we are going to
look at what causes unstable or oscillatory
thrust or movement instead of having a steady
and uniform operation and burning
steadily, we will address if it will explode
under some conditions or lead to failure.
We
will deal with it in something like six to
seven classes as it tends to be important
and this
is some area where research works still goes
on in the area of rockets.
The ninth chapter, will deal with electrical
rockets. What do you mean by electrical
rockets? We told ourselves for any rocket,
we need to push an object in space. We will
try to see how we can generate electrical
forces. Different forms of generating electrical
forces using electrostatics and electromagnetics.
The tenth chapter would on be nuclear rockets
and other advanced rockets. What do we
mean by nuclear; I could use nuclear energy
to generate a force. I could also use space
time curvature like relativity to generate
a force. And some of these things will consider
as the last segment of this course.
Let me now briefly talk about one or two books
which I will be following: A good book
for this particular course.
is by Sutton, it’s on rocket propulsion
elements. I think the publisher is Wiley,
year of
publication is 2001. This book gives a very
good description of rockets but the
mathematics of rockets is somewhat missing
and I had published a book, the name is
Rocket Propulsion. It was published by Macmillan,
in 2010. This was based on my
teaching of the course over the last 6 to
7 years.
The third book which gives the good description
about the different rockets is by H S
Mukunda, the name of the book is Understanding
Propulsion and is published by
Interline, Bangalore in 2004. One important
book which I should have said at the
beginning is a book by Hill and Patterson,
the name of the book is thermodynamics of
propulsion, the publisher is Reading. It is
an old book; it was first published, I think
in
1970 or so but the second edition is published
in 1992. We have copies of these books in
our library. This book deals with the thermodynamics
of propulsion, including many of
the propulsion elements. I will 
introduce more books on specific subjects
as we go along.
Let us now get started. What do we mean by
motion in space? Anybody would like to
guess in what way it will be different than
motion on ground.
We need to first define what is space: Is
anything above us space? Say, we 
go on up and
up or we go sideways go to infinity. Is it
space? We talk of space capsules, we talk
of
planets, we talk of galaxies. How would you
define space? You are telling me that
anything outside the atmosphere is space.
What really is space about and what do you
mean by atmosphere? We are here, in
Chennai. Chennai is normally a hot place and
let us try to plot the temperature in the
air
or in the atmosphere above Chennai has a function
or let us say altitude z. We know, we
say since the sun is heating the earth, earth
tends to get hot.
May be the temperature at the surface of the
earth is around 35 to 40 degree Centigrade.
As we go higher and higher up, that means
as we increase the altitude, the temperature
decreases until at an altitude of around,
let us say around 10 to 11 kilometres, the
temperature is around minus 50 degree Centigrade.
These are notional numbers.
Thereafter the temperature begins to increase
again. That means, temperature drops to
minus 50 degree Centigrade at an altitude
of around 10 kilometres and then begins to
increase again.
Why does the temperature decrease? The Earth
receives radiation from the Sun and gets
heated and the surface of the Earth is relatively
warmer and as you proceed away from
the surface, the temperature drops and this
zone where in the temperature drops is known
as troposphere.
A jet aircraft flies at an altitude of around
between 8 to 10 kilometres. Let us say, this
is
where the jet aircraft flies and it flies
where the ambient temperature is between minus
40 to minus 50 degrees Centigrade. You would
have heard this announcement while
flying in an aeroplane that your aircraft
is cruising at an altitude of around 10 kilometres
where in the ambient temperature is of the
order of minus 45 degree centigrade or minus
50 degrees Centigrade.
If you go up still further after the temperature
drop, the temperature increases, the
increase in temperature is because in this
area you have lot of ozone available. The
ozone
sort of gets heated by the solar radiation,
it absorbs the solar radiation, the temperature
increases and this increase manifest for another
40 to 50 kilometres.
Let us say 50 kilometres and the region of
the increasing temperature is what we call
as
the stratosphere 
but when we go still higher altitude let us
say higher than 50 kilometres,
the pressure in air is so small or the molecules
of air are so small that they are unable to
absorb any radiation from the Sun.
Therefore, the temperature again drops with
further increase of altitude from around 100
kilometres. But if you go to still higher
altitudes you have the molecular oxygen reacting
with other molecules and you have the temperature
going up.
The region wherein the temperature drops again
is what we call as a mesosphere 
and the
region of temperature increase because the
individual atoms and molecules are 
getting
heated by reacting with each other to increase
its temperature is what we call as the
ionosphere. This continues for something like
another 100 to 200 kilometres.
If I were to plot the pressure of air, may
be as a function of an altitude z in let us
say in
kilometres. At the surface of the Earth, the
pressure is around 100 kiloPascal and the
pressure monotonically drops, keeps on falling
until maybe at the ionosphere, you hardly
have any air left. This is where we said that
the temperature increases.
The concept of temperature fails in this region
because there is no continuum. And it is
the individual molecules of some of these
gases which tend to get heated to high value.
Now the question is what do we define as space?
Is it anything above the surface of the
Earth going through the troposphere, stratosphere,
mesosphere, and ionosphere and
beyond?
That means, space is sort of endless. It keeps
on going till infinity. Not being able to
define space precisely in terms of extent,
let us examine what is there in space?
We cannot define something which is endless.
We have a look on what constitutes it?
And if you go back and see what is there in
space; you see that there are something like
10 to the power of 11 (1011) galaxies not
in total space but in the space which we can
observe. In the observable space, we say we
have something 1011 galaxies. That means,
space is still beyond but what I can see is
only this.
What are galaxies? Gravitationally bounded
system of stars and each galaxy has a system
of stars and lot of may be some dark matter,
something like gas, dust, etc., in it.
Let us consider one galaxy to which we belong,
which is the Milky Way galaxy.
Therefore, what we have said is, space is
endless, in the near observable space, we
have
something like 1011 galaxies and our attention
has now come to the galaxy which we
belong to or in which we live, which is called
as the Milky Way galaxy.
Why the Milky Way? It comes from the some
Roman or Greek mythology, which says
that the colour is something like milk and
there are some stories around it. We will
not
get into those details but just say when we
talk of number like 1011, we are talking of
a
very large number. At the beach you have lot
of sand particles and I go to all the beaches
around the world and collect all the sand
particles, then we are nearing a value of
1011 .
One particle among all of them corresponds
to our Galaxy out of all the galaxies.
Therefore, we have shrunk ourselves and you
can see, you how small we are in relation
to space.
If now you really see what constitutes the
Milky Way galaxy: well you have a large
number of stars in it. And what are stars?
Massive objects in which nuclear reactions
are
taking place. They emit light and heat. Then
you could also have something like dark
matter between the stars, you could have some
gas and stellar dust or dust: could have
gas, you could also have lot of different
things in it.
You would have heard of black holes; what
are they? You could have it in in our Milky
Way galaxy. You know what happens is that
sometimes the stars shrink to very small
size after their life time is over. Therefore,
you have infinite mass concentrated in a very
small volume and when we have large mass concentrated
in a small volume, it is capable
of attracting, that is the gravitational pull
will be large.
We will get into the gravitational pull towards
the end of this class and therefore, what
we say is we have black holes, we could also
have other objects like quasars. What do
you mean by quasar: Quasi stellar radio sources.
These quasars are objects which are
again travelling at near about the speed of
light itself.
Therefore, you have lot of things there in
our Milky Way galaxy and out of all the stars
in it, let us figure out one star which we
call as the Sun. And therefore, we focus
ourselves maybe from a large number of stars
to one star. We note that we have come to
one galaxy out of all the galaxies and now
we talk of the Sun which is a single star
and it
is about this which we will be basically interested
in for the present discussion.
Let us put this together with some dimensions.
If you look at the Milky Way galaxy, let
us see the extent of this; it somewhat cylindrical
in shape. The diameter is around 10,000
light years. Why do I say light year and not
say kilometres because it so huge. And what
is the magnitude of a light year? The distance
travelled by light in one year.
The speed of light as you know is 3 into 10
to the power of 8 meters per second. In 1
year have 365 days multiplied by 24 hours
multiplied by 60 per minute, 60 per second.
And therefore, one light year will therefore
correspond to so many meters which should
be around, I think, something like 9.5x1011
kilometres or so.
Therefore, we are talking of a large diametrical
content of the cylindrical Milky Way
galaxy and its height is something like 2500
light years. And in this you have number of
stars. We are getting focussed around one
particular star called the Sun or the solar
system.
We are concerned with the solar system. From
the large number of galaxies in the
observable part of endless space and we come
down to the solar system.
What does the solar system consists of? It
consists of the Sun, a single star out of
the
large number of stars in our galaxy and you
have planets going round the Sun. May be
starting from Mercury, then you have Venus
little bigger. Then we have the Earth, what
is next Mars. What would be 
the next one, Jupiter. Next one Saturn, two
more Uranus
and Neptune. Therefore, you have 3 plus 5,
8 planets which are going around. You know
previously we had included another planet
known as Pluto giving nine planets or
“navgraha” but Pluto has been decommissioned
as a planet because it is not fully formed.
It is something like a loose mass which is
still going along with a belt here which known
as a Kuiper belt.
I will come back to this belt because it gives
inputs regarding some asteroids coming
and hitting earth. All what we are said is
in the solar system, we have something like
eight planets going around the sun and this
is part of the space with which we are
immediately interested.
This solar system also consists of something
like 31 moons. How do we define a moon?
There are certain objects which go around
the planets and they go around like satellites
around it. There are 31 moons and Earth has
a particular moon which is going around the
Earth and this is the moon of the Earth. So
also, we will have moon for Saturn, we have
moons for Jupiter and there are something
like 30 other moons in the Solar system.
When we are dealing with all these eight planets
going around the Sun, it is necessary to
have some idea of what constitutes these planets
may be Earth, let us put down the mass
of the Earth, let us put down the diameter
of the Earth. I have it with me. The mass
of the
Earth is 5.974 into 10 to the power 24 kg,
the diameter of the earth is 12756 kilometres.
These numbers are important and I will circulate
a table to you giving the mass of the
different planets and their diameters. But
just to get an idea: mercury is about the
smallest planet around one-third the mass
and diameter of the earth as it were.
The largest would be something like Jupiter.
These planets go around the sun and it is
the motion of planets which provided or which
prompted Newton to formulate the
universal law for gravitation. I think I should
repeat this point in a slightly different
way
after consolidating what is said so far:
Let us therefore quickly revise through what
we have done so far: we said propulsion or
rocket propulsion deals with pushing in space.
For pushing in space, one of the forces
which we could consider is the gravitational
force.
Let us start with the gravitational force.
It becomes necessary for us to go back into
the
solar system to understand it. Look at the
revolution of the different planets around
the
sun as it where. Now let us just take one
particular case: I take the Earth as shown
in this
figure and I say it is going around the sun.
Earth is going around the sun. You know people
have been watching the motion of
planets around the Sun for years together
and around the year between 1570 to 1610,
we
had a famous person by name, Johanas Keplar.
He introduced three laws which govern
the motion of planets like Earth around the
Sun.
The three laws were: 1. All planets move in
elliptical path, i.e., have elliptical orbits.
By
orbit, I mean the path of the planet around
the Sun. But if you read the newspapers
around the month back, there was news that
the orbits are not really elliptical but they
are
wavy orbits something like a wavy elliptic
orbit.
As per Johanas Keplar: we have the orbits
in an elliptical path which is the first law
of
orbital motion of planets. The second law
was on equal areas. Suppose we join in the
centre of the sun with the centre of the Earth.
We find out what is the area swept during
the elliptical orbit. We find that the equal
areas are swept out in equal times.
Let us put it together: this is the Sun which
is at the focus and you have something like
an elliptical path. Let say this is the major
axis and then you have an elliptical path
this is
the second foci, you have an ellipse. This
is the Earth going around the Sun. First law
says it is an elliptical path, the second
law says, may be equal areas are swept out
at
equal times.
If this is the time taken for this area is
swept out by the imaginary line joining the
centre
of the earth with the centre of the sun. And
similarly in an equal area will be swept out
during the motion from here to her for the
same timee. All it tells is, if I come to
this
particular path in which the minor axis, it’ll
travel a longer path here compared to a
shorter path along the major axis.
The third law is one which deals about symmetry
of orbits. All what it tells is you have
the Earth, you have may be Mercury in here
by, you have may be Neptune far away. It
tells that the time of 1 revolution divided
by the radius, is such that the orbital time
t
square divided by the distance cube is a constant.
That is the distance from the Sun to the different
planets divided by the time of orbit of
the particular planet is the particular constant.
These are the three laws of the orbital
motion has formulated by Johanas Keplar.
Why are we getting into orbital motion? We
want to understand something about
gravitation. And Newton comes out with the
Universal Law of Gravitation based on
these laws of orbital motion of planets. What
does Newton find?
Well. The story goes like this. He watches
an apple fall on the ground from a tree. He
immediately connects the apple falling from
a tree to the elliptical orbits or orbital
motion of the different planets around the
sun. What is the commonality? How can we
identify what is the common factor between
these two. Let us take another look at the
planetary motion that we were dealing with
it. This is the Earth as it is going around
the
sun like this in an elliptic orbit.
May be the Earth is travelling some distance
like this, it falls through some distance
because its elliptical. Again the Earth let
us say, it would had a horizontal velocity
it will
go like this but in the process of going horizontally,
it falls through some particular
distance. Again it goes through some it comes
over here, again it comes like this. In
another words, if I had given a horizontal
velocity to the earth, it keeps on falling
towards the Sun at each instant of time as
it progresses at constant horizontal velocity.
In
another words, if the Earth were to go horizontally
at a given velocity, it falls by a certain
distance as it travels.
That means, we have a constant linear velocity
and it keeps falling on to the Sun. It
looks as if the Earth is freely and continuously
falling. It is no different from an apple
which falls on to the ground from the apple
tree. Actually, if we look at ourselves today
all of us are freely falling towards the Sun.
Just in the same way, as a fruit or a stone
is
falling. Therefore, Newton is able to relate
some commonality between an apple falling
to the ground and the planets falling towards
the Sun and it becomes something known
as the Universal Law.
Newton did not do the experiments himself.
He did nothing to really say that, I derive
the
gravitational law like this, or that. He based
it on observations of Johanas Keplar and
others who preceded him like Galileo Galilee
who as you know dropped a piece of a
feather and an iron ball and found that in
vacuum both of them will take the same time
to
come to the ground. Just based on the observations,
he was able to formulate the
Universal Law for Gravitation. But before
I get into the gravitational law, its necessary
for me to go into some more details like how
do you measure forces, distances and
velocities and their units. We need to be
clear on what are the parameters and the units.
We wanted to describe motion in space. I think
we must be very clear because a time has
come when I need to put some numbers, like
to apply or derive equations. We can say
we are all engineers, we know about mass,
length and time. I can use these three
fundamental quantities and describe motion
in space. How will you describe mass?
Quantity of matter, unit is kilogram. But
what is a kilogram. It is some reference kept
in
a lab near in Severs near Paris since let
say, 1819 or so. Some standard is kept which
we
call as kilogram. It is kept very carefully,
you know in a desiccator under very controlled
condition such that it will not get worn out
or will not form scales on it.
It is a platinum rhodium alloy which has a
mass of 1 kg and it has been duplicated at
different places and used as a standard. Well.
We say this is 1 kg. So, also when I say
length is in metres. What is a meter, again
a reference kept at the same lab since may
be
last 150 years or so. And this is the particular
length scale which is given; the length of
this standard. It’s again an exotic alloy
of platinum rhodium but then there are some
problems; though it is stored in the best
of conditions and you have some duplicates
in
some other countries also, it keeps eroding
or scales are formed on it. Some changes do
take place over a long period of time. Therefore,
it is not a good standard and we need a
better standard. How will you have a better
standard? In the year 1982, i.e., quite
recently, scientists suggested to express
the length standard through physical constants.
What is the physical constant to be used?
Whatever happens the length would be the
same, it cannot change may be after a million
years the meter will still be the same since
a physical constant is used.
C
The physical constant used for defining the
length is velocity of light in vacuum. All
of
us know that, light is propagated as an electromagnetic
wave and the speed at which the
light is propagated, we say is C meters per
second. The question is can we use this
constant to define length? It is a constant
because the electromagnetic waves propagate
through vacuum at a constant speed. Let us
say C meters per second and rather than
define the length in terms of a standard like
what we considered viz., a standard of
length, which is kept near Paris, we would
like to define it with respect to this constant
velocity of light in vacuum. How do we do
it? We say the distance travelled by light
is
C meters in one second. In 1/C seconds, the
distance travelled will be one meter. The
duration, we are considering, is one over
C (1/C) so many seconds. Second and second
get cancelled and we get one meter. Therefore,
the more recent definition of length scale
is with respect is, with reference to the
velocity of light in vacuum which is C meters
per
second. The precise value of C is:
299,792,458 meters per second i.e. about 3x108
m/s. Therefore, the definition of length
of one meter is the distance travelled by
light in vacuum over the duration of
1/299,792,458 seconds. This is how we define
the length scale of a meter.
Therefore, what is it we have done so far?
We have considered something like the
definition of mass as a standard kilogram,
may be length has a standard meter but now
we are telling ourselves meter corresponds
to the distance travelled by light in vacuum
for a duration of one over let us say 299,792,458
seconds. But then, we have still not
defined time.
How do we define time? We must be very clear.
Time is something related the duration:
let us say we have a pendulum; the pendulum
goes up and down. The duration of one
cycle of the pendulum may be, pendulum starts
here, goes here, comes back here is what
we say is a duration of one cycle of this
pendulum which we could say as one second.
But then, it is difficult to have a period
like a standard pendulum being used to describe
the time scale and its easier for us to define
the time scale based on the duration of an
event such as a solar day.
This is the most simplest to describe. We
have the Earth, may be revolving around its
axis and it revolves around the sun. One revolution
of the earth around its axis is what
we call as one day. May be we call mid-day
(middle of the day), as when sun is
vertically above us. May be, the sun is vertically
above a particular part of the Earth, we
call it as mid-day at that part. And we go
to the next mid-day, next time the sun is
vertically above at that point and that corresponds
to 1 period of rotation and we call it as
one solar day . That means, in 1 solar day,
a day consists of 24 hours, again each hour
consists of 60 minutes and each minute consists
60 seconds.
And therefore, the one solar day consists
of something like let us say 86400 seconds
and
we can therefore define the time. There is
one problem in this definition though. We
said
earlier that the Earth is revolving in an
elliptical orbit around the sun and it is
also
rotating on its axis as it is revolving around
the sun. The period of rotation is therefore
not exactly 1 day but is slightly shorter
because as it is rotating on its axis, it
is also
revolving. And therefore, the exact period
of one rotation on its axis is not exactly
24
hours but it is something like 23 hours 56
minutes and 45 seconds and this duration is
what is known as a sidereal day. There is
a difference between solar day and the sidereal
day.
Therefore, we have complicated the day, instead
of having one solar day. We need a side
real day which is smaller than 86400 seconds.
Now there are perturbations in the rotation
and also in the path of the Earth around the
Sun. it. And therefore, it is very difficult
to
really define time absolutely very accurately
in terms of either sidereal day or in terms
of solar day.
It becomes necessary to have some other standard
for defining time. This is based on the
period of a wave. Cesium133 material is an
isotope element and it emits radiation. It
emits radiation in different bands. What we
mean when it emits radiation is that it gives
out packets of photons as energy. These radiations
are emitted at discrete frequencies i.e.,
each one having a specific period. So, many
periods of radiation are getting emitted.
Therefore, we look at one specific band namely
at the ground state of cesium. And at
this ground state of cesium, you take one
hyper fine level and you say, many number
of
periods which are emitted. That means, you
say specific number of periods of radiation
which is emitted at the ground state in this
particular hyper fine level is what we will
call
as one second. Therefore, how can we represent
this hyper fine level?
We just said that at this ground state Cesium
is emitting radiation. Each wavelength
corresponds to a certain time. I count a large
number of these wavelengths and the
number of periods or the number of wavelengths,
amounting to something like
9,192,631,770 periods or wavelengths equal
one second. Corresponding to this ground
state 
we have 1 period of radiation or 1 wavelength
is 1/ 9,192,631,770 seconds.
And this is how we define time: namely in
this ground state 9,192,631,770 periods of
radiation emitted is what constitutes 1 second.
And this is an accurate way of defining
time.
To recap: we have defined mass in kg as a
standard, we have defined length as meter
as a
standard, the standard length being on the
basis of the velocity of light. Then we defined
time seconds as a standard.
And now we can derive a set of units, the
length or distance divided by time has units
meter per second and this is what we call
as velocity. When I say distance: it is a
vector,
and therefore, velocity is a vector. And if,
I say momentum, we said mass into velocity
or rather the units is equal to kilogram into
meter per second is becomes momentum. We
say change of momentum is impulse and therefore,
impulse will have units to be same as
momentum namely kilogram meter per second.
We also said rate of change of
momentum is what constitutes force or rather
the impulse divided by the time is force.
And therefore, force could be defined as rate
of change of momentum, that is 1 over
second into we have momentum change as kilogram
meter per second or rather the units
of force becomes kilogram meter per second
square (kg m/s2) which is what we call as
Newton. Therefore, we have defined through
these three basic definition of mass, length
and time, the velocity in meter per second,
momentum in kilogram meter per second,
impulse again kilogram meter per second and
force which is kilogram meter per second
square.
Having defined these quantities may be its
time to go forward and examine how we can
describe using these units the motion in space
of the different bodies and this is what we
will do in the next class.
