How was MOM placed in Martian orbit?

In the previous post we had shown how the Martian Orbit Insertion ( MOI ) will be carried out and also reviewed it in light of  MAVEN MOI that was carried out 2 days prior to MOM( Mars Orbiter Mission ..  also called Mangalyaan )  MOI .

A quick recall is here:

MOM entered Mars' gravitational sphere of influence on 22Sept2014. During its descent its speed increased very rapidly ( i.e. acceleration also increased ) as it approached near the surface of Mars. At this point when the MOM was about 2500 kms from Mars' surface the retro rockets started reducing the speed and slowly it entered in the regular orbit around Mars.

Although it appears as simple a thing as pressing the brake pedal in the car , it is an involved and complex  process and we will see the actual course of incidents that have taken place and how and why behind it in this post.

Antenna switch and Orientation reversal:

Much before the MOI time ( at 2248 Hrs GMT on 23rd Sept ) the High Gain Antenna ( HGA ) of MOM was switched off and in its place the Medium Gain Antenna ( MGA ) was brought into operation. This was done because MGA has a wider beamwidth than HGA and it would allow communication with Earth even if MOM  antenna is not exactly pointing to Earth due to some unexpected catastrophe.


Adjacent figure shows the MOM moving from left to right. Under normal configuration the Liquid Apogee Motor ( LAM , the green portion on the leftside face in figure ) which had helped in raising the orbits while orbiting Earth is pointed to the back.  ( MOM is moving from left to right In the adjacent figure and the LAM and  8 other small thrusters are pointed to the rear  ).

The LAM would be used to create a braking torque during MOI and so it has to be pointed to the front. This change in attitude was initiated at 0127 GMT on 24th Sep and lasted 20 minutes. Technically this is termed as ' Forward Orientation'
A period of 1 minute is given after completion of Forward Rotation  for the system to stabilize in the new state and actual MOI is initiated at 0148 GMT.

Immediately after the MOI is over, the MOM rotation is started to normalize the orientation. This 'Reverse Maneuver  lasted 22 minutes ending at 02:34 GMT.

Eclipse and Occultation:

A small deviation from the current topic:

Even as the attitude change was going on, MOM went in the shadow of Mars @0143 GMT technically termed  as 'MOM enters Eclipse'.

Also 4 minutes after MOI had started ( 0152 GMT ), the MOM disappeared from Earth view as it went behind Mars at that time and therefore it couldn't communicate with Earth ,This phase is technically called as occultation. Since MOM is already in eclipse there is no Solar Energy to charge batteries and so to conserve energy the telemetry transmitter is switched off because anyway no communication was possible during this occultation.

The eclipse continued upto 0207 GMT  and occultation ended @0215GMT and telemetry was resumed  @0218GMT.

MOI Requirement defined :

 

The MOM has a planned regular orbit of 80000
kms near apoapsis ( maximum distance from the surface of Mars )  and  430 kms at periapsis ( Minimum distance from the surface ). Applying simple Kepler's laws near the periapsis, we obtain Height, Speed and Acceleration  that the MOM would have in this orbit near periapsis and it is plotted in dashed lines in this figure.

The Speed and Acceleration of MOM before MOI as it approached 2500 kms near the surface of Mars at 01:48 GMT is plotted as Solid lines in the left top corner. The speed at this instant has reached 5.18 kms/sec while acceleration is 0.89 m/sec/sec.  The aim of the whole MOI operation is to change these quantities and bring them to the required values shown in dotted lines. How is it done is shown in the next diagram.

MOI Operation:

Red line in adjacent figure shows acceleration during this critical operation ( numbers are in kms/sec/sec ). Height of MOM from the surface is a blue curve. Green line shows speed in kms/sec relative to Mars surface.
X axis is time axis from 0145GMT to 0225GMT of 24th Sept.

As soon as retro rocket start @ 01:48:40 GMT,  ( at about 2500 kms from the surface of Mars ) we can clearly see the sudden drop ( vertical portion ) in forward acceleration from 0.89 to 0.137 m/sec/sec.

This retarded the previously increasing speed from 5.18 kms/sec to 4.38 kms/sec,  a drop of 0.8 Kms/s over the burn duration.

Acceleration also drops from 0.137 to -1.55 m/s/s in this period.

1st Orbit start:

About midway through MOI, acceleration becomes -ve and MOM starts rising ..  this is the periapsis at the start of 1st orbit.

As soon as the retro rocket stops @ 02:11:50 GMT the MOM regains its natural speed around Mars ( as its satellite under the influence of Martian gravity ) and the acceleration which had fallen to -1.55 jumps to -0.73 m/s/s. and MOM starts its 1st orbit around Mars. This point becomes the periapsis.

 .

A small observation worth to take note of:

 Notice that the LAM retro action  tried to reduce the speed but the fall is more powerful under the influence of Martian gravity, so MOM speed continues to increase despite retro action for sometime.( Peak speed of 5.18kms/sec @ 0156GMT) . This is the gathered momentum  by MOM during freefall.  Finally however the thrusters succeed in reducing the speed and as soon as this speed matches with the required speed  ( 4.38 kms/sec ) in actual orbit    ( dashed and solid green lines match )  the thrusters are turned off .
Now the actual operation of MOI is over.

Autonomy of MOI:

At the time of MOI, MOM was at a distance 224 million kms from Earth ( Equivalent to 12.5 Light minutes ) and so there is a 12.5 minutes delay in one way signal transmission. It follows therefore that one can't control MOM online and therefore the whole operation of MOI had to be carried out by onboard computers without waiting for decisions from Earth. Whole operation was as per the preloaded commands and so proves the maturity of ISRO scientists in correctly modelling the anticipated situations at Mars end and assimilation of Martian parameters.

Added to that is the fact that the MOM was in radio shadow from Earth during a major portion of MOI operation.This did not allow even to know what happened during MOI untill MOM emerged out of radio shadow.

Fundamentals on Modulation

Any communication over a longer distance involves modulation. So just before entering into the satellite specific subjects we will do a run through on Modulations. ( Now in a more formal way ).

BASIC COMPONENTS OF COMMUNICATION:

As explained in earlier post three components are always involved in a communication:
i. An Information or Data Or Message which is to be sent. In technical parlance it is called as Baseband ( BB ).
ii. A  Carrier which is modulated by changing one of its component ( Amplitude or Frequency or Phase ) based on the value of Baseband
iii. And  A Medium through which the modulated carrier will travel. It could be a Copper wire or space or Fibre cable through which a light is passed.
iv. We also saw that the Baseband can be Anlog or Digital and also seen that Digital is nothing but converting the analog baseband into a digital value by ( this is a new word but again old wine in new bottle ) Quantization. ( remember 1000 Rs converted to 010101011000   format we said there will be Rounding Off error …  well that is the process of Quantization and that error is the Quantization error. An important property of BB in digital case is that it will be generated at a fixed frequency called Data Rate. The change of state from 1 to 0 or 0 to 1 is called as a Transition.
v.
Some terms associated with digital signals are graphically shown here and are self explanatory:

 From now onwards we will concentrate only on Digital signals because Analog modulation is rarely in use now a days.  Even in Digital modulation our main focus will be on Phase Modulation  …  again because that is the one which is in use for most of the high efficiency systems.  What is high efficiency? We will shortly see that because before that we must understand what is Bandwidth and  we will try to understand that right away.

SPECTRUM AND BANDWIDTH:


Recall what is a carrier. It is a sine wave of a certain frequency. Suppose that this frequency is 70 MHz and has an amplitude of 1V. How will it appear on a graph having Frequency as X axis and amplitude as Y axis.? It will look like shown in left hand drawing  below. Idealy  it should look a thin fine single line.

         

This representation of Amplitude versus  Frequency is called as Frequency Spectrum.  A practical Frequency spectrum as seen on an instrument called Spectrum Analyzer is shown in right photograph.

Although apparently it looks like a clean vertical line if we expand it to a large extent then we see very small jitter in frequency.
 

It is not a single line because practically there is never a rock stable  frequency. It will always jump in phase and frequency  ( A  70 MHz oscillator will give 70.00001 MHz,70.000024 MHz, 69.00002MHz, 70.0000 MHz, 69.000042 MHz  and so on at different instances   .  Naturally most of these wanderings will be near the exact frequency but some stray frequencies  will also show their presence on spectrum display ) causing the thickness instead of a clean line.


That was about a clean sinewave. How does the spectrum of a square wave look like?  To answer that let’s see how a square wave can be generated using sine waves. ( Please ignore the imperfections due to hand-drawn figure )

In this diagram two sine waves ( Red and Green shown on top portion )with frequencies of f and 3f are added. ( i.e. if f= 1khz then 3f=3khz or if f=1 MHz then 3f= 3MHz …  what is important is that they are in the ratio of 1:3 or second frequency should be 3 times the first one.  Such frequencies are called as harmonics ..  Red is the 3rd harmonic of Green )  The addition results in a near square wave as shown in bottom portion.
If we add next odd harmonic  ( i.e. 5f ) then a we get a waveform which is still nearer to a square wave as shown in right bottom portion of figure.

Addition of more odd harmonics 7f,9f …  will bring the output waveform still nearer to a perfect square wave.

A professionally drawn image with higher harmonics is reproduced here on left from a very good article ( http://www.skm-eleksys.com/2010/10/fourier-series-in-electrical.html  ).

In converse we can say that a square wave is made up of many odd harmonics of sine wave, the lowest frequency ( f )  being equal to the square wave frequency.So its spectrum should show all the odd harmonics that it is made up of.

Actual spectrum of a square wave is on right. Notice several vertical thin lines each representing a sine wave. ( The small components near bottom are due to imperfection in squarewave used for making the spectrum display and we can ignore them. )


       
Just for academic interest. In the above description we have taken odd harmonics. What happens we take even harmonics and add them?  We get a Triangular wave instead of a square wave.

Such studies is the subject of Fourier Analysis and Harmonic Analysis.  We will not go in those details here.

Decibel, db, dbm, dbW ..  etc Explained

Although in  previous  figure amplitude was shown as 1 Volt for clarity, any  Spectrum Analyzer  almost always represents the Y Axis  in dbm that is ‘ the amount of RF  power delivered to load when referred to 1 mw’. Please do not faint I will explain.
In electrical systems voltage is a measure of amplitude. ( Like we say 230V is the voltage of household supply in India ). When this voltage is connected to a 100W bulb,  then 230V is applied across the filament of lamp and it causes current to flow through filament which heats the filament  and it starts glowing due to the heat produced. Naturally the filament is causing a load of(  V^2/R ) which is 100W. ( R is the resistance of filament of bulb ).
Same thing happens In Radio Frequency Communications also.  The RF signal from transmitter ( Technically called SOURCE ) is connected to a LOAD ( Equivalent of Lamp in electrical circuit ). The RF energy generated in Source is transferred to the load.
Now here comes the difference.  In electrical circuit we don’t bother much about the capacity of Source and the Load because the source has almost infinite capacity ( compared to a single lamp that we have connected ). But in RF connections it is not so simple. Rf energy is generated with a highly complex oscillator and has to  always  be  transferred  in  total to the load  ( We will see later if the two are mismatched then there is possibility of them getting burnt or an arcing to happen ) ,   and this happens when the source and the load are perfectly matched.
  The source generates 1 W power. The source has an internal impedance ( impedance is similar to resistance but its value changes with frequency ) of 50 Ohms. This power is connected to the load which is also 50 Ohms. One more concept that now needs to be explained is that the line connecting two devices in RF circuit  is called a transmission line and it also has an impedance. The connection between source and Load is done through a line which also has an impedance of 50 ohms.

That is Maximum power gets transferred from source  to load when the two are matched.
Now we said 1 Watt of power.    In RF circuits Watt or similar units are rarely used.
We use what is called as a decibel system. It is a logarithmic system to show a ratio between two powers i.e. 10*log(ratio).


 By definition decibel it is represented by 20*log(voltage ratio)  or 10*log( power ratio )

 E.g.  Suppose there is an amplifier which amplifies the signal voltage 25 times.  So we represent voltage gain in  db as

Instead suppose the Power ratio was 25, then we get

That explains about how relative ratios are shown in db. But we also must be able to define some absolute levels.  ( Ratio of 25 can mean 1W is amplified to 25W, or 100W is amplified to 2500W. it is only a ratio.
We said earlier ..  The carrier amplitude is 1V. Now this is an absolute value. You can’t have .2V as 1V or 20V as 1V. It is an absolute value 1Volt. )
In such cases we have to define ratio with some fixed ( absolute ) level.
E.g. 5V is 5 times of 1V so it will be computed as 20log( 5/1 )  and since it is defined w.r.t  1V reference level  it is called as dbV.  So 5V is = 13.98 dbV.
Some other Reference Decibels that we regularly come across are,

 
A Common approximation used for quick calculation is  Power ratio of 2 ( doubleor half the power ) = 3 db ( actually it is 3.010) .   Some more quickies are  10 times power = 10 db,   2 times voltage = 6 db,    10 times voltage = 20db.

PSK, BPSK, QPSK Modulation systems

In an earlier post we have seen that the carrier has a form A*sin(ωt+ɸ), ɸ, the phase, specifies where in its cycle the oscillation begins at t = 0. Adjacent  figure shows  4 possibilities of how 90 deg phase shifted waveforms will look like. Thick line on left is the start time indicator, ( T=0 ); and one can see how the four waveforms start at different phases at T=0.

Such type of modulation where the Phase of the carrier is changed as per the Digital value of Baseband is called as Phase Shift Keying (PSK). This gives various possibilities and therefore is most preferred where high data rates are involved. Two most common PSK modulation schemes are BI Phase Shift Keying ( BPSK ) and Quadrature Phase Shift Keying ( QPSK ). We will go in some detail about these two.

How can we generate this BPSK modulation?  Right side figure symbolically shows a BPSK modulator.

The phase of the carrier is changed as per the input value of Baseband resulting in two types of outputs:

A combo graph of Baseband and Modulated carrier is shown below for the baseband  data stream 01101110100

Notice  that whenever BB changes its state from 0 to 1  or  1 to 0 , the carrier changes phase by 180 o ( see expanded view ).

Instead of just 180 we can have 4 waveforms spaced at 0, 90, 180 and 270. But there is a small problem. In BPSK we had 0 or 1 as the two states of Baseband but for QPSK we require 4 states. How we do that? To overcome this we now use four states, each consisting of a pair of bits from two data streams  viz   00, 01, 10 and 11. Each pair is called as a symbol and so for each symbol there will be a distinct state on output carrier as plotted  in next diagram.

For generationg these symbol codes an encoder is used which strips the incoming serial data into two streams I and Q ( They are actually abbreviations for In-Phase and Quadrature ) which are applied to each half of modulator.At the receiving end a special decoder is used which will combine the demodulated I and Q data streams into a single serial data output which is the replica of original data. Encoder actually serves another very important function, that of security key. The encoding is done by using some algorithm and one can keep his data secure by keeping the encoding algorithm a secret. A corresponding Decoding Key is required at receiving end and data reproduction can be done only by using that key.

 We can imagine a QPSK modulator to have been made up of  two identical  BPSK modulators fed with quadrature phased carriers for modulation. This results in one giving a 0/180 phase outputs and the other givinging 90/270 phase outputs  which connected to an adder which  combines both the BPSKs.

In our next dose we will cover demodulators and some other communications topics.

PSLV-C18 to put four satellites in orbit

Now more clarity has emerged from ISRO about the co-passengers of Meghatropiques on PSLV C18 flight.

The flight is scheduled for launch on Oct 12th @ 11 AM IST.

The other three satellites on board this flight are
The 10-kg SRM Sat , 3-kg Jugnu  and a  Luxembourg  satellite VesselSat.

Note that AIS-SAT which we reported in an earlier post has now been renamed as  Vesselsat

Details are in the news clip here:
http://www.thehindu.com/sci-tech/science/article2512630.ece

Unfortunately as usual the official  ISRO website
 http://www.isro.org/pressrelease/scripts/pressrelease.aspx
is silent after July12 2011  news release about GSAT 12 .

I had written  an email to ISRO pointing to an error in the graphical display in their live transmission of GSAT 12 launch but they have not even acknowledged it,    forget about reaction.

PSLV to Carry Meghatropiques and AIS Sat 1

PSLV in its 18th commercial flight ( PSLV C18 ) is expected to carry French Satellite Megha-Tropiques and  Orbcom's AIS-Sat-1 (equatorial)satellite.

Most powerful PSLV launches communication satellite GSAT 12

In the 18th successful launch of PSLV, viz PSLV- C17, launched GSAT-12,a 1,410 kg communication satellite.

53 hour countdown starts for PSLV C17 launch

As per ISRO press release a 53 hours countdown has started in preparedness and checkout of rocket and other subsystems for the launch of GSAT 12 using a PSLV rocket in flight PSLV C17.

Most-powerful PSLV to launch GSAT-12 next week

Indian Space Research Organisation is using the most powerful configuration of its rocket PSLV to launch a communication satellite from Sriharikota on July 15 as it braces for the nearly Rs 200 crore mission. ISRO opted for this step as there is a large unfulfilled and pressing demand for communication transponders.