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## Monday, December 9, 2013

### Mangalyaan / MOM / MARS ORBITAL MISSION leaves Earth

( How will the Martian orbit be established?  Read  here  )

As explained in previous post ISRO carried out TMI ( Trans Mars Insertion ) orbit maneuvour at 0042 Hrs IST  on 1st Dec 2013.

Just before describing that operation we dwell on the subject of how the Orbit Raising Maneuvour is carried out.

The process of orbit raising and TMI  can best be explained using an analogy of the Rocking Boat seen in Amusement Parks.

In the biginning the boat  is moved to a small height and released. so it swings like a pendulum under the influence of gravity. Now every time it comes down it picks up speed and rises and again its speed becomes zero at certain height on the other side of swing and it turns back from that point and again tries to return to the first position from where it was released. But the operator does a trick..  when it is at peak of height and about to drop due to gravity he switches on motor to add speed during this brief period when the velocity is small. Even though the applied impulse is small it is significant in comparison to the very small velocity near the peak and so the boat climbs higher on other side. In this way every subsequent swinging cycle a small impulse raises the height. Note that if the boat was to be raised ONLY with applied brute force,  a very large force would have been required. But here we use a small force at appropriate time and let gravity add the actual required force.

A similar trick was used for raising the orbit ..  a small force is added near perigee ( lowest point of RED curve in adjacent figure ) when the satellite is turning back and the instantaneous velocity is zero at the point of reversal ( Blue curve  ). (The satellite has to stop and reverse so for a fraction of second its instantaneous velocity is zero ). LAM is fired at that time and so in the next orbit satellite takes a higher orbit.

In case of Mangalyaan 6 ORMs were carried out as shown in adjacent figure.

During TMI also a similar method was used but in a slightly different manner. In this orbit Perigee was to have occurred at 1300 Hrs IST. But  at 0042 Hrs IST i.e. before the perigee occurred, the LAM was operated for 1329 secs imparting an increase in velocity by .648 kms/sec to the original velocity of about 1.8 Kms /sec. This increase in velocity- prior to perigee- made the s/c to move faster in remaining portion of orbit and so after crossing perigee the MOM  did not turn back towards Earth ( as it was supposed to in an undisturbed orbit ) but kept moving straight ahead with the attained velocity and moved continuously  away from Earth.

On 2nd Dec 2014 it crossed 3,85,000 Kms which is the radius of Moon's orbit around Earth. It thus became the first object from India which crossed this distance ( Earlier Chandrayaan, the Moon mission of ISRO had revolved around Moon at this distance ).

If left undisturbed it would have continued in this direction continuously. But one more phenomenon occurred on 4th Dec 2014. It crossed Sphere of Influence of Earth's Magnetic Gravitational field.

What is Sphere of influence of Earth’s Magnetic Gravitational field?:

( see bottom chart in this figure. Field is maximum near Earth and it reduces as we move away from Earth surface. )

-  Earth is planet of Sun, so  Sun’s Magnetic Gravitational field keeps Earth go about the Sun in elliptical ( but almost circular ) orbit.  Therefore this Sun’s Magnetic Gravitational field is almost constant throughout around path of  the orbit. At a distance of 9,25,000  both these fields are equal. So as the craft crosses this distance the major force acting on the spacecraft is Sun’s field and so it becomes a part of Solar system ( Till it reaches the field of influence of Mar’s magnetic gravitational field at a later date in Sept ‘14  ).

Now onwards the Mangalyaan will travel to Mars as if it is a part of Sun's planet ..  only difference is that it will not take a near circular orbit as other planets do but it will be a half orbit which started start at Earth an will end at Mars as shown in figure below. Inner circle is Earth's orbit, Outer is Mars'.  AND THE RED SOLID LINE IS Mangalyaan orbit connecting them.

Notice that even a small deviation in the beginning from intended orbit will cause large deviations at the end of flight when s/c nears Mars so it is utmost important that it is on the right track in the beginning itself. So ISRO has just now ( 0100 GMT 11dec2013 ) carried out a correction to properly orient it.

The s/c was about 2.9 million  Kms from Earth.
Also remember that at this distance the communication is delayed by about 10 seconds oneway !!!!

Naturally more corrections will be carried out when the s/c turns around in the orbit ( rightmost point in the figure )  and also near the end of trajectory ..  else the s/c can never enter into Mars' magnetic gravitational field.

After entering into its field the s/c needs to be slowed down  ( reverse of TMI carried out to deviate from the Earth orbit  ) so that it can become a satellite of Mars ..  else it would fly past it.

Many a queries pour in asking " How far is MOM from Earth now? "
Since the answer to this question is always a changing value, I have made below a ready reckon-er chart showing distance of MOM from Earth w.r.t Date as horizontal axis.

Note that this a Straight line distance between 2 objects and NOT the ' Distance  travelled along elliptical orbital path ' ( this is available in the next graph ).

MOM was released from Earth's orbit on 1st Dec 1300 Hrs IST and it started travelling away from Earth. This event is called TMI ( Trans Mars orbit Insertion ). On 4th Dec it crossed the border of Earth's Magnetic Gravitational Sphere of influence because beyond this distance the Earth's magnetic Gravitational field is less than Sun's Magnetic Gravitational field strength and the MOM truly became a part of Sun's several satellites and planets travelling in an elliptical orbit containing both the Earth and the Mars. This elliptical orbit is not exactly in the same Ecliptic plane that the other planets are revolving around Sun ..  this MOM orbit is inclined to Ecliptic at an angle of 2.4711 deg.

Following graph shows the dist travelled ( in 10^6 kms by MOM in this orbit since the TMI on 1st Dec 2013. Remember that the Earth is no more at the point where TMI took place. It is only a historic point but still this graph gives the distance travelled from Earth.

Figure on left shows the difference between ' distance traveled by MOM'  and ' distance between Earth and MOM '.

Thick Red path is the path that MOM would take to travel from Earth to Mars. Blue circle is Earth's orbit and Green circle is Mars' orbit.  1 to 5 are 5 arbitrary positions ( not to scale ) of Earth and Mars. Dashe black line on lower left is the distance that MOM would have travelled after TMI on 1st Dec 2013 and current position of MOM. Pink line is the distance between Earth and MOM. Notice thst distance between Eath and MOM is not linearly varying over a period of time ( see the yellow background graph above ) whereas the distance along the orbital path of MOM is almost linear ( there are small variations in speed due to the difference in distance from SUN along Apogee and Perigee of MOM orbit about SUN  ).

A point of special interest is position 3 of Earth and Mars. This is the position occurring on 8th April 2014 ( 0620 IST )  when the distance between Earth and Mars is minimum ( 92375644 Kms i.e. about 0.6175 AU )  and on 14th April  when SUN, Earth and MARS are in one line ( Mars is said be in  opposition ) .

Actually this ' nearest position '  is the reason why both MOM ( 244 days flight time after TMI ) and MAVEN  ( 242 days flight time ) started in November  2013 because then the travel distance would be minimum and the Transfer orbit would be nearly equally ( about 122 days on both sides )  spaced around this point ending the travel in September 2014.

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#### 2 comments:

1. Sir, would it not be earth and sun's gravitational field as opposed to magnetic fields?

2. My Bad .. Saumitra.

It shoul have been gravitational field and not magnetic field

Thanks for pointing out .