( 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.
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
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'
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
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.
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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