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Monday, April 7, 2014

Spotlight MOM

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

Q: Why Mars?
A:  Mars is the fourth planet from the Sun and so it is the neighbour planet with Earth like features :
Although thin, Mars has an atmosphere. It has surface features like  impact craters, volcanoes, valleys, deserts, and polar ice caps of  similar to Earth. It has tilt in rotational axis that produces the seasons. It has Mountains and canyons. It has two moons. Therefore it was explored by spacecrafts and probes from 60s.
Therefore India’s choice of 1st interplanetary spacecraft naturally was the Mars.

Q:  Why this time?

A.  April 8th ,2013 is a special day in relation between Earth and Mars.

 Mars  will be nearest  (92375644 Kms ) to Earth at 0620 IST.  ( see graph  above.. vertical axis is dist in Light years ) 

This closeness opportunity comes once every 26 months  ( approx ) as seen in the table below.

Date of Closest Approach                Dist bet Earth and Mars
        Jan. 29, 2010                              99.3 million km
        Mar. 03, 2012                            100.7 million km
       Apr. 08, 2014                              92.4 million km
       May. 22, 2016                             75.3 million km
       Jul. 27. 2018                               57 6 million km  ( The closest approach in near future )
       Oct. 13, 2020                              62.1 million km

It takes about 244 days for the spacecraft to travel to Mars in a Heliocentric orbit ( explained later ). So the MOM spacecraft had to start about half of this time before 8th April i.e. 122 days ..  around Dec 1st , 2013. That is the reason why MOM was launched using PSLV on Nov 5th 2013. NASA also launched its Mars probe , MAVEN during the same ‘ window of opportunity of shortest time to Mars in 26 months '  i.e. 18th Nov 2013. 
This window was upto Dec 7th ..  else one would have to wait for next opportunity after 26 months.

Q. MOM was launched on 8th Nov and reach Mars 14th Sept 2013. 
MAVEN was launched on 18th Nov and will reach Mars on 22nd Sept. 
Is MOM orbit design inferior to MAVEN.  

A. You can't compare the two missions on any scale except that Origin and Destination are same.

MAVEN ( launch weight 2500 Kgs approx) was launched using a very powerful Atlas V Centaur rocket. This rocket carried it to about 770 Kms. Then it was powered  continuously by increasing its speed using a small rocket which was still attached to the spacecraft. This increased its speed upto the required Interplanetary Transfer orbit speed. MAVEN was spin stabilized in this phase. So it was directly put in Transfer Orbit. 

MOM on the other hand had a weight of 1340 Kgs. It was launched using PSLV upto about 250 Kms and was launched in 248 X 23550 Kms orbit. In 6 subsequent burns near Perigee of its 440N Liquid engine  brought it finally in 11864 Kms Apogee orbit.  ( this is explained later as an answer to another question.  

Apart from launch their Interplanetary Transfer orbit is also different ..  MOM has its inclination of 2.22 deg while MAVEN has inclination of 2.02 deg.

Q, But wasn’t the MOM launched in Nov ..  not Dec?  

A.     True.  But that was the launch of PSLV which carried MOM into Earth orbit of 23550 Kms. The travel to Mars was actually started on 1st Dec.   This was raised thru 6 successive Orbit Raising Manoeuvres ( ORMs ) to a final Earth orbit of  1.93 Lakh Kms as explained in  next para.

Incidentally  NASA also launched MAVEN on 18th Nov

Q. What is Orbit Raising Manoeuvre ( ORM )?

A.  MOM has  small  rocket like structure at the backend called Liquid Engine ( LE ) which is activated to provide a push in forward direction. This can exert a force of upto 440N. Its operation can be controlled remotely from Earth.

We know that the satellite reverses its direction  around Earth at the perigee point. If we increase its velocity at this point then it will move faster and will rise higher than the current apogee.  Perigee was more or less constant at about 250 Kms in all the Earth orbits.

This technique was used  by firing the 440N LE with a controlled time in each orbit that the ORM was planned. ( ORM was not carried out in a few orbits in initial phase when some other activities and measurements were being done. )

Date         Burn time     Achieved Apogee
5-11           Launch            23550     
7-11           416                    28825     
8-11           570.6                 40186
9-11           707                    71636
11-11                                   78276
12-11         303.8               118623
16-11        243.5                192874

Q. How then was the MOM sent out of Earth’s gravitational influence?

A. MOM was in 4 day ( 3.74 days to be precise )  orbit from 16th Nov 2013. After 3 such orbits when the MOM was near 3/4th of 4th orbit  ( orbits are measured from perigee to perigee ..  4th orbit ending perigee was to have occurred @ 1300 Hrs IST on 1st Dec 2013 ).
But at 0042 Hrs  IST LE was fired for a long duration of 1329 seconds which increased its velocity by 0.649 kms /sec. This increase in velocity caused the velocity near perigee point ( recall that the velocity increases to maximum velocity near perigee ) to cross the escape velocity ( Earth moves @ 29.7 Kms/sec in its orbit and the velocity required to travel in interplanetary Transfer Orbit to Mars is  about 33Kms/sec ) near perigee point and this caused the MOM to go beyond perigee point without turning back to Earth. Beyond this point it started travel away from Earth and was influenced more and more by Sun’s gravitational field which finally culminated into the injection to  Trans Martian Orbit travelling at about 2841245 Kms/day  ( this varies slightly as the MOM changes its distance from ‘ Earth to Sun dist ’  to ‘ Mars to Sun dist’ in orbit around Sun ).
Q. MOM was travelling @ about 33Kms/sec. With this speed it should have crossed Earth’s Gravitational Sphere of Influence ( Radius = 925000 Kms ) in  a few hours then why did it cross it on Dec 4th ..  i.e. more than 3 days?
A. True that MOM was travelling at about 33 kms/sec ..  but the Earth is also travelling @ about 29.7 Kms/sec. So relatively MOM was moving away ( faster than Earth ) from Earth at about 3.3 Kms/sec which translates to some 28445 Kms/day.  At this rate it should take 92500/28445= 3.25 days from TMI ( 1st Dec 1300 Hrs ). 
Therefore it took more than 3 days to cross the Sphere of Influence ( SOI ) of Earth’s gravitational field.

Q. How do the orbits of Earth, Mars and MOM look  w.r.t. Sun?

( The 3D figure was created using free 30 day trial copy of GRAPHIS software )

Q. When did MOM cross the ecliptic from South to North?
A.  MOM orbit is inclined to Ecliptic @ 2.47 deg. 
On  20th Dec 2013 MOM crossed the Ecliptic from South to North.

Q. When and why are orbit corrections planned?
A. MOM was launched in Inter Planetary Transfer orbit on 1st Dec 2013. It has to travel about 700 million Kms over a period of about 122 days. Any small deviation from the planned orbit will make it to deviate in a large error at the end ..  i.e. on 14th Sept 2014 the MOM has to arrive at a place where the Mars will be on 14th Sept.

Note that presently this is point is only a blank location with only some X,Y,Z coordinates. Neither Mars nor MOM is there. Whole gambit of orbit planning is such that MOM will reach that place at exact time so that it intended relative positions of MOM and Mars are achieved. A late arrival of MOM will find that the Mars has gone ahead and so it can’t enter it gravitational field ( which again is only 577000 Kms as compared to 925000 Kms of Earth ).
Early arrival of Mars will also meet the same fate and will miss Mars.

It is therefore very important that MOM follows precisely the planned path and so observations and corrections are carried out to its orbit at three critical points.

1.      After the TMI , communication was shifted from  Low gain antenna  to Medium gain antenna. Then several attitude determination exercises were done and error estimates were made and 1st correction was done on 11th Dec2013.
2.      Currently there are no operations being done except precise determination of MOM path. Today ( 8th Apr ) it would have completed almost half of its intended Interplanetary transfer path. So one orbit correction must have been planned now to ensure that its elliptical curvature is properly oriented and intercepts the Mars orbit at the right place at right time.

3.      A final correction will be required when MOM nears its rendezvous with Mars .. again to meet the requirement and also as a preparatory step to properly inject MOM into Mars orbit. 

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