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Sunday, November 17, 2013

Graphical representation of Mangalyaan ( MOM ) in near future

ISRO carried out 5th planned Orbit Raising Manouver ( ORM ) on 16th Nov at 01:27 IST. 

This raised the orbit apogee to 192874 Kms as per ISRO statement and final injection is planned at  0049 Hrs ( some references say at 0036 Hrs )  on 01Dec 2013.

Our calculations yield Apogee ( Height above Earth's Surface ) to be 194653.7 Kms and Perigee of  about 846Kms.  The perigee occurs on 01Dec2013 at about 1300 Hrs IST.

So the OUT OF EARTH's Gravity action ( injection into Sun's Orbit or Heliocentric Orbit or Trans-Mars Injection ) is planned at 1,20,000 kms height. 

In the meantime we computed variation of the s/c ( spacecraft ) altitude over a period of time.

The graphic above shows change in Altitude of Mars Orbiter, Mangalyaan, from 17th Nov to 2nd Dec 2014. The last cycle from above figure ( pertaining to perigee occurring on 1st Dec 2013 is expanded below. Note that the velocity has been multiplied by 10000 in the graphic. At the time of 0049 Hrs the Height is 1,20,134Kms and Velocity is 1.653 Kms/sec  ( shown within Green band in the left ). Velocity at perigee is 10.3 Kms/sec ( Max of blue graph ) in normal circumstances. At that time LAM will be operated and under its effect the velocity will increase as shown with RED arrow starting within green band.Note that due to addition of extra force the s/c will attain such a velocity that  after perigee it will not return towards Earth but will continue to fly away in the same direction with the same velocity as shown with RED arrow.

Same fact is shown a three dimensional illustration in next figure on right.

 Figure on right shows ( partially ) the orbit after 5th ORM and the blue line shows the path that s/c will take during Trans-Mars Injection ( TMI ). Full orbit could not be shown due to system limitations.
As stated in earlier post the s/c ellipse is inclined at about 19 deg w.r.t equator.  Ecliptic makes an angle of 23 deg with equator so effectively the orbit is about 23+19=42 deg w.r.t. ecliptic which approx corresponds to the 150 deg inclination of the probe at Mars. So the s/c has to travel in that plane which is oblique to ecliptic when released from Earth's gravitational force.

Left figure shows the same geometry when seen from a point above North pole. Observe that the sunlight on Earth is from the bottom left corner.
Numerical calculations show that the farthest point of ellipse ( apogee ) is directed towards Sun  so that when released from this orbit it will be influenced by Solar gravity and will be pulled towards it. But care will be taken to see that the s/c is released in such a direction that it becomes a Man made 'planet' orbiting Sun. In due course it will come near the Mars and then again a correction will be carried out so that it gets deflected towards Mars and gets into its field as shown in next sketch.

BTW here is reference to Solar system positions on Dec1   and on 21Sept2014.

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