MOM ( Manglyaan ) : Notes about distances and speeds

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

Several quarries crop up in various forums about distances referred to in various informative posts by different authors.

Distance between MOM and Earth  at some point of time  for example is referred by some as 24 million  kms   while another person says it is 190 million  kms. Who is right?   Well ..  both in their contexts.

This note tries to explain why the anomaly.

 First we see how the total lifecycle of MOM looks like from launch to TMI to planned Insertion into Mars

orbit.

Pink line is the orbit of  MOM. The initial horizontal undulations in left figure are the orbit raising maneuvers carried out during Nov  2013.
 Dark blue line is the MAVEN spacecraft of NASA which was launched directly out of Earth's gravitational  influence on 18 Nov 2013.
Green line is the movement of Mars plotted from 1st Nov 2013 starting in the diagram for top edge. Its orbit is shown around Sun upto end Sept 2014 which is the point at lower right corner in the diagram. Notice that both MOM and MAVEN are reaching into Mars orbit around that time.

The small spherical beads are the positions of the three respective objects plotted at 10 day interval starting from 1st Jun 2014.

Around 20th Jun ( 3rd marker positions ..  3rd Blue showing MOM position and 3rd red showing Mars position are about 24 million kms apart. So on that day 'MOM is 24 Million Kms from Mars'. True!!  But ..  MOM can't directly jump to Mars.  ( Gravitational Rule enforcement authority of Constable Kepler does not allow sudden right turns. It does not fall in his 3 laws )  For reaching Mars it has to travel a distance of about 180 million Kms along the pink line where the Mars will be around mid Sept. So some one will say that ' MOM is 180 million Kms from Mars' ..  which is also true in the context that he is talking about. So the first way of expressing distance is a 'physical separation' at that instant whereas the second way tells how far the MOM has to travel to meet its destination. And ..  both are right in their context.

( The 3D figures were created using free 30 day trial copy of GRAPHIS software )

Same situation is seen from a different angle in the figure in right. Notice how the MOM distance varies from Sun during this period. It is shortest somewhere in Dec 2013 region. Then it increases and is maximum in Aug 2014 just prior to insertion into Mars orbit.

We know from Kepler's laws that the speed of MOM will vary inversely w.r.t. its distance from Sun during this period because it is in orbit around Sun. So it follows that MOM speed should vary as per this radial distance. We plot on left the actual computed speed of MOM in kms/sec  and MOM's diststance from Sun over its lifecycle during this transfer orbit period for reference purpose.
( sudden increase in speed at the end is the speed that MOM will move with when it will be in Martian orbit. Note that this increase is not due to its distance from Sun but due to its distance from Mars as now it is in Martian orbit. )

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