( First published @ 9/16/14 6:07 PM Pacific Daylight Time ).. revised on 18th sept.
A Power point presentation on basics of MOM is available here.
MOM/Mangalyaan ( मंगलयान ) /.Mars Orbiter Mission and MAVEN spacecraft were launched by ISRO and NASA in November 2013, We had been following the various aspects about those as they unfolded in our previous 3 posts ( 1, 2, 3 ), Current post may be the last update in this blog about their orbital aspects.
Now the MOM and MAVEN are in the last phase of their travel from Earth to MARS and in a few days they will start revolving around Mars and become a part of Martian satellite system. We recall our earlier posts.
Presently all the 3 bodies viz. MARS, MAVEN and MOM are orbiting around Sun such that the orbits of MOM and MAVEN will almost nearly intersect with MARS ( as seen at the bottom right in adjacent figure .. and our focus today is on that portion only)
We also looked at how the speed of varied over its trans martian orbit between Earth and Mars.
So presently MOM is moving @ about 20Kms/sec and MAVEN is also no different in its speed. This movement is under the influence of Sun's gravitational field and if Mars did not have its gravitational effects then MOM and MAVEN would have continued in the same orbit after coming near the Mars on 24th and 22nd Sept respectively and we have plotted below the paths they would have taken in the absence of Martian gravity.
Mars has its orbital velocity around 25 kms/sec whereas both MAVEN and MOM are currently moving at approximately 22 kms/sec. So both are approaching towards Mars @ about ( 25 - 22 ) = 3 Kms/sec till they would have come nearest to Mars ( MAVEN to about 7000 kms and MOM to about 6500 kms ) and then they would continued to move away at about 3 kms/sec. ( provided Mars does not have a gravitational field. ) [ Just for bravity.. an actual example from one of the data sets yields .. ( 25.68 - 22.49 ) = 3.18 kms/sec ]
BUT....... Mars can't disobey Mr. Isaac Newton ..
So it has its gravitational field extending around it, and, at about 577000 kms from its center this field has the intensity same as that of Sun. So if any object comes nearer than that then it gets influenced by Martian Gravity ( hence this area around Mars is called as Sphere of Influence , SOI ) rather than Solar Gravity and it will ultimately strike Martian surface or if its velocity is sufficiently high to overcome Mars' gravity, then it would move ahead ( albeit with a deviated trajectory ).
In the adjacent figure we plot the MAVEN trajectory ( because it gets into Martian orbit earlier than MOM ). The large blue sphere is the Sphere Of Influence ( SOI .. with 577000 kms radius mentioned in previous paragraph ) just before MAVEN and MARS come within 577000 kms of each other.( Sept 20th, 01:10 GMT )
As the time progresses, both bodies ( Red dots ) move ahead but come closer due to their trajectories around Sun. However as soon as they come nearer ( within the SOI ), MARS 'grabs' MAVEN from Sun's gravitational field and as it moves nearer, the speed of MAVEN increases ( just like an object falling to Earth when dropped from an aeroplane.) and it tries to fall to the Martian surface. This has been plotted below .. Blue background figure pertains to MAVEN and Yellow to MOM. Notice that as the bodies come closer to Mars ( Blue lines going down towards the surface of Mars ), the speeds of MAVEN and MOM ( Red lines ) increase exponentially.
BUT.. and this is the most critical operation .. just when it is near to the intended perigee distance ( in the planned Martian orbit of MAVEN ) the retro rockets are fired which reduce the free falling speed and direct MAVEN into its intended orbit.
In adjacent figure we plot the MAVEN movement at 3 instances spaced equally in time.
Position 1 is a free fall situation where the MAVEN speed increases from 3 kms /sec to as high as 5 kms/sec under MARS' gravity. At that instant the retro rockets start trying to reduce the MAVEN speed. MAVEN however continues to fall for some time, but slowly the retros succeed in reducing its rate of fall and after some time it actually starts decelerating the MAVEN and this prevents its crash (or injection into a different hyperbolic orbit .. depending how far the speed reduction has taken place ) on Martian surface - instead it starts now to move around Mars as its satellite.
Notice the reduction in distance travelled by MAVEN between 1and2 and 2and3 in figure indicating clearly that the speed has reduced.
What was said in last paragraph is best explained with a practical figure of MAVEN entering Martian orbit..
Initially the acceleration ( in kms/sec ) is increasing ( rising portion of curve ) but before the craft comes near the surface of Mars, retro rockets are fired which actually create a deceleration. ( falling line in the middle indicates that acceleration has moved rapidly from +ve region to -ve region. ).
When retro rockets stop operartion ( after 33 minutes ) , the craft again gains acceleration but by now its path has been deviated and so it starts orbiting around MARS under its gravitational influence.
Notice that MAVEN approached MARS from upside ( that is, from NORTH ) .. we will return to this observation a little later.
A similar study for MOM is here.
( STATUTORY WARNING: Those with a weak heart should take care that they don't fall off the chair as you would be sitting at the edge of the chair and your heart rate would rise due to the events explained below taking into consideration the odds )
MOM will enter 377000 kms radius Sphere of Influence (SOI) of Mars @22sep 0057GMT and will be pulled by Mars gravity gradually increasing its speed as it free falls towards the surface of Mars.
Presently the surface on which the thrusters that maneuver MOM is pointed towards the rear for carrying out corrections in trajectory. The final correction to trajectory may be taken up @ 9 GMT on 22nd Sept. Note that even during the TCM ( i.e. about 8 hours after entering SOI ), MOM would still be moving at 3.18 km/s.
On 24th 0127 GMT, even as it is falling with speed of 4 kms/sec, the craft is reoriented so that the thrusters face forward ( for the next orbit maneuver of retro thrust to reduce the speed and to direct it in the required orbit ). The re-orientation is completed @ 0147 GMT. MOM would by this time be coming down with a speed of 4.48Km/sec.
After the disturbances due to reorientation have died, i.e. 5 seconds later, the Retro action starts with the firing of LAM using 8 thrusters .. the fall speed by now is 4.68 km/s. Even as the thrusters start their effort to reduce the speed of MOM, the falling speed continues to increase due to the gathered momentum upto 5.89 km/s and then speed starts falling. The LAM firing also directs the craft in the desired direction so that it achieves the required orbit around Mars. The LAM operation ends @0216GMT.
As shown in figure there the MOM speed would increase from 3.18 Kms/sec to 5.89Kms/sec @ 0216GMT.
Now notice that MOM approached Mars parellel to equator unlike MAVEN which approached over Noth pole. The reason for these two approaches is that the final orbits of MAVEN and MOM are inclined @ 75 deg and @ 19 deg respectively. This is evident from the ' cross roads ' seen between MOM and MAVEN release in the combination diagram shown above.
In the above flow of sequence we did not have time to mention a couple of more chilling facts: @ nearly the same time when LAM operation starts MOM would go behind Mars as seen from Earth. Secondly , even if it was visible, whatever happens at MOM will be known to Earth only after 12 minutes due to the distance between Earth and MOM. So all this ( and next described operations ) are being done under the unsupervised pre-loaded command sequences. So the success indicates how well are we in anticipating the situation through modelling.
A detailed look at dynamics of acceleration during this critical operation is shown in this graphic. ( numbers are in kms/sec/sec ) corrosponding to sky blue curve. ( X axis is time axis from 0110GMT to 0310GMT of 24sep. )
Violet curve is the speed normalized to fit in this graph with that of acceleration. Actual speed variation shown corresponds to 3.88 km/sec at left to 5.89km/s at peak near center which falls to 4 km/s at lsft edge.
We have also marked the events of reorientation ( between red dots ) and retro rocket firing ( Between Green dots ) on acceleration curve.
Notice that the LAM retro action started at first green dot on left ( 0152 GMT ) .. it has tried to reduce the speed but the fall is more powerful, so MOM speed continues to increase despite retro action. This continues and for sometime eventhough the acceleration has started reducing ( blue line coming down ), the gathered momentum makes the craft to increase its speed for sometime. Finally however the thrusters succeed in reducing the speed ( reversal near center of violet line ) .. the thrusters are also turned off at that moment.( green dot near the center of graph ). Now the total operation of MOI is over.
Incidentally, the point where speed reversal has taken space forms the lowest point near the surface of MOM prior to first perigee which would occur after the craft completes one revolution.
A Power point presentation on basics of MOM is available here.
MOM/Mangalyaan ( मंगलयान ) /.Mars Orbiter Mission and MAVEN spacecraft were launched by ISRO and NASA in November 2013, We had been following the various aspects about those as they unfolded in our previous 3 posts ( 1, 2, 3 ), Current post may be the last update in this blog about their orbital aspects.
Now the MOM and MAVEN are in the last phase of their travel from Earth to MARS and in a few days they will start revolving around Mars and become a part of Martian satellite system. We recall our earlier posts.
We also looked at how the speed of varied over its trans martian orbit between Earth and Mars.
So presently MOM is moving @ about 20Kms/sec and MAVEN is also no different in its speed. This movement is under the influence of Sun's gravitational field and if Mars did not have its gravitational effects then MOM and MAVEN would have continued in the same orbit after coming near the Mars on 24th and 22nd Sept respectively and we have plotted below the paths they would have taken in the absence of Martian gravity.
BUT....... Mars can't disobey Mr. Isaac Newton ..
So it has its gravitational field extending around it, and, at about 577000 kms from its center this field has the intensity same as that of Sun. So if any object comes nearer than that then it gets influenced by Martian Gravity ( hence this area around Mars is called as Sphere of Influence , SOI ) rather than Solar Gravity and it will ultimately strike Martian surface or if its velocity is sufficiently high to overcome Mars' gravity, then it would move ahead ( albeit with a deviated trajectory ).
As the time progresses, both bodies ( Red dots ) move ahead but come closer due to their trajectories around Sun. However as soon as they come nearer ( within the SOI ), MARS 'grabs' MAVEN from Sun's gravitational field and as it moves nearer, the speed of MAVEN increases ( just like an object falling to Earth when dropped from an aeroplane.) and it tries to fall to the Martian surface. This has been plotted below .. Blue background figure pertains to MAVEN and Yellow to MOM. Notice that as the bodies come closer to Mars ( Blue lines going down towards the surface of Mars ), the speeds of MAVEN and MOM ( Red lines ) increase exponentially.
Position 1 is a free fall situation where the MAVEN speed increases from 3 kms /sec to as high as 5 kms/sec under MARS' gravity. At that instant the retro rockets start trying to reduce the MAVEN speed. MAVEN however continues to fall for some time, but slowly the retros succeed in reducing its rate of fall and after some time it actually starts decelerating the MAVEN and this prevents its crash (or injection into a different hyperbolic orbit .. depending how far the speed reduction has taken place ) on Martian surface - instead it starts now to move around Mars as its satellite.
Notice the reduction in distance travelled by MAVEN between 1and2 and 2and3 in figure indicating clearly that the speed has reduced.
What was said in last paragraph is best explained with a practical figure of MAVEN entering Martian orbit..
Initially the acceleration ( in kms/sec ) is increasing ( rising portion of curve ) but before the craft comes near the surface of Mars, retro rockets are fired which actually create a deceleration. ( falling line in the middle indicates that acceleration has moved rapidly from +ve region to -ve region. ).
When retro rockets stop operartion ( after 33 minutes ) , the craft again gains acceleration but by now its path has been deviated and so it starts orbiting around MARS under its gravitational influence.
Notice that MAVEN approached MARS from upside ( that is, from NORTH ) .. we will return to this observation a little later.
A combination picture showing various actions happening in the final few minutes of both MAVEN and MOM entering respective Martian orbits.
A similar study for MOM is here.
( STATUTORY WARNING: Those with a weak heart should take care that they don't fall off the chair as you would be sitting at the edge of the chair and your heart rate would rise due to the events explained below taking into consideration the odds )
MOM will enter 377000 kms radius Sphere of Influence (SOI) of Mars @22sep 0057GMT and will be pulled by Mars gravity gradually increasing its speed as it free falls towards the surface of Mars.
Presently the surface on which the thrusters that maneuver MOM is pointed towards the rear for carrying out corrections in trajectory. The final correction to trajectory may be taken up @ 9 GMT on 22nd Sept. Note that even during the TCM ( i.e. about 8 hours after entering SOI ), MOM would still be moving at 3.18 km/s.
On 24th 0127 GMT, even as it is falling with speed of 4 kms/sec, the craft is reoriented so that the thrusters face forward ( for the next orbit maneuver of retro thrust to reduce the speed and to direct it in the required orbit ). The re-orientation is completed @ 0147 GMT. MOM would by this time be coming down with a speed of 4.48Km/sec.
After the disturbances due to reorientation have died, i.e. 5 seconds later, the Retro action starts with the firing of LAM using 8 thrusters .. the fall speed by now is 4.68 km/s. Even as the thrusters start their effort to reduce the speed of MOM, the falling speed continues to increase due to the gathered momentum upto 5.89 km/s and then speed starts falling. The LAM firing also directs the craft in the desired direction so that it achieves the required orbit around Mars. The LAM operation ends @0216GMT.
As shown in figure there the MOM speed would increase from 3.18 Kms/sec to 5.89Kms/sec @ 0216GMT.
Now notice that MOM approached Mars parellel to equator unlike MAVEN which approached over Noth pole. The reason for these two approaches is that the final orbits of MAVEN and MOM are inclined @ 75 deg and @ 19 deg respectively. This is evident from the ' cross roads ' seen between MOM and MAVEN release in the combination diagram shown above.
In the above flow of sequence we did not have time to mention a couple of more chilling facts: @ nearly the same time when LAM operation starts MOM would go behind Mars as seen from Earth. Secondly , even if it was visible, whatever happens at MOM will be known to Earth only after 12 minutes due to the distance between Earth and MOM. So all this ( and next described operations ) are being done under the unsupervised pre-loaded command sequences. So the success indicates how well are we in anticipating the situation through modelling.
A detailed look at dynamics of acceleration during this critical operation is shown in this graphic. ( numbers are in kms/sec/sec ) corrosponding to sky blue curve. ( X axis is time axis from 0110GMT to 0310GMT of 24sep. )
Violet curve is the speed normalized to fit in this graph with that of acceleration. Actual speed variation shown corresponds to 3.88 km/sec at left to 5.89km/s at peak near center which falls to 4 km/s at lsft edge.
We have also marked the events of reorientation ( between red dots ) and retro rocket firing ( Between Green dots ) on acceleration curve.
Notice that the LAM retro action started at first green dot on left ( 0152 GMT ) .. it has tried to reduce the speed but the fall is more powerful, so MOM speed continues to increase despite retro action. This continues and for sometime eventhough the acceleration has started reducing ( blue line coming down ), the gathered momentum makes the craft to increase its speed for sometime. Finally however the thrusters succeed in reducing the speed ( reversal near center of violet line ) .. the thrusters are also turned off at that moment.( green dot near the center of graph ). Now the total operation of MOI is over.
Incidentally, the point where speed reversal has taken space forms the lowest point near the surface of MOM prior to first perigee which would occur after the craft completes one revolution.
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