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PostPosted: 09 Nov 2013 00:02 
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http://lasp.colorado.edu/home/maven/fil ... eline1.jpg

maven's flight path is a longish one riding on more powerfull atlas-v without a slingshot. Another thing in the equation is the effect of suns gravity. Maybe that has some role in the trajectory.


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PostPosted: 09 Nov 2013 00:10 
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arvin wrote:
http://lasp.colorado.edu/home/maven/files/2011/03/MAVEN-timeline1.jpg

maven's flight path is a longish one riding on more powerfull atlas-v without a slingshot. Another thing in the equation is the effect of suns gravity. Maybe that has some role in the trajectory.


So, the "more powerfull" still used up more energy than the ISRO solution. Even within the "longish" variety there is a more efficient solution - it seems to me.

I am sure that ISRO would have used the same mechanism to tackle the 53 million shorter route. They did that to reach the moon too. Just more efficient (or less fuel consumption).


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PostPosted: 09 Nov 2013 00:10 
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Neela wrote:
BTW, why should we meet Mars when it is 300 million km away? Why not when it is "just" 54 million km away?

Well firstly that distance of 54 million km is only true for certain time frame when earth and mars are closest to each other and this happens to be far too smaller than the total time needed for mangalyan to travel that distance , in any case the launch window from earth is dependent on position of Sun because Mangalyan needs to transfer from earth's orbit to sun's before it makes it's final transition to an orbit around Mars.

Following imho explains it in a better way.

http://plato.acadiau.ca/courses/phys/as ... bitrnf.htm


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PostPosted: 09 Nov 2013 01:11 
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arvin wrote:
Another thing in the equation is the effect of suns gravity. Maybe that has some role in the trajectory.
Even as we sit right on earth or in an orbit above earth, we are under the influence of the sun.

negi, good link for a quick study. But what did you mean by the following. Sun is going nowhere with respect to the planets.

Quote:
in any case the launch window from earth is dependent on position of Sun because Mangalyan needs to transfer from earth's orbit to sun's before it makes it's final transition to an orbit around Mars.


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PostPosted: 09 Nov 2013 02:20 
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INDIA’S FRUGAL MISSION TO MARS
Quote:
Space programs are easy targets during difficult times; their long-term benefits appear frivolous next to putting food on tables or jobs on the market. NASA, for instance, lost seven hundred million dollars in funding between 2011 and 2012, in the teeth of the recession. But it has been difficult for Mangalyaan to provoke any credible outrage, primarily because the I.S.R.O. has cost the taxpayer so little. Mangalyaan’s seventy-three-million-dollar budget is a pittance compared to the twenty billion dollars that India will spend this year to provide subsidized food to two out of every three of its citizens, or the $5.3 billion that will be spent this year on a rural employment plan.

The financing of Mangalyaan has thus barely chipped at the edifice of the Indian welfare state. In fact, at 0.0039 per cent of its G.D.P., India’s expenditure on Mangalyaan has been neither lavish nor extraordinary; the United States spent a similar percentage of its G.D.P., 0.003 per cent, in 1962, on the doomed Mariner 1 probe to Venus, which cost eighteen and a half million dollars. The annual budget of the I.S.R.O. is just seven hundred million dollars, or 0.038 per cent of India’s G.D.P. This year, NASA will spend sixteen and a half billion dollars, around 0.1 per cent of the American G.D.P.

But the payoffs of space programs can justify their expense. While the exact economic impact of R. & D. spending is difficult to quantify, numerous studies over the years have found significant returns, as much as seven or nine times the investment. The benefits are not just monetary: in a press conference on Tuesday, the I.S.R.O. chairman argued that India’s expertise with weather satellites, patiently developed over the years, had enabled predictions precise enough to save thousands of lives during a coastal cyclone the month before. What is impossible to quantify, however, is the ignition of imaginations that attends such successes—the spurt of optimism and confidence that can urge people, even for a brief moment, to lift their eyes upward and aim a little higher.


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PostPosted: 09 Nov 2013 02:25 
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Bade wrote:

negi, good link for a quick study. But what did you mean by the following. Sun is going nowhere with respect to the planets.

Quote:
in any case the launch window from earth is dependent on position of Sun because Mangalyan needs to transfer from earth's orbit to sun's before it makes it's final transition to an orbit around Mars.

negi mushay got caught by our resident fizzics brof! :D
perhaps negi meant the traversal path from earth's orbit to mars orbit jump.


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PostPosted: 09 Nov 2013 02:36 
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Neela wrote:
BTW, why should we meet Mars when it is 300 million km away? Why not when it is "just" 54 million km away?

That would be the distance covered by the probe if it could fly at infinite speed, i.e. it leaves earth at the point it is nearest to Mars and reaches Mars at exactly the same time. But because the probe has a finite speed, the mathematics is slightly more complicated.

First, I would give a simplifying solution. Let us assume that the earth and Mars go around the sun in perfect circular paths. Also let us disregard the 'radius' of the orbits of the spacecraft around earth and Mars as insignificant to the interplanetary distance. Now, once you have fixed the speed at which you can eject the spacecraft in the helio-centric orbit, the time taken by the craft to cross the Mars's orbit is going to be fixed (say 'x' time units). The question is would Mars also be at the point of intersection of the both the orbits at that the same time? This is a simple equation to solve. Fix a initial point of reference. At this point, you know the initial angular displacement between earth and Mars around the sun wrt to an arbitrary a reference point. The angular velocity of the earth and Mars is also fixed. The spacecraft will be travelling in an elliptical path. However it's angular velocity follows simple properties. Now the question can be simply formulated as "at what angular displacement of the earth should you inject the spacecraft into it's helio-centric orbit, so that angular displacement of the spacecraft and the Mars is the same after 'x' units of time".

(Added later: pictorial description: via ISRO)
Image

However this gets a little more complicated:
1. Because earth and Mars are not in circular orbit. The angular velocity around the sun is not fixed, but it is well defined. So what? The question that you would ask will still remain the same.
2. What if I can inject the spacecraft into its heliocentric orbit at different speeds, i.e. 'x' is no longer constant. Yes, so what? It is just one more level of differentiation to find the minima.
3. But it is not a superman who is launching the spacecraft from Earth to Mars. You have to reach the point of ejection into the heliocentric orbit. How to get there optimally?

Nothing very complex. It is lots of class XIth mathematics. Just lots of it :wink: .


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PostPosted: 09 Nov 2013 03:05 
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From MOM facebook page ..

Quote:
MOM’s Midnight Manoeuvers !

Third orbit raising manouever of ISRO's Mars Orbiter Mission Spacecraft to raise the apogee to about 70000 km height, completed successfully !


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PostPosted: 09 Nov 2013 07:26 
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From ISRO's page:
  • The third orbit raising manoeuvre of Mars Orbiter Spacecraft, starting at 02:10:43 hrs(IST) on Nov 09, 2013, with a burn time of 707 seconds has been successfully completed. The observed change in Apogee is from 40186km to 71636km.


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PostPosted: 09 Nov 2013 08:16 
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That is heartening. Thanks.


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PostPosted: 09 Nov 2013 10:30 
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Bade I should have been clearer I meant mangalyan's orbit raising exercise for transferring it from an orbit around earth to the final orbit around mars will have to be done depending on relative position of the 3 participating bodies.


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PostPosted: 09 Nov 2013 11:14 
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Methinks that MAVEN is using the high energy route owing to a development of a NASA comfort zone with successes in ejecting objects on earth-solar escape trajectories (Voyager 1, Voyager 2, New Horizons).

Orbiting any object between Venus and Saturn orbits is fraught with similar complications. ISRO has realized that and I hope they will be able to design solutions for exploring Jovian, Saturnian system and Earth-like planets outside Solar System.


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PostPosted: 09 Nov 2013 11:24 
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negi'ji or anybody - have you watched rumali roti being made by the process of tossing up in the air?

Well, think about it, sending mangalyan is basically tossing up high and high till the point where its trajectory intersects with Mars. And as it nears mars, it needs to be slowed down so that it stays in Mars gravity well.

So first the satellite is lofted to some 21k kms up, it falls back towards the center of the earth (however since the trajectory is parabolic and not straight, it does not fall back to earth but loops around)., at perigee, another kick is given to raise the height to some 28k and then another kick to raise it to 40k kms and another kick to loft it to 71k.

At one stage it is given a final kick to get out of Earth's gravity well and towards Mars. See the analogy to rumali roti?

Saik, if you throw rumali roti very high (you want it as high as possible) it will go and stick into the ceiling. Similarly Mars gravity being weaker than Earth, anything that escapes Earths' gravity well has to be slowed down to be captured in Mar's gravity well!


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PostPosted: 09 Nov 2013 14:13 
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May be ot here but how did voyager cross the asteroid belt? Its a minefield


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PostPosted: 09 Nov 2013 14:37 
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http://voyager.jpl.nasa.gov/faq.html

Question: When we send spacecraft through the asteroid belt to the outer planets, how do we navigate the craft through the belt?

Answer: Pioneers 10 and 11 had preceded the Voyagers to Jupiter and the asteroid belt was a major concern for them. By the 1960's more than 3000 minor planets had been discovered and their orbits well determined. Even 50,000 minor bodies spread over the volume of space occupied by the asteroid belt would produce little direct danger, although a chance collision with an uncatalogued object was possible.

"While the largest of the asteroids were known and their orbits charted, many of the asteroids moved in unknown orbits. Although the risk of a spacecraft colliding with a charted asteroid was negligible, there was no way to estimate how many particles the size of a grain of sand might be present in the asteroid belt to collide with the spacecraft and seriously damage it". (From Pioneer, First to Jupiter, Saturn and Beyond, NASA SP-446, 1980) Only by going there could the danger be properly assessed - and Pioneer was first.


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PostPosted: 09 Nov 2013 15:08 
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Negi , Indranil,
Thanks.


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PostPosted: 09 Nov 2013 15:41 
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dhanyavad, negi ji.. wow, that's one heck of capability to have..


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PostPosted: 09 Nov 2013 19:43 
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@Disha ji,

Nice way to explain. But for the first 3 orbits, the kicks were not provided every time the SC was at its apogee perigee. They did it only when it was at the perigee and it was nighttime in India. The only explanation I have for this is better communication and tracking. Is there any other reason?


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PostPosted: 09 Nov 2013 20:38 
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^^^ Is there any website that tracks mangalyaan all the time? Since the LAM motor firing timings are published by ISRO, that would tell us the exact location of the SC (if such a tracking website is there). un-related note: first orbit's period of revolution was less than 12 hours...i.e. 2 (or more) perigees in a day. On a different note, is the ISRO diagram inlined above technically accurate? The direction of the initial orbits relative to sun is interesting (if we assume that they reflect the actual paths).


Last edited by SriKumar on 09 Nov 2013 20:53, edited 1 time in total.

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PostPosted: 09 Nov 2013 20:53 
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indranilroy,

Velocity increases are usually performed at periapsis (perigee in our context) because a given quantity of fuel provides a given quantity of thrust, which increases the velocity by a fixed amount. However, kinetic energy goes up by the square of velocity, so you always get more "bang for the buck" when the spacecraft is at periapsis and therefore has a higher velocity than at apoapsis (and at lower velocity). This is called the Oberth effect.


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PostPosted: 09 Nov 2013 20:57 
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I apologize if it has been posted before. Here is a link to very interesting US's NPR radio interview on Mangalyaan http://www.npr.org/2013/11/08/243950748 ... in-on-mars.


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PostPosted: 09 Nov 2013 21:19 
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Raman wrote:
indranilroy,

Velocity increases are usually performed at periapsis (perigee in our context) because a given quantity of fuel provides a given quantity of thrust, which increases the velocity by a fixed amount. However, kinetic energy goes up by the square of velocity, so you always get more "bang for the buck" when the spacecraft is at periapsis and therefore has a higher velocity than at apoapsis (and at lower velocity). This is called the Oberth effect.

Raman sir,

Thank you. The last post was written in a hurry and that apogee-perigee was a typing mistake.


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PostPosted: 09 Nov 2013 21:26 
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SriKumar wrote:
^^^ Is there any website that tracks mangalyaan all the time? Since the LAM motor firing timings are published by ISRO, that would tell us the exact location of the SC (if such a tracking website is there). un-related note: first orbit's period of revolution was less than 12 hours...i.e. 2 (or more) perigees in a day. On a different note, is the ISRO diagram inlined above technically accurate? The direction of the initial orbits relative to sun is interesting (if we assume that they reflect the actual paths).


http://www.n2yo.com/?s=39370


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PostPosted: 09 Nov 2013 21:46 
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For people like me, who have forgotten everything that we studied yesterday, remembering things read in high school / college days is out of question. Hence I was trying to explain myself in simple layman terms by imagining analogies.

1. Throwing a stone at a dangling mango on a tree branch.
2. Throwing a stone at a running dog.
3. Throwing a stone at a running dog, while riding a cycle.
...
...
...
N. Throwing a satellite from Earth at Mars.

And that is mind boggling. The science behind it might be simple for some of you, but imagine hurtling a spacecraft at a point in space from a moving Earth, and expecting Mars and the spacecraft to have a rendezvous after 300 days? Well that is Science because of the predictability.

And, the things that a country learns by developing such capabilities will have thousand usefulness - very hard to explain to people.


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PostPosted: 09 Nov 2013 22:15 
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krishnan wrote:
SriKumar wrote:
^^^ Is there any website that tracks mangalyaan all the time? Since the LAM motor firing timings are published by ISRO, that would tell us the exact location of the SC (if such a tracking website is there). un-related note: first orbit's period of revolution was less than 12 hours...i.e. 2 (or more) perigees in a day. On a different note, is the ISRO diagram inlined above technically accurate? The direction of the initial orbits relative to sun is interesting (if we assume that they reflect the actual paths).


http://www.n2yo.com/?s=39370
Thanks. I had seen this website earlier but unfortunately it does not have a record of prevoius paths, it just shows current data. But that is actually quite nice too. Altitude and veolcity are updated in real time....it is now coming towards earth. So, with the announcement from ISRO that the next firing is on Nov. 11th, i.e. 2 days away, one can actually see in real time when the motor is fired and the change in satellite parameters on this website! ISRO Sez:
Quote:
The fourth orbit-raising operation will take place on November 11 when the apogee will reach about one lakh km.


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PostPosted: 10 Nov 2013 00:21 
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I have heard some queries outside that were not raised here so far.

1. Why can't we progressively increase the apogee of the Mangalayan moving around the earth to reach Mars orbit? Instead why we are sling-shooting it around the Sun?

2. Why ISRO's Mangalayan craft has to loop earth unlike NASA's MAVEN?


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PostPosted: 10 Nov 2013 00:42 
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Kanson wrote:
1. Why can't we progressively increase the apogee of the Mangalayan moving around the earth to reach Mars orbit? Instead why we are sling-shooting it around the Sun?


Actually we are doing the former onlee; second part is what happens because of Gm1m2/r^2. Too lazy to crunch numbers at this hour but Sun is only 1.496 billion km from us while Mars on it's closest approach is about 54.6 million km from us, I think when apogee raising maneuver is carried out there will come a time when the mangalyan at it's farthest point in orbit around earth will experience a stronger gravitational pull from the Sun and that is when it will be made to leave earth's orbit (and this time with an appropriately fired LAM at Apogee (not perigee ) ). Now Earth's orbital speed is a bit higher than Mars so this entire launch window in planned in such a manner that Mangalyan will have to travel the least amount of distance to Mars when it transitions from one orbit to another.

May be a quick way to verify above would be to take a point say 25 million km radially outwards from the centre of earth towards periphery of the solar system and calculate gravitational pull on mangalyan from both earth and the sun , that should answer this question .

--sorry edited wrong post :mrgreen:


Last edited by negi on 10 Nov 2013 02:07, edited 3 times in total.

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PostPosted: 10 Nov 2013 00:48 
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actually we need the spirals depicted with the earth's revolution/orbit. in the figure indranil posted, we have concentric orbits shown without \time aspect, but the intention to show is seen "mars position at departure".. as it proceeds, and the time it takes for each orbit jump, we need positional shift of earth's orbit in the pic for each orbital maneuver. the center of ellipse will not be the same spot on earth's orbit.


Last edited by SaiK on 10 Nov 2013 00:50, edited 1 time in total.

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PostPosted: 10 Nov 2013 00:49 
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indranilroy wrote:
Nothing very complex. It is lots of class XIth mathematics. Just lots of it :wink: .

Yeah physics actually but then that's splitting hair; XIth std is basically honeymoon period between Xth and XIIth boards so at least I kind of slept over Kepler's laws and mechanics in that year . :oops:


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PostPosted: 10 Nov 2013 00:52 
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basically a dotted spirals along the earth's orbit until it reaches the final orbit jump is what needed to connect and make it more meaningful drawing.


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PostPosted: 10 Nov 2013 01:06 
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has one used GMAT?
http://gmat.sourceforge.net/blog/

http://gmat.sourceforge.net/doc/R2013a/help.html#N1010A

Image

download: http://sourceforge.net/projects/gmat/fi ... t/download


Last edited by SaiK on 10 Nov 2013 01:09, edited 2 times in total.

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PostPosted: 10 Nov 2013 01:07 
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negi wrote:
Kanson wrote:
1. Why can't we progressively increase the apogee of the Mangalayan moving around the earth to reach Mars orbit? Instead why we are sling-shooting it around the Sun?

Actually we are doing the former onlee; second part is what happens because of Gm1m2/r^2. Too lazy to crunch numbers at this hour but Sun is only 1.496 billion km from us while Mars on it's closest approach is about 54.6 million km from us, I think when apogee raising maneuver is carried out there will come a time when the mangalyan at it's farthest point in orbit around earth will experience a stronger gravitational pull from the Sun and that is when it will be made to leave earth's orbit (and this time with an appropriately fired LAM at Apogee (not perigee ) ). Now Earth's orbital speed is a bit higher than Mars so this entire launch window in planned in such a manner that Mangalyan will have to travel the least amount of distance to Mars when it transitions from one orbit to another.

May be a quick way to verify above would be to take a point say 25 million km radially outwards from the centre of earth towards periphery of the solar system and calculate gravitational pull on mangalyan from both earth and the sun , that should answer this question .


When Mars is at closest point to Earth, we are talking about Gravitational pull of three bodies (earth mar and sun) on Mangalayan not just between Sun and Earth, isn't it?

The question raised is, When Mars is closest to Earth, why just go on increasing the apogee of the Mangalayan craft which is currently rotating around the earth to reach Mars directly? Will it not take lesser time? By shooting it around Sun it takes more distance to travel and more time?


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PostPosted: 10 Nov 2013 01:17 
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Kanson wrote:
When Mars is at closest point to Earth, we are talking about Gravitational pull of three bodies (earth mar and sun) on Mangalayan not just between Sun and Earth, isn't it?

The question raised is, When Mars is closest to Earth, why just go on increasing the apogee of the Mangalayan craft which is currently rotating around the earth to reach Mars directly? Will it not take lesser time? By shooting it around Sun it takes more distance to travel and more time?

^ Well firstly that time window when Mars is closest to earth is too small because earth's orbital speed around Sun is higher than Mars and Mars is the smallest of the 3 bodies exerting force on Mangalyan. So I think for the most part Mars is not even in the picture until the point when Mangalyan approaches the planet close enough to be made to decelerate and parked in an orbit around it. Mangalyan will go around the Sun (will not complete even a single orbit, I suppose) and it's orbit will be raised till it get's parked in an orbit around Mars.


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PostPosted: 10 Nov 2013 02:07 
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Kanson wrote:
I have heard some queries outside that were not raised here so far.

1. Why can't we progressively increase the apogee of the Mangalayan moving around the earth to reach Mars orbit? Instead why we are sling-shooting it around the Sun?

2. Why ISRO's Mangalayan craft has to loop earth unlike NASA's MAVEN?


1. Time, distance and velocity plus fuel. The course currently plotted is ideal for all those factors. The break out orbit currently plotted gets you a lot of speed for the amount of fuel expended. Every time you expand the orbit around earth it costs you in payload package vs fuel.

2. The Atlas not only has a large 1st stage to get into orbit, it has a powerful 2nd stage to break out of earth orbit and head to Mars. So the US doesn't use hohman transfer orbits for Mars.


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PostPosted: 10 Nov 2013 02:10 
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Quote:
May be a quick way to verify above would be to take a point say 25 million km radially outwards from the centre of earth towards periphery of the solar system and calculate gravitational pull on mangalyan from both earth and the sun , that should answer this question .

So I quickly did this exercise with a figure of 1300 kg for Mangalyaan .
Force exerted by Earth on Mangalyan at that distance is about 820 Newtons vs a piddly 5.63 Newton by Sun.


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PostPosted: 10 Nov 2013 05:31 
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negi sirji,

You really slept through your class XI. Just kidding :-o .

Anyways you don't need mass of orbiter for this calculation, it is a constant. Let us say:
Me= mass of earth
Ms= mass of sun
Ms/Me = 332946.

Under our simplified assumptions:
Re = radial distance of the orbiter from earth = 25*10^6 km.
Rs = radial distance of the earth from sun + radial distance of the orbiter from earth = 150*10^6 + 25*10^6 km = 175*10^6 million km.
Rs/Re = 7

The ratio of suns force: earths force on the orbiter = (Ms/Rs^2) : (Me/Re^2) = (Ms/Me) : (Rs/Re)^2 = 332946 : 49 = 6794:1

Actually you can calculate at what distance, the earth's gravitational attraction becomes 1/10th of that of the sun. It is near 8,00,000 kms (not much larger than the apogee of the 5th orbit of 2,00,000 kms).


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PostPosted: 10 Nov 2013 07:07 
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moon's attraction would be a bigger factor than sun's for the first phase of MY-1's journey. these factors would be introduced in the calculation as perturbation AFA I understand. you can't solve 3 (or more) body problems exactly.


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PostPosted: 10 Nov 2013 08:56 
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excellent animation to explain few things we are talking here:


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PostPosted: 10 Nov 2013 08:59 
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Indranil mass of sat is not needed for the ratio but needed for absolute individual forces , I wanted to get the latter , anyways I digress.

In light of the above numbers I have a question now which is a more general one in nature but related to this topic i.e.

In theory what is the farthest point in orbit a satellite in an elliptical orbit around earth can achieve without changing the perigee (I assume that is what we are doing with Mangalyan we are only increasing the apogee and not altering the perigee right ?) ? Is that value dependent on only earth's gravitational pull and satellite's orbital speed and mass ?


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PostPosted: 10 Nov 2013 09:41 
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negi wrote:
Indranil mass of sat is not needed for the ratio but needed for absolute individual forces , I wanted to get the latter , anyways I digress.

In light of the above numbers I have a question now which is a more general one in nature but related to this topic i.e.

In theory what is the farthest point in orbit a satellite in an elliptical orbit around earth can achieve without changing the perigee (I assume that is what we are doing with Mangalyan we are only increasing the apogee and not altering the perigee right ?) ? Is that value dependent on only earth's gravitational pull and satellite's orbital speed ?


The perigee does not remain the same. Every successive parking orbit has a progressively larger semi major axis. However all these orbits share one focal point, which is the center of the earth. So the perigee also increases when you increase the apogee, but by a much smaller amount because of the high eccentricity of the ellipses.

The question that you are asking is actually answered by Disha ji in a previous post related to making chapatis. You can calculate the escape velocity of the spacecraft at any distance from earth. If you could impart this velocity to the spacecraft at any point of its elliptical orbit, it will just fly out tangentially at that point out of earth's influence. Raman sirjee (infact you in your tukka bheed gaya post) told us when it takes the least effort to do this.

Rahul M wrote:
You can't solve 3 (or more) body problems exactly.

Why not? And though not exact, you could solve n-body problem very very precisely. And 3 is a very small value for n. I wanted to create a very efficient parallel algorithm for the same for my Masters thesis. Needless to say I failed to achieve the run-time complexity I wanted to. None the less, n equal to a few million in multi-dimensional space is easily handled by a medium sized cluster.

But nobody has answered my question. :(( Space gurus please share some gyan.
indranilroy wrote:
For the first 3 orbits, the kicks (raising of orbit) were not done every time the SC was at its apogee perigee. They did it only when it was at the perigee and it was nighttime in India. The only explanation I have for this is better communication and tracking. Is there any other reason?


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