Chandrayan-2 Mission

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Re: Chandrayan-2 Mission

Postby Amber G. » 26 Aug 2020 01:33

Mort Walker wrote:^^^
It is not irrelevant that imaging of CY2 is better than LRO. ....?

For the Nth time:
Just curious, if there is any understanding/realization/ of the most basic relevant facts...
eg -
- LRO' comes as close as 50 km to the moon's surface (vs about 100 Km of CY2 orbiter)..
- The light conditions, sun's angle etc, at the time of closet approach to the area (which comes may be once a month) can *vastly* differ.

It is *much* more complicated than reading up specs on resolving power..
Besides, again for the nth time: Vikram, even in the ideal condition, will be a few pixels in either cameras .. CY2 cameras primary functions was not to identify debris but to map the surface of the moon.
Just saying.. hope this is helpful.

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Re: Chandrayan-2 Mission

Postby Mort Walker » 26 Aug 2020 01:36

Amber G. wrote:I have a challenge for @csaurabh ,@mort walker, @barath and others - who are lecturing and giving crash courses to us scientists and pontificating about ‘andh visvas’ and what not..

]Forget about Vikram, here is a simple “search” for an ordinary number (positive integer) – see if you can find it.

This positive integer, when you square it, multiply by 421 and add 1 to it, comes out to be a perfect square. Can you find this number?

(IOW find a positive integer n where (421 n^2 + 1) is a perfect square)

You are allowed to use all your resources, including computers and experts you know. This is an experiment to see how long does it take. I will wait for 2 weeks here.

(This is not particularly a hard problem, at least not for those who go for science / math /engineering a neither are mathematical tools use to solve such simple problems are hard…some may even use a computer to use brute-force (not unlike software comparing pixels to look for Vikram) . Though, I would not need a computer to solve it.)

Request to other folks, those who are mathematicians/scientists/engineers and find this problem easy here to hold off giving the solution for 2 weeks – they may give, say 2nd or 3rd digit of the answer but not the whole answer.


What is the point of this particular math puzzle other than proving one can do a series analysis with a logarithmic base? You can do this numerically or or with an exact answer. What are you trying to prove - I am a scientist and better than engineers?

You didn't understand what csaurabh said earlier. As data is collected by various electro-mechanical sensors. The voltage variation over time is a complex waveform that contains amplitude, frequency and phase information. This is converted by analog-to-digital converters into 16-bit data streams of I and Q data that is transmitted back to earth. No one is asking for this raw data, what they're asking for is that the processed data come out in the public domain.

This isn't just for CY-2, but CY-1, MOM and upcoming CY-3. NASA does this, the ESA (AFIK) does this. ISRO seems to operate like the CSNA. If it is classified or sensitive, then ISRO missions need to be that way where no live coverage or the build up viewing stands are necessary. Just a few words saying satisfactory.

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Re: Chandrayan-2 Mission

Postby Mort Walker » 26 Aug 2020 01:41

Amber G. wrote:
Mort Walker wrote:^^^
It is not irrelevant that imaging of CY2 is better than LRO. ....?

For the Nth time:
Just curious, if there is any understanding/realization/ of the most basic relevant facts...
eg -
- LRO' comes as close as 50 km to the moon's surface (vs about 100 Km of CY2 orbiter)..
- The light conditions, sun's angle etc, at the time of closet approach to the area (which comes may be once a month) can *vastly* differ.

It is *much* more complicated than reading up specs on resolving power..
Besides, again for the nth time: Vikram, even in the ideal condition, will be a few pixels in either cameras .. CY2 cameras primary functions was not to identify debris but to map the surface of the moon.
Just saying.. hope this is helpful.


I understand the issue of a few pixels and looking for Vikram is futile. A person who had access to NASA data claimed to have found debris. ISRO doesn't need to answer that, but if it's own data, even in limited form, can put these issues to rest if it is in the public domain.

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Re: Chandrayan-2 Mission

Postby Amber G. » 26 Aug 2020 02:14

Mort Walker wrote:What is the point of this particular math puzzle other than proving one can do a series analysis with a logarithmic base? You can do this numerically or or with an exact answer. What are you trying to prove - I am a scientist and better than engineers?
.

Nothing nefarious! :) just to calibrate the level of math/science understanding in the audience here. As you say problem is not very hard, so just for fun, can you put the exact answer of the number - which one can easily verify. No hurry, no reason to be hyper/feel insulted, no reason to look for ulterior motives. Math is basis of all science, after all.
Let us wait and see.

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Re: Chandrayan-2 Mission

Postby Mort Walker » 26 Aug 2020 02:38

Amber G. wrote:
Mort Walker wrote:What is the point of this particular math puzzle other than proving one can do a series analysis with a logarithmic base? You can do this numerically or or with an exact answer. What are you trying to prove - I am a scientist and better than engineers?
.

Nothing nefarious! :) just to calibrate the level of math/science understanding in the audience here. As you say problem is not very hard, so just for fun, can you put the exact answer of the number - which one can easily verify. No hurry, no reason to be hyper/feel insulted, no reason to look for ulterior motives. Math is basis of all science, after all.
Let us wait and see.


The audience? Okay I'm very poor at math and only realized it follows a series where the value of (421^n) + 1 becomes very large (>10^21) quickly with the first few perfect squares of n.

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Re: Chandrayan-2 Mission

Postby Amber G. » 26 Aug 2020 05:37

..only realized it follows a series where the value of (421^n) + 1 becomes very large (>10^21) quickly with the first few perfect squares of n.

It is NOT 421^n but simply 421 n^2 (or 421 times n^2) which will not become >10^21 even for the first billion perfect squares of n.

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Re: Chandrayan-2 Mission

Postby Amber G. » 26 Aug 2020 07:20

disha wrote:
And it is even more remarkable to put CY2 in polar orbit.

So questions for the members:

1. How many satellites are there in Moon's polar orbit?

From what I know ..the important/famous functional spacecraft currently orbiting the moon is the Lunar Reconnaissance Orbiter (LRO), CY2 ARTEMIS (two spacecraft): ArtemisP1, p2//, Chang'e 5-T1 The command module of this Chinese spacecraft has been in a stable orbit. ..THEMIS is orbiting but don't how how functional it is).. there may be 10 or so others..but most practically speaking not functional .. many were deliberately "de-orbited" / crashed on the moon to learn etc..
Recently, after years of trying, earth bound laser was able to be bounced off from LRO (big deal indeed)..CY1 was observed by earth bound radio - telescopes.
Just checked Wikipedia entry - unfortunately , IMO, it is not up-to-date

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Re: Chandrayan-2 Mission

Postby Mort Walker » 26 Aug 2020 07:31

Amber G. wrote:
..only realized it follows a series where the value of (421^n) + 1 becomes very large (>10^21) quickly with the first few perfect squares of n.

It is NOT 421^n but simply 421 n^2 (or 421 times n^2) which will not become >10^21 even for the first billion perfect squares of n.


Sorry it was confusing with the 421 in there, I was thinking this is some sort of Taylor series that you're quizzing on. 421n^2 + 1 makes it easier.

The expression: 421n^2 + 1 will have two solutions where n is (-i/sqrt421, i/sqrt421).
When n=0 the expression becomes 1 which is a perfect square, but 0 is not a positive integer.

Like I said, I'm not good at math puzzles and would have to think about it a bit more. Let me know if I'm on the right track.
I still don't see the relevance of this discussion, but no harm unless you think it's not worthy to talk to anyone who isn't a theoretical physicist.

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Re: Chandrayan-2 Mission

Postby Barath » 26 Aug 2020 09:42

Amber G. wrote: the trajectory etc can be calculated *very* precisely and location/orientation really does *not* any scientific value. If it did, one would/could easily plan for it.

Hope this helps.


Not really. You know your trajectory, up to a point. You know your spacecraft orientation, thrust and thrust vectors, up to a point. You know the local gravity (as necessary) and the local contour maps. But given that your trajectory was out of control, your spacecraft was out of control, attitude and thrust are changing and off nominal, you might want to interpolate behavior from that indicated in your last telemetry and where it finally crashed.

This may not be the critical causative event but I assume it does provide some insight. It's also unclear if all the telemetry before loss of contact was complete to extent desired and uncorrupted, so there's a trivial chance it might validate that or fill in gaps

No one planned for going out of control and crash, so I don't understand your 2nd last sentence. It's precisely in context of post crash failure analysis that we're discussing. For which one might just as confidently argue that there was a plan (Vikram was identified and located)
Last edited by Barath on 26 Aug 2020 10:06, edited 1 time in total.

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Re: Chandrayan-2 Mission

Postby Mort Walker » 26 Aug 2020 10:01

Amber G. wrote:Added later: The orbits are calculated by me, so if there is an error (I don't believe there is any significant error) don't blame ISRO. The ephemeris ( data for current orbit) was taken from JPL/NASA/horizons's database.
ssd.jp..nasa.gov -- Revised: 2020-Aug-24 Chandrayaan-2 Orbiter Spacecraft / (Moon) -152


It's very nice you're able to calculate the orbits based on JPL/NASA ephemeris. CY-2 is an Indian spacecraft and would have been even nicer you could use a database provided by ISRO. SMH as to why we're even arguing about ISRO's transparency when one has to use another country's data to track India's moon orbiter.

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Re: Chandrayan-2 Mission

Postby Amber G. » 26 Aug 2020 22:49

Mort Walker wrote:
Amber G. wrote:Added later: The orbits are calculated by me, so if there is an error (I don't believe there is any significant error) don't blame ISRO. The ephemeris ( data for current orbit) was taken from JPL/NASA/horizons's database.
ssd.jp..nasa.gov -- Revised: 2020-Aug-24 Chandrayaan-2 Orbiter Spacecraft / (Moon) -152


It's very nice you're able to calculate the orbits based on JPL/NASA ephemeris. CY-2 is an Indian spacecraft and would have been even nicer you could use a database provided by ISRO. SMH as to why we're even arguing about ISRO's transparency when one has to use another country's data to track India's moon orbiter.


Thanks. Yes, it is awesome that JPL/NASA's tools (especially graphics and animation tools) most of us can use. Cool part is since, it has ephemeris of Sun, planets, moon and *many* satellites, one can merge so one can see relative positions, can chance coordinates and can actually view the *actual* background (moonscape and light conditions etc). I (and may be others) have posted many such pictures in this thread (around last year). I am not sure, but I may have posted here a video made from that animation in brf where one can 'fly' on/with Vikram and can enjoy the moon scape approaching..:).

(Last birthday, I got a Virtual Reality set, and it is fun to enjoy those "rides" and even "walks" in 3-D. ).

I am not critical of ISRO as the back-ground of many scientist in these fine institute is very similar.. I leave people here with one of the photo taken by CY2 ..Nice one, one can see Mitra (named after physicist :) Sisir Kumar Mitra) from my collection. :)..(Most likely I have posted it in brf last year :) - sorry for duplicate but it is one year anniversary)
Image

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Re: Chandrayan-2 Mission

Postby Mort Walker » 26 Aug 2020 23:44

AmberG,

Yes, having all of those ephemeris on-line is handy. People use to have large volumes of books that contained ephemeris of just the earth and moon. I remember back in the 1980s calling US Naval Observatory in Washington D.C. and giving them mm/dd/yr and lat/lon locations on the globe to get just a particular day's information for janam-kundli accuracy. This was a service they provided free at the time. I hope data, like you acquired, can some day be provided by ISRO for earth, moon, sun and planets. Many of the ancient sages of India made ephemeris that were used by Ptolemy and most likely incorrectly credited to him for developing.

I do like your pictures.

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Re: Chandrayan-2 Mission

Postby Cyrano » 27 Aug 2020 00:43

We are used to seeing images of lunar surface full of craters. These images seem to show convex mounds ?!
Perhaps gurus can explain? Thanks

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Re: Chandrayan-2 Mission

Postby Amber G. » 27 Aug 2020 01:59

Amar_P, lunar surface can be seen in detail via many sources, so you may like to get your own answers. (Nothing to explain - there are mounds, craters, odd shapes etc :) ) (LRO/LROC data - available thru many libraries - google moon etc .. you can visit any particular place there, just like google earth)... Even in this brf thread I have copied quite a few of the interesting places)..

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Re: Chandrayan-2 Mission

Postby Amber G. » 27 Aug 2020 02:13

I put a photo here, some time ago (see my post on 1 year update) about Vikram's landing place.
For the record, let me post a picture here for reference.

Vikrams impact site and associated debris field.

Image

The photo is copied from Arizona State University's data base (based on NASA/GSFC) etc. The picture is based on composite photos taken by LRO - 11 November 2019 and input by ISRO/ NASA etc (Minor croping/editing/labelling is by me - accurate to best of my knowledge )

For scale: The whole picture is about 3km x 3 km - or little bit more )

Green dots indicate *likely* spacecraft debris (suspected by various sources). Blue dots are disturbed soil, (likely where small bits of the spacecraft churned up the regolith.) " S" indicates debris identified by Shanmuga Subramanian.
(Color, and size of dots are much bigger, so they can be seen -- NO the actual pixels are barely noticeable in before/after photos)

(As said before, these dots are just "dots" - identified by comparing it with older pictures - one can *not* confirm or "identify" the object as the best these are presence/absence of a few pixels here and there)


Hope this is helpful.

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Re: Chandrayan-2 Mission

Postby Amber G. » 27 Aug 2020 03:13

More photos from the memory lane:

(All posted here a year ago)
Orbits: Looking from a) Earth and b) Moon
(Yes, we have fuel for about 7 more years - Update)

ImageImage


Blue dots are the primary and secondary landing sites (All before Vikram even got separated)

Image
Image

More such views:

Image
Image

First photo from CY2 released by ISRO..
Image

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Re: Chandrayan-2 Mission

Postby Amber G. » 27 Aug 2020 08:05

Barath wrote:
Amber G. wrote: the trajectory etc can be calculated *very* precisely and location/orientation really does *not* any scientific value. If it did, one would/could easily plan for it.

Hope this helps.


Not really. You know your trajectory, up to a point. You know your spacecraft orientation, thrust and thrust vectors, up to a point. You know the local gravity (as necessary) and the local contour maps. But given that your trajectory was out of control, your spacecraft was out of control, attitude and thrust are changing and off nominal, you might want to interpolate behavior from that indicated in your last telemetry and where it finally crashed.


At the risk of repeating the point for the nth time...:)

Barathji - I sincerely suggest - if you have time and interest and basic physics understanding check out my one year old posts saythis or <this> (Actually many posts there, some by people who know what they are talking about, like SSSsavli etc are quite good .. I actually take time to explain basics in a simple way .. basically it gives back ground on what factors are critical and how one predicts trajectory etc). So you may find them helpful.

But allow me to clear some points, hope this is helpful. (This is assuming you have interest in learning and not just debating :) ..).

===> Trajectory is hardly "out of control" or space craft is hardly off the path ....:) :) ..

When all is said and done: Vikram was within one of the site chosen by ISRO weeks before. It selected/chose the final landing place and landed *exactly* at the landing point. IOW ISRO knows (without *any* doubt) the impact point within perhaps a few 10's of meters. . Even others (including some amateurs with radio-telescopes who were monitoring Vikram's beeps and trajectory) know the location within about a hundred meters or so.

==> I gather from your comments that you may not be aware -- But Vikram's final moments are not like a plane/drone/missile getting off target on earth. Ironically if there was air on the moon, the landing would be a child's play.

===> Put simply, the critical part, (the last few minutes maneuvers ) was making sure that the speed at touchdown was reasonable, stay clear of big boulders, land straight down etc. Some 2 km above, in the final braking and the most crucial part, something went wrong (no, trajectory did NOT go out of control)..Most likely inertial guidance system couldn't keep the bearings straight - or glitch in the computer / .. it's altimeter or in its obstacle avoidance camera etc. (My guess, the primary reason was inertial guidance system losing a gimbal type lock and computer was not fast enough to resolve it - (Disclaimer: ISRO has not confirmed the root cause ) hopefully they will resolve it in the next one)

===> This was NOT unexpected . Most of us (and in ISRO) were hoping that it may work but knew that virtually every other attempt like this in the past resulted in a failure. ISRO did NOT invest too much in Vikram's other pay load (They did not include even a RTG) as they were not really sure that it will succeed but hoped it will give enough data for the next mission.



No one planned for going out of control and crash, so I don't understand your 2nd last sentence. It's precisely in context of post crash failure analysis that we're discussing. For which one might just as confidently argue that there was a plan (Vikram was identified and located)

This does not make much sense to me, as the plan was, roughly speaking, in case of failure (which they were ready for) they will learn for the next mission... This is not any kind of secret.. just check out comments by any reputable source.
Sure tabloids would scream "Vikram was located/identified" .but saner voices would just say "it is likely that some of the changes in pixels seen near the impact site may belong to Vikram .. (one just have to wait for more data (more before/after photographs to make that case stronger.

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Re: Chandrayan-2 Mission

Postby csaurabh » 27 Aug 2020 16:59

Look what happens when I don't check forums for a couple of days :lol:
I am going to ignore that nonsensical arithmetic question. What does he think this is, math olympiad? LOL
I am an entrepreneur in the space sector, based in India. I interact with these people on a regular basis. I think I would rather trust my own senses and experiences than the word of some 'US-based' ivory tower nincompoop ( insert jokes about academics living in la-la-land and ignorant of realities)

ISRO's PR efforts have generally been poor and Chandrayaan 2 and its failures are just an example of that. What is there to debate about it, it is obvious. These are nationally funded programs. In a democracy, people have a right to know. I think the current attitude of secrecy is really not helping. RTIs shouldn't need to be filed for something that is of no strategic value.

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Re: Chandrayan-2 Mission

Postby Amber G. » 27 Aug 2020 23:13

Wow! Priceless reaction ! I am saving the screen shot of above, lest it disappears. :).

@csaurabhji no need to get unhinged just because someone posted a math problem here. As you said, you could have ignored it ! (But still, who knows, among you, or your circle, some one may have some interest or ability to do simple math problems..like those whose AI may look for patterns in debris may find patterns in integers to find a simple number :)) Math is basis of all sciences and pixels in a photo are nothing but binary digits!

I *never* would have thought of asking a math olympiad level question to you - you don't seem to be that type, so no worries. :) This is last from me about this so please relax.

***
But I do have a comment about, repeated references to " Chandrayaan 2 and its failure". Last one from me, but posting it here nevertheless as I seriously think it is important.

As said before, there are many scientifically challenged ddm's in the world. For many the sole mantra is rant against mainstream scientific organizations in India or "'US-based' ivory tower nincompoops". (To be clear - no one should take it personally as it is not directed toward one person but general trend of articles in media).

In my humble opinion, Brf does not need one of the same here. Many of old timers like me visit brf to catch-up on interesting news items (and sometimes contribute to provide their POV) :) )- missed in other media, do not find such posts helpful.

It is one thing to provide input, even personal opinions but there is a fine line between endless, statements which have no basis and ignore even the most basic scientifically verifiable facts.

I am sad to see this trend creep in so many of brf threads.

***

Looking back at my (and some others) posts, I am fairly proud that they give an unique pov - often missed by ordinary news papers - presented in a clear concise way - even for experts. Hope people find those posts useful. I reposted some of the earlier posts here above for reference in that spirit.

Over and out.. back to lurking mode (unless something exciting happens here :) or a serious question directed to me over my comments ).

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Re: Chandrayan-2 Mission

Postby Anant » 27 Aug 2020 23:31

Amber G. wrote:Wow! LOL! I am saving the screen shot of above, lest it disappears. :).

@csaurabhji no need to get unhinged just because someone posted a math problem here. As you said, you could have ignored it ! (But still, who knows, among you, or your circle, some one may have some interest or ability to do simple math problems..like those whose AI may look for patterns in debris may find pattern to find a simple number :)) Math is basis of all sciences.

I *never* would have thought of asking a math olympiad level question to you - you don't seem to be that type, so no worries. This is last from me about this so please relax.

***
But I do have a comment about, repeated references to " Chandrayaan 2 and its failure". Last one from me, but posting it here nevertheless as I seriously think it is important.

As said before, there are many scientifically challenged ddm's in the world. For many the sole mantra is rant against mainstream scientific organizations in India or "'US-based' ivory tower nincompoops". (To be clear - no one should take it personally as it is not directed toward one person but general trend of articles in media).

In my humble opinion, Brf does not need one of the same here. Many of old timers like me visit brf to catch-up on interesting news items (and sometimes contribute to provide their POV) :) )- missed in other media, do not find such posts helpful.

It is one thing to provide input, even personal opinions but there is a fine line between endless, statements which have no basis and ignore even the most basic scientifically verifiable facts.

I am sad to see this trend creep in so many of brf threads.

***

Looking back at my (and some others) posts, I am fairly proud that they give an unique pov - often missed by ordinary news papers - presented in a clear concise way - even for experts. Hope people find those posts useful. I reposted some of the earlier posts here above for reference in that spirit.

Over and out.. back to lurking mode (unless something exciting happens here :) or a serious question directed to me over my comments ).



Amber G, here are my 2 cents. I am an Indian American stem cell scientist. What I do, I do well. Do I use math on a daily basis? Yes. Is it at the same level as what you do? No. Does this matter to me? Not really since it isn't in my wheel house. I have always held you in high regard and been impressed by your ability to handle the vitriol. That being said, it seems like you are imposing a litmus test for others to chime in their 2 cents and that's what gives me takleef if you will. If you're brilliant in your field, that's wonderful and I cheer you on for that. What might be simple to you might not be simple to others. In the same manner, you might come across as worse than my undergraduate students in my lab. It's an issue of intelligence, repetition and context. No one is good at everything. Everyone has their sweet spot, as do you and I.

I think the bigger complaint people have is the lack of transparency by the ISRO and the converse, transparency of NASA. There is no doubt to me that ISRO is an excellent organization which does wonderful things given its budget etc. Nevertheless, just because the mission failed in part, doesn't give them permission to roll like an armadillo and hide. From what I understand, this mission was funded by Indian tax payers. Nothing in this mission was intended to compromise or incorporate national security secrets. Therefore, it is justifiable to say that Indian tax payers have a right to know what happened. To ad hominem dismiss their requests just makes ISRO look like a sore loser and undercuts their accomplishments, even within Chandrayan-2. What would happen if an Indian Astronaut died in a manned mission? Would they hide the root cause then also? If you notice, NASA has had numerous astronauts die in space, during re-entry and on the ground. Each was followed by a publicly transparent inquiry. Why can't ISRO do the same? If you have insight into why this is, please do share it. Otherwise, please keep your mathematics problems to the math/physics thread which I do read with some keenness even though I am not a mathematician nor does it impact my daily work.

Thanks.

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Re: Chandrayan-2 Mission

Postby Mort Walker » 28 Aug 2020 00:16

The problem here is that the failure of CY-2 was an engineering problem. There was no problem with the orbital mechanics. The problem comes when you use mathematics to characterize a problem that you don't fully understand when building a spacecraft. Lots of variables you miss and incorrect assumptions. The math isn't wrong, but rather the application is. Think of a furniture carpenter who uses the right tool to make a beautiful cabinet. The engineer must use his/her mathematics tools the same way. A physicist and mathematician will marvel at the beauty of the tool and how it can be used to make other beautiful things.

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Re: Chandrayan-2 Mission

Postby suryag » 28 Aug 2020 00:18

Would like to quote thyagaraja here - endaro mahanubhavulu vaarandariki vandanamulu - you are all very accomplished in your fields please stop sniping here, warnings will follow

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Re: Chandrayan-2 Mission

Postby sanjaykumar » 28 Aug 2020 02:02

Thank you Anant jee.

Your post was a model of how to make a point with some decorum.

A physicist I know of was exceptional at what he did. Yet when his relative was dying of metastatic cancer, he insisted that she have ozone insufflated into her vagina.

A 50 year experience in a particular field guarantees that one is exceptionally obtuse in several others. This realisation comes late to many but is the key to intelligent humility. Of course one can make claims to wide expertise and confirm the Dunning-Kruger effect.

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Re: Chandrayan-2 Mission

Postby Anant » 28 Aug 2020 03:01

sanjaykumar wrote:Thank you Anant jee.

Your post was a model of how to make a point with some decorum.

A physicist I know of was exceptional at what he did. Yet when his relative was dying of metastatic cancer, he insisted that she have ozone insufflated into her vagina.

A 50 year experience in a particular field guarantees that one is exceptionally obtuse in several others. This realisation comes late to many but is the key to intelligent humility. Of course one can make claims to wide expertise and confirm the Dunning-Kruger effect.


You're welcome Sanjaykumar jee.

Peace out to everyone.

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Re: Chandrayan-2 Mission

Postby Vayutuvan » 28 Aug 2020 03:06

One small anecdote to make people smile a little at the egos of famous mathematicians. This is form the book Four Colors Suffice by Robin Wilson (ISBN 0-691-11533-8) which I highly recommend.

I quote:
... Indeed, a story is told about the distinguished number-theorist Hermann Minkowski in the first decade of the twentieth century. While lecturing on topology at Gittengen University, he mentioned the four-color problem:

'This theorem has not yet been proved, but that is because only mathematicians of the third rank have occupied themselves with it', Minkowski announced to the class in a rare burst of arrogance. 'I believe I can prove it.'

He began to work out his demonstration on the spot. By the end of the hour, he had not finished. The project was carried over to the next meeting of the class. Several weeks passed in this way. Finally, one rainy morning, Minkowski entered the lecture hall, followed by a crash of thunder. At the rostrum, he turned towards the class, a deeply serious expression on his face.

'Heaven is angered by my arrogance', he announced. 'My proof of the Four Color Theorem is also defective'. He then took up the lecture on topology at the point where he had dropped it several weeks before.


By the way, the theorem was proved using a computer at Urbana by Appel and Haiken on March 17, 1978. Haiken has started his collaboration with Heech in 1970.

This was the first major proof which used what is called Experimental Mathematics today.

It is silly to separate Mathematics into Pure and Applied. They are completely intertwined right from the beginning of mathematics.
Last edited by Vayutuvan on 28 Aug 2020 03:09, edited 1 time in total.

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Re: Chandrayan-2 Mission

Postby Vayutuvan » 28 Aug 2020 03:08

Anant wrote:Peace out to everyone.


Iowa City. It is a lovely university town with one of the most beautiful campuses I have seen yet.

Vayutuvan
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Re: Chandrayan-2 Mission

Postby Vayutuvan » 28 Aug 2020 03:10

People interested in Experimental Mathematics discussion, please come to Math dhaga. I will post some thoughts of mine there.

suryag
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Re: Chandrayan-2 Mission

Postby suryag » 28 Aug 2020 04:39

Stick to topic folks

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Re: Chandrayan-2 Mission

Postby Amber G. » 28 Aug 2020 07:05

Mort - I am going to comment on your post(s) in Physics dhaga.. when I get some free time.
Anant - I will comment in some other more appropriate dhaga which you may be interested to see - sometime in near future.

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Re: Chandrayan-2 Mission

Postby idan » 30 Aug 2020 15:59

Amber G. wrote:
To add:

For those who are interested in scientific understanding may find this interesting..Those who find such post offensive please ignore.. here is some orbital mechanics in picture.. (Anyone can use well known tools to draw the following - the following is based on what I put here in brf last year... Nothing much has changed since then as far as basic orbits are concerned.

Image

Orbits: (Green LRO, other CY2). (Remember, moon surface below is spinning)

(Moon's North is thin vertical line - as you can see CY2's orbit is pretty close to exact polar orbit)

For example, LRO's recent image - approximately 900 million illuminated pixels are in the target area (about 1km x 1 km) .. each pixel is slightly bigger than a meter ([NASA/GSFC/Arizona State University has more details.).

ISRO's CY2 camera, is supposed to have a have a slightly better resolution but It is further than LRO's closest approach (which is about 50 km). I believe that CY2's slightly elliptical orbit is such that, it is slightly closer to the surface than average near the Vikram landing sight. .. As said before other conditions such as light etc are also a factor. In any case looking for Vikram is more complicated than many think,

Point is hope people (at least those who are interested in science) have some perspective.. how often CY2's orbiter passes over the target area (less than once per month or so)..CY2's object was *never* to analyze the crash site.


Hope this is helpful.

Added later: The orbits are calculated by me, so if there is an error (I don't believe there is any significant error) don't blame ISRO. The ephemeris ( data for current orbit) was taken from JPL/NASA/horizons's database.
ssd.jp..nasa.gov -- Revised: 2020-Aug-24 Chandrayaan-2 Orbiter Spacecraft / (Moon) -152


LRO is in an eccentric polar mapping orbit with orbital period of 2 hours. The orbital velocity is 1.6 km/s. LRO stays on near side of moon ~ 1 hour out of every two.

The Vikram lander debris first located by Shanmuga (S in the image) is about 750 meters northwest of the main crash site and was a single bright pixel identification in that first mosaic (1.3 meter pixels, 84° incidence angle). The November mosaic shows best the impact crater, ray and extensive debris field. The three largest pieces of debris are each about 2 x 2 pixels and cast a one pixel shadow. This portion of the Narrow Angle Camera mosaic was made from images M1328074531L/R and M1328081572L/R acquired on 11 November 2019. The November mosaic had the best pixel scale (0.7 meter) and lighting conditions (72° incidence angle).

Image

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Re: Chandrayan-2 Mission

Postby Barath » 30 Aug 2020 20:37

Amber G. wrote:Barathji - I sincerely suggest - if you have time and interest and basic physics understanding check out my one year old posts saythis or <this>


Please, no ji for me
Thanks for the links, but those links are irrelevant AFAIK. While background is useful, discussions of Chandrayaan trajectory going off-base start from around page ~20x

===> Trajectory is hardly "out of control" or space craft is hardly off the path ....:) :) ..

[/quote]

We have a failure in communication. I do not understand how trajectory during fine braking phase below 2 km can be described as nominal/or in control. Around and subsequent to that is what we are talking about (though some deviance and root cause can predate it). In this period, the spacecraft attitude (due to guidance/control) and thrust are possibly not in nominal. There's been unconfirmed reports of tumbling and of excessive braking thrust [Again Isro has not posted the actual failure / root cause analysis report, let alone failure sequence so one cannot contradict it]

We're not talking about things upto the rough braking phase end..

When all is said and done: Vikram was within one of the site chosen by ISRO weeks before. It selected/chose the final landing place and landed *exactly* at the landing point.


The spot indicated was within 500m with debris flung over 750m or more. Now you could say it is well within the margin of error. But the telemetry was received for most of the descent. So I'm hoping that the data in combination with simulations, one could usefully reconstruct parameters and actions in the last 2 km that are best fit . Maybe, maybe not. /shrug.

Now Apollo 11 ran 4 miles downrange and about 1 1/2 minutes earlier, based on 40 sec longer powered distance, and Armstrong's manual operation/intervention. But that was a different era in guidance and precision. So possible ?


==> I gather from your comments that you may not be aware -- But Vikram's final moments are not like a plane/drone/missile getting off target on earth. Ironically if there was air on the moon, the landing would be a child's play.


No air !?! Maybe there is water instead ! In fact I remember Chandrayaan-1 with NASA M3 discovered water. So one should send ships instead of spacecraft ! That's why the failures ! Nobel prize if someone confirms that there is no air ! Hey, how about this sail ship ? /sarcasm /joke



([b]no, trajectory did NOT go out of control)



I think we have a failureto communicate. Braking engine thrust, thrust variations and loss of guidance/loss of refined attitude/guidance might result in small deviations in trajectory and landing point. Maybe this is completely swamped by normal tolerance and errors, maybe not ?


..Most likely inertial guidance system couldn't keep the bearings straight - or glitch in the computer / .. it's altimeter or in its obstacle avoidance camera etc. (My guess, the primary reason was inertial guidance system losing a gimbal type lock and computer was not fast enough to resolve it - (Disclaimer: ISRO has not confirmed the root cause ) hopefully they will resolve it in the next one)


Quite possible. IIRC,there was discussion about "hunting" behaviour before..from about 4-5km on down. A public failure report (with root cause) published would, hopefully, be unambiguous.


===> This was NOT unexpected . Most of us (and in ISRO) were hoping that it may work but knew that virtually every other attempt like this in the past resulted in a failure.


ISRO allowed the hype to build up where Vikram/Pragyan was perceived as the standard for success and failure. The "sexy" overrode a more rational and realistic sense.


ISRO did NOT invest too much in Vikram's other pay load (They did not include even a RTG) as they were not really sure that it will succeed but hoped it will give enough data for the next mission.


Would you have insight into the different payload options considered and how they were chosen? That would be pretty interesting. All I am aware of now was payload restrictions/risk that were re-visited after Russian feedback and move to GSLV III

Also, since you are apparently concerned about explaining things for the n'th time and that maybe I'm just doing this for debate - no more posts for some time from me

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Re: Chandrayan-2 Mission

Postby Amber G. » 31 Aug 2020 03:02

ramana wrote:Don't bother. Any thing worthwhile ISRO will tell.


Nicely put. No doubt, ISRO has confidence, trust and admiration from Modi, GoI, DST, IIT's, IISc;s NASA, MIT and scientific and administrative bodies in India or abroad. Sure we have clowns in NYTimes who still draw Mangalyaan and Cow cartoons, or WPost citing anti-CAA, Islamophobic trend of India, or our own brf clueless "experts" shouting endlessly about "failed CY2 Mission" and "out of control space crafts/trajectories)! Nefariously secretive institutions!

REALLY??? SERIOUSLY????

Do these people even realize that Vikram was just a part of the CY2 mission, or what one means by a trajectory - do they even know if earth is flat or round? seriously?

Now we have droves of people coming here and pontificating, including some, who never before participated in the thread, or those who, by their own admission, know nothing about the subject matter?

Ramanaji - it may be helpful, if admin's of this thread articulate clearly what kind of posts people like to see here.

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Re: Chandrayan-2 Mission

Postby Amber G. » 04 Sep 2020 23:46

Down the memory lane: Posted this last year on this date:

"Trip so far, as perfect as it gets. Congratulations ISRO."

#Chandrayaan2 Lander Vikram potential landing sites Manzinus C and Simplelius N craters align with the orbit at the landing time on Sep 7th at around 2 am. A perfect polar orbit and a perfect alignment. Great work ISRO.
Screen grab from animation (using data supplied by ISRO)

Image

(Update: CY2 orbiter and systems remains as perfect as it gets.)

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Re: Chandrayan-2 Mission

Postby Varoon Shekhar » 05 Sep 2020 06:58

I remember the day, it was the first Friday in September, so it's a year! The anticipation, the excitement..alas

Were there any more credible theories as to why the Lander failed?

And still awaiting a detailed report from ISRO about all the technologies that did work. They mentioned variable propulsion. There must be several more.

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Re: Chandrayan-2 Mission

Postby Amber G. » 08 Sep 2020 06:11

Meanwhile Big news on the science front - it is in many mainstream media too..
(Also gives some perspective, it takes lot of time to analyze, study the data)
ISRO’s Chandrayaan-1 Reveals Rusting of Moon; Scientists Point at Earth's Atmosphere as Possible Cause
--The formation of rust can be attributed to the presence of two key elements—water and oxygen when in contact with iron.
-- Through magnetotail oxygen from Earth travel to the Moon.
-- Chandrayaan-1 is credited with discovering clues of water ice on the poles of the Moon.
Data from the Indian Space Research Organisation (ISRO) has revealed that the Earth’s natural satellite Moon might be rusting. The new research suggests that the moon is turning slightly red, indicating the formation of a reddish-black mineral form of iron named hematite on its surface, particularly at the poles.

The formation of rust or iron oxide can be attributed to the presence of two key elements—water and oxygen—when they come in contact with iron. The lunar surface is littered with iron-rich rocks, which may facilitate this chemical reaction when combined with the other two elements. However, the Moon does not have any rich source of water and is devoid of oxygen in its atmosphere.

"It's very puzzling," said Shuai Li from the University of Hawaii, who is the lead author of the study. "The Moon is a terrible environment for hematite to form in." So, what triggered such a chemical reaction over the moon? Scientists say that the main reason behind this change could be the Earth’s atmosphere.

Researchers noticed this phenomenon on the Moon while examining data from the Moon Mineralogy Mapper (M3) instrument onboard ISRO’s Chandrayaan-1 spacecraft. The data obtained from the M3 revealed the Moon's pole had a different composition as compared to its surface.

For iron to convert into rust it needs oxidizers, which can steal electrons from the iron and thus initiate rust formation. To understand the cause, the team examined the bombarding of hydrogen from the solar wind. However, it had the opposite effect since hydrogen is a reducer—which donates electrons instead of taking it. Therefore, solar winds may not be the reason behind rusting on the Moon’s surface.

The airless Moon may lack atmosphere to support the formation of oxygen, but it hosts traces of oxygen that travels from Earth to reach the lunar environment. Therefore, researchers say the Earth’s magnetotail—an elongated region of the planet’s magnetosphere—plays a significant role in this change observed over the Moon.
<snip please read the story linked >
..
That’s where the data from Chandrayaan 1 again comes into play. Researchers used the data obtained by the Indian space agency’s maiden Moon mission—which remained functional till August 28, 2009. The mission is credited with discovering clues of water ice on the poles of the Moon along with mapping out different types of minerals formed on the lunar surface.

Researchers extensively studied the data obtained from the Moon Mineralogy Mapper instrument onboard spacecraft. The presence of water has been only detected on the poles of the lunar surface in the form of frozen water, which remains almost entirely in shadow.

<snip>



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