Question about Apollo 13 explosion

[Messierhunter]

You might want to consider GMAT. Its propagator objects look like they will model Earth's gravity non-uniformities better, it can model solar radiation pressure and can use the Jacchia-Roberts model for the upper atmosphere.

Excellent, thanks for the info and link. I'll try that first.

Regarding AMSO's accuracy, the Moon's position in Orbiter is accurate to within very small amounts so I expect that the trajectory would need to be suitably close to the real thing. This document might also be useful to check it: Apollo 13 Trajectory Reconstruction via State Transition Matrices

Very interesting paper, it also infers some info about the delta-V caused by the explosion, but it naturally takes into account the cumulative venting over a nearly 6 hour period, which would not directly equate to just the initial explosion that sent the panel into deep space. I think AMSO will do for now and I can go back and try to refine it if it doesn't.

 

[Gunner_CAF]

I also wonder what happened to all the panels that covered the LM at launch. They were released after the trans-lunar injection burn, so wouldn't they all have traveled a similar path?

Gunner

 

[Andy44]

I also wonder what happened to all the panels that covered the LM at launch. They were released after the trans-lunar injection burn, so wouldn't they all have traveled a similar path?

Gunner

That's a good question. The SLA panels of all the trans-lunar Apollo missions were placed on free-return trajectories along with the Apollo vehicles. When they were jettisoned, the panels were given small delta-V at a right angles to the initial path. My guess is that they probably wound up rounding the moon and reentering Earth's atmosphere, as I wouldn't think they gained enough delta-V to avoid it, but I may be wrong.

Apollo 13, however, had maneuvered into a hybrid orbit after seperating from the booster but before the accident, so the SLA panels and the SM debris panel would be in very different orbits.

 

[tblaxland]

To clarify, Apollo 12-14 S-IVB's were on free return trajectories after TLI. The SPS was used to put the CSM's on hybrid trajectories. Those SLA panels probably re-entered, if not on their first pass of Earth, then shortly thereafter.

Apollo 15-17 were inserted directly into hybrid trajectories. IIRC, the hybrid trajectories had high pericynthions which suggests to me that the SLA panels would have ended up in high Earth orbits (I don't think the hybrid trajectories were so far out that they would have ended in heliocentric orbits).

 

[Andy44]

Apollo 15-17 were inserted directly into hybrid trajectories.

Didn't know that. I guess they were getting pretty confident at that point.

 

[Messierhunter]

So I was playing around with GMAT last night and I noticed it only seems to accept various earth-centric state vectors, but the state vectors put out by orbiter for Apollo 13 at the point of the explosion are heliocentric. What's the easiest way to convert state vectors from one reference point to another?

 

[tblaxland]

So I was playing around with GMAT last night and I noticed it only seems to accept various earth-centric state vectors, but the state vectors put out by orbiter for Apollo 13 at the point of the explosion are heliocentric. What's the easiest way to convert state vectors from one reference point to another?

Simply subtract the Earth's Cartesian heliocentric state vectors from the spacecraft's state vectors to have them Earth-centric. You will also need to swap the y & z components to convert from Orbiter's left-hand system to GMAT's right hand system. Orbiter's state vectors are w.r.t to the ecliptic, IIRC GMAT has a default Earth-centred ecliptic coordinate system. Alternatively, you can always create your own heliocentric coordinate system: http://gmat.ed-pages.com/wiki/tiki-index.php?page=Coordinate+System+Objects

 

[Messierhunter]

Simply subtract the Earth's Cartesian heliocentric state vectors from the spacecraft's state vectors to have them Earth-centric. You will also need to swap the y & z components to convert from Orbiter's left-hand system to GMAT's right hand system. Orbiter's state vectors are w.r.t to the ecliptic, IIRC GMAT has a default Earth-centred ecliptic coordinate system.

Thanks, that's exactly what I needed to know. Hopefully I'll get some time this weekend to crunch the numbers and come up with some predictions. Just for fun I ran out a simulation of AMSO to see if the S-IVB from A11 is anywhere close by and it looks like it last made a close pass in June 2003 (which also happens to be the month and year the A12 S-IVB is thought to have left earth orbit again).

 

[tblaxland]

Just for fun I ran out a simulation of AMSO to see if the S-IVB from A11 is anywhere close by and it looks like it last made a close pass in June 2003 (which also happens to be the month and year the A12 S-IVB is thought to have left earth orbit again).

In that regard, I'm not sure how accurate the trajectory of the S-IVB's are in AMSO. IRL they made a propulsive vent manoeuvre and I'm not sure how well that is modelled in AMSO.

 

[kneejo]

just been watching Apollo 13 the movie, paying attention to the details, I was wondering about something. When on the return to earth, they have to get a calculation on the correction burn. Houston makes a calculation and then later has to correct it, because they 'forgot' to subtract the weight of the moon-rocks they didn't bring back with them.

This made me wonder; how does Nasa calculate these things? And why could they make such an error as not to include a weight like that? Do they make all the calculations in advance, before the mission even starts and is that where the rocks are assumed in the calculations?

I'm reading up on Nasa missions at the moment, but maybe someone can explain here how they do this, just for the fun of knowing it.

 

[tblaxland]

This made me wonder; how does Nasa calculate these things? And why could they make such an error as not to include a weight like that? Do they make all the calculations in advance, before the mission even starts and is that where the rocks are assumed in the calculations?

I don't know about the historical accuracy of that event (its been a while since I watched the movie with Jim Lovell's commentary) but it is possible. Correction burns, by their very nature, cannot be calculated in advance since they are correcting for differences between the modelled trajectory and the measured trajectory. The spacecraft masses at various stages would be estimated in advance and would include such things as lunar samples but these estimates are also refined during the mission to take into account actual versus predicted propellant and consumables usage. In summary, I would say it is possible.

BTW, IMDB's description of the event is somewhat different to yours: http://www.imdb.com/title/tt0112384/goofs. My recollection is that the burn data correction happened in the movie the way you described.

 

[Zatnikitelman]

From the book "Lost Moon"/"Apollo 13" It wasn't a weight issue. Everything falls at the same rate due to gravity mostly (yes, spaceship has its own gravity etc. etc.) But the trajectory shallowing was caused by a steam sublimator giving a very very very VERY tiny nudge. Over the...whatever miles from orbit down to the surface or during docking, it's not going to make enough of a difference to really be measurable, but on the one and a third light-second coast, tiny changes tend to build up.

 

[tblaxland]

Everything falls at the same rate due to gravity mostly (yes, spaceship has its own gravity etc. etc.) But the trajectory shallowing was caused by a steam sublimator giving a very very very VERY tiny nudge.

Yes, that explains the main reason why the correction was required (it is mentioned in Lovell's commentary IIRC). The mass would effect the burn duration, which was kneejo's question.

 

[kneejo]

http://www.spectrum.ieee.org/aerospace/space-flight/apollo-13-we-have-a-solution/0

this is an extensive story I found. it contains interviews with the actual crew and mission control members. Quite a good read, after seeing the movie.

It seems the rock-issue was put in the movie because the real explanation would have become too technical to put in this movie.

Without any knowlegde about space-travel it is already a very technical movie, so they had to make a compromise. Still very realistic.

I just had to download the AMSO addon, gonna try this mission myself. The XR can go in the hangar for a while.. time to do it Nasa-style

 

[mbartley]

To clarify, Apollo 12-14 S-IVB's were on free return trajectories after TLI. The SPS was used to put the CSM's on hybrid trajectories. Those SLA panels probably re-entered, if not on their first pass of Earth, then shortly thereafter.

In the book "Lost Moon" there is a part (I just re-read the book, but forget exactly where in there this is) where Capcom tells the Apollo 13 crew that their S-IVB just crashed into the moon. Does that mean they separately maneuvered the CSM-LEM stack and the S-IVB out of free-return trajectory? How much could the S-IVB maneuver after TLI?

 

[tblaxland]

In the book "Lost Moon" there is a part (I just re-read the book, but forget exactly where in there this is) where Capcom tells the Apollo 13 crew that their S-IVB just crashed into the moon. Does that mean they separately maneuvered the CSM-LEM stack and the S-IVB out of free-return trajectory? How much could the S-IVB maneuver after TLI?

After TLI, the stack was on a free return trajectory.

Shortly after separation, the S-IVB did two manoeuvres, first an APS (auxillary propulsion system) burn, and second a propulsive vent manoeuvre, ie, the remaining propellants are allowed to vent out through the engine bell but they are not ignited. I can't find the numbers for Apollo 13. On Apollo 14 the propulsive vent manoeuvre yielded a delta-V of 10.96 m/s and was aimed such that the S-IVB would impact the Moon. The APS burn on Apollo 12 was 2.9 m/s and served two purposes, partly to target lunar impact and partly to ensure separation between the CSM and the S-IVB so that the S-IVB would not collide with the CSM when doing the propulsive vent (as an aside, this evasive manoeuvre was done by the CSM on Apollo 8, 10, & 11).

Later on, the CSM did a manoeuvre with the SPS engine (23.2 m/s) to put it on a hybrid trajectory.

 

[Messierhunter]

I agree. From my readings of the Apollo Flight Journals, roll, pitch then yaw, was the standard convention for communicating attitudes (except to note that the angles were actually Tait-Bryan rotations composed in the order pitch-yaw-roll, or Euler angles composed roll-yaw-pitch, as evidenced by the scales on the FDAI).

As for converting that into Orbiter, you first need to know what the REFSMMAT orientation was at the time.

I'm still working on this subject and after doing some digging through the transcript and other sources, it looks to me like this would have been the REFSMMAT in use at the time of the explosion:
http://www.ehartwell.com/afj/PTC_REFSMMAT
Seems to make sense, since they had been in PTC until they were asked to assume a 60 90 0 orientation. The trick for me is, how do I figure out within orbiter what the orientation of the earth-moon line was during TLI at a moment much later in the mission?

 

[tblaxland]

The trick for me is, how do I figure out within orbiter what the orientation of the earth-moon line was during TLI at a moment much later in the mission?

I'm guessing the epoch to be used was TIG rather than shutdown. Ignition was at 21:48:46 GMT, put that into the Scenario Editor then [ame="http://www.orbithangar.com/searchid.php?ID=3824"]use State Vector MFD to get its position[/ame].