Andrew Cooper: Were the recent asteroid flyby and Chelyabinsk meteor strike events linked?

Posted: March 5, 2013 by tallbloke in Analysis, Astronomy, Astrophysics, cosmic rays, Cycles, Gravity, solar system dynamics, Uncertainty

An interesting comment has been placed on the 2012DA14 flyby thread by talkshop regular ‘Scute’ (Andrew Cooper) which investigates the possibility that the Russian Meteor was indeed related to the asteroid. This was dismissed at the time but Scute’s investigation of the orbital dynamics seems to raise doubt about this:

russian-meteor

The Chelyabinsk Meteor and a possible link with 2012DA14

I think the idea of the Russian meteor being related to 2012DA14 should be resurrected. I say resurrected because the idea was so roundly slapped down by NASA within hours of the impact and never discussed again. Most of the information below was gleaned from NASA’s own JPL Horizons ephemeris for 2012DA14.

Let me begin by addressing a few myths that seemed to sew it up regarding the lack of any link between the two

Firstly, the direction of approach was not on the night side of the earth but on the day side (2012DA14 flipped under and up round the back only in the last 5 hours) and the radiant was not, as variously described, “the South Pole” or -81 degrees (implied by the above as being -81 to the night side), but at -69 degrees on the sunward side.


Secondly, the radiant had a right ascension of almost exactly 00 hours ,that is, 30 degrees east of the sun (which was at 21 hours 54 min of RA on the day) in the equatorial plane. The Russian (Chebarkul) meteor came in at 13 degrees east of the sun in local horizontal coordinates.

Thirdly, the incoming trajectory of the meteor was not north-south but on an azimuth of 99 degrees i.e. 9 degrees south of east. Since it was sunrise this meant that the meteor came from a direction close to the sun (13 degrees east of it), in other words, coming in over a great circle running down the globe to the south, although a better approximation would be south east, This was possible because the Earth’s axis was tilted back by 12.5 on that date, making a late sunrise for Chebarkul, so watching the sunrise on a somewhat tighter, northern latitude line meant looking along a straight line that soon scribed south eastwards in lower latitudes (rather than curving round the 55 degree North line).

Fourthly, 2012DA14 was not going “too slow” for a related fragment to arrive at 17km/second: its radiant, relative velocity to the Earth before being accelerated was 12600mph. That is 5.6 km/ sec. If you add to that the freefall velocity of 11.2 km/sec (the corollary of escape velocity) you get 16.8 km/sec. Add to that the eastward rotation of the earth at 55degrees north at an Azimuth of 9 degrees south of east (0.2 km/sec) you arrive at precisely 17km/sec. This is the same calculation that Zuluaga and Ferrin (and now, NASA) must have done in reverse for their version of the reconstruction of the trajectory: I calculated the radial speed of their hypothesised orbits at the Earth’s position (r value/ radius from sun=1AU) on the day of impact (but without the Earth’s gravitational influence added) and ended up with 34.8 and 35.2 km/sec for the 2 posited orbits. That amounts to 5 and 5.4 km/sec relative to the Earth, respectively. Adding the freefall velocity and the eastward rotation you get 16.4 and 16.8km/sec. The difference between these posited orbits and the posited 2012DA14 fragment is that they invoke the head-on trajectory solution with little or no curvature as they are pulled into the gravity well. If it’s a bulls-eye hit the curvature is zero. The Zuluaga and Ferrin video shows the meteor coming in from about 3 degrees above the solar plane. The NASA video now shows the same.

I believe there are multiple solutions between head on (3 degree inclination) and an 11.6 degree inclination (11.6 deg being the solar plane analogue to the -69 degree radiant from a geocentric view). These various solutions involve increasing degrees of curvature as the meteor is pulled into the Earth’s gravitational well but curvature in freefall doesn’t make the final velocity any slower. By the way, none of these high curvature scenarios would involve capture in orbit- it’s either impact or escape along a hyperbolic path back out of the well. And high curvature means a 50 degree ‘q angle’ (half way through the turn). It’s the q angle that determines how far round to the north the meteor can curve and still impact rather than miss and escape.

The last myth is that at 55 degrees latitude Cherbarkul is too far North for any fragments to hit. This is not true because from a -69 degree radiant, the ‘equator line’, or tangent line, that 2012DA14 could see from below was shunted upward (from the real equator) on the sunward side by 21 degrees. Due to the vagaries of the trajectory of any purported fragment (see below), it would still require around 55 degrees of hyperbolic turn from that raised equator line onwards, although that describes a track all the way to Chebarkul- atmospheric entry would begin at 50 degrees round. For an idea of the sort of curvature needed for the fragment, I plotted a curve from first principles (subtracting the freefall component of velocity from the baseline, straight velocity of 17km/sec) and came up with a q angle of 50 degrees. For some perspective, the Apollo missions came in on a hyperbolic orbit at 11.2 km/sec and still got 69 degrees round the back of the globe, regardless of rotation and a sedate 1080 mile reentry. Even 2012DA14 curved 30 degrees or more for a q angle of 15 deg and that was under the influence of one tenth the gravity. 50 degrees is probably an upper limit but that is exactly what is required for a 2012DA14 fragment riding along on the radiant angle to turn in hyperbolically and hit Chebarkul at a low trajectory.

One other point, though not classifiable as a myth is that 2012DA14 is being characterised by NASA as a CO or CV type chondrite (carbonaceous with calcium and aluminium inclusions) based on spectral observations whereas they say the Chebarkul meteor is a stony chondrite because the few pieces found so far “are reported to be silicate rich”. This, they say, rules out any link. This may be true but the whole tenor of their delivery is one of running scared and has to be looked at in the light of the following quotes, all within a minute on one video:

[re 2012DA14] “there was no danger of a collisions, NASA assured people”

“… In a one in a million chance that still has NASA scientists shaking their heads”.

“These are rare events and it’s incredible to see them happen on the same day.”

As things stand as of 5th March 2013 , I feel that the evidence presented here is more convincing than some spectral measurements not chiming with a few reported silicate bearing fragments.

meteor-asteroid

The radiant is on the right at 00hours 30M. The purported fragment didn’t have to be on this line , just slightly displaced and parallel to it a few hours back up range at say 80-100,000 miles.

So we now have a completely different, sunward radiant of -69 degrees of declination. In fact, for a fragment travelling 50,000 miles sunward from the track line of 2012DA14 and 16 hours ahead, it would probably come in from nearer to a -66 to -67 degree trajectory before being really hiked round on its hyperbolic orbit (its close encounter-to-impact trajectory). 2012DA14 itself turned in by 2-3 degrees from its side of the track in the last day before starting its 30 degree hyperbolic turn. A -66 or -67 incoming trajectory for the hypothetical fragment means the raised ‘equator line’ was up to 24 degrees higher on the sunward side, reducing the required curvature even further, possibly to 47 degrees before atmospheric entry. Indeed, that sunward fragment track, displaced as it is seemingly arbitrarily, at 50,000 miles over and parallel to 2012DA14 actually allows for 10-12,000 miles or 2 degrees of inward curvature from 03:00 on 14th February, 24 hours up range. This is before being really hiked in from a -66 to -67 degree point at about 22:00 UTC on February 14th, some 5 hours from impact.

You can download the ephemeris for 2012DA14 from JPL horizons website (click ‘web interface’ and enter ‘observer’ ‘geocentric’ and dates from 1st Feb 2013 to 28th Feb 2013 at hourly intervals). I suggest the entire month so as to give a better feel of what’s going on. It’s easy to scroll up and down quickly. It doesn’t show speeds but I got the figure of 12600 mph from a news item and checked it against the orbital speed and inclination of 2012DA14 for the vertical component, then derived the horizontal geocentric component from that. Those vectors do pretty well add up to a 12600mph, 69 degree slope until one or two days out (300k to 600k miles). The JPL video has 2012DA14 at about 13,500 mph at 4 hours out. I apologise for the lack of links, they are currently playing havoc with my formatting. I might do another separate comment with some links.

I have described the trajectory of the hypothetical fragment. Now I need to describe where to look for it in a forensic sense- using astrodynamics software to rerun different scenarios with the meteor exiting from a narrow window around the proposed path. If anyone here has astrodynamics software, please feel free to join in and prove it one way or the other. I have no software so feedback would be welcome.

The best place to look for the fragment is emerging from a window bounded by a geocentric declination of between -59 and -65 degrees and a right ascension of between 22H and 2H 30 minutes. The declination angles of the window aperture are less than the radiant and trajectory angle because the fragment is now cutting up through the angle lines, past the radiant, trying to get level with the earth in the same way that 2012DA14 cut the other way through the angles to come up the back: the radiant becomes irrelevant at this point and that’s why it was totally misleading to talk about a -81 degree radiant.

Also, because the fragment is cutting up through the declination angles, its own trajectory angle cannot be described with declination angles any more- except for a bulls eye geocentric hit. It has to be aiming over the top of the Earth to get a chance of being pulled in hyperbolically over the ‘new’ equator line for a hit. This means that whatever declination angle is chosen for the instantaneous position of the emergence of the fragment through the window, its actual trajectory angle would need to be greater by 3 to 6 degrees or so in order to aim it away from the geocentre to two or three thousand miles out from the equator line, that is, two or three thousand miles from the disc it sees above it and with the same right ascension as the RA of the fragment emerging at the window. This angle cannot be geocentric because it has to look as if it will miss the Earth. Looked at another way, it is a line running parallel to a declination angle that starts 3 to 6 degrees in from the fragment emergence point, measured radially inward. This jiggling of inputs for the fragments own inclination is nevertheless bounded by the upper limit of 69 deg, the true radiant angle. There is also potentially a small amount of leftward (solar plane y axis) component as they emerge round towards the 2H 30 mark because these are trying to pass by the side of the Earth but get caught. I think these, around the 0 to 1H mark (0 to 30 degrees of right ascension) are the best candidates.

That arrival window describes a curved slit sitting somewhere roughly below where the southern tip of New Zealand was at the time of impact. The fragment would be emerging at a trajectory angle of between -65 and -69 degrees of declination (that is, its own path angle as opposed to the box perimeter angles). This needs to be set at 10 hours 20 mins (clock time) up range (about 150k to 170k miles?) so that the fragment would be coming through it at 17:00 UTC on February 14th 2013. Some time not long after that the trajectory angle would start to curve in noticeably on its hyperbolic path.

I extended the window round to 2H 30M because of the angle discrepancy between the radiant and the final trajectory. This was up to 17 degrees when playing with equatorial-to-horizontal coords for Chebarkul (but one-way calcs made this inexact) and only 8.5 degrees using old fashioned cotton stuck to a globe.

Incidentally, using the globe method resulted in a view, looking downrange along the trajectory, identical to the several Youtube videos of 2012DA14 when freeze-framed at 3:20 UTC on 15th February. It was the view from DA14 as the Chebarkul meteor hit- you can see the beginning of the meteor’s ground track over Taiwan before it disappears over the ‘equator line’ at 22 deg north. You can see that its hyperbolic trajectory extends round and down past and almost parallel to you to your right, in other words, the same trajectory but displaced 50k miles to the right. This ‘almost parallel’ track would correspond to the sunward track of the fragment not being quite sunward but with a slight right ascension from that track of a few thousand miles so that the fragment came from further round towards 2H 30 but up and in on the correct line. This allows for the 8.5 degree disparity.

It should be said here that 2012DA14 seems to have corkscrewed itself by between 5 and 12.5 degrees depending on where you make the cutoff between true radiant and local approach. It is apparent in the ephemeris (you can’t see its subtlety in any video or diagram). It may seem to defy physics (not orbiting on a great circle) but I would ascribe it to the slowing down 2012DA14 as its orbit goes from inside track to outside track and its relative prograde motion with respect to the Earth went nearly to zero. It was almost stationary in the prograde vector, sitting at -86 declination and ready to be plucked up along the most convenient longitude line. Because there was some forward motion still, it did get plucked up pretty well opposite but not 180 degrees- the entire pass was 4 or 5 degrees inside one hemisphere, resulting in a 5 to 12.5 degree twist. If this happened to the proposed Chebarkul fragment, it would have skewed in exactly the necessary way to bring it round to this new ‘wrong’ 8.5 degree-off trajectory and heading over Taiwan, China, and into Chebarkul. This is why the search box extends round to 2H 30M. It’s because the fragment oversteps ever so slightly before skewing. For that reason, once you get round to 00H to 2H, the trajectory emerging from the box will have a sideways component to the left (positive RA) ie not radially inward. These candidates will be skewing 8-10 degrees anticlockwise as you look down on them as they rise and will probably do so over the last 80,000 miles. This is how their local ‘radiant’ is skewed round. That’s if DA14 is anything to go by.

The fragment would be travelling at about 13,000 mph through the window but it would be best to plug into the software ephemeris details for 2012DA14 for the speeds from far out so as not to start at an arbitrarily high speed. However, beware of piggy-backing on 2012DA14 data to extrapolate hypothesised fragment data. I have seen, among other things, a rather amusing graph that relied on like-for-like parallel trajectories with earth skimming fragments refusing to bend round under the influence of 10 x the acceleration 2012DA14 was experiencing. That is their ‘proof’ that the fragments can’t make it north of the equator. That was on a respected astronomy blog.

If all goes to plan, you should see all manner of near misses, flying over Asia and Russia, a few direct hits on the Southern Hemisphere in a wide band from New Zealand northwards and a few Northern Hemisphere hits, one of them right on Chebarkul. You’ll have to play with it though, maybe venture a little way outside the window if needs be. The worst that can happen is some very interesting near misses- but I really do think there will be hits. This need for playing around is reflected in the fact that some solutions could imply the need to add 5 or 10,000 miles to the track line displacement further uprange (back down the slope) for a possible 60,000mile or so displacement. You can’t use the 2012DA14 trajectory, displaced and pasted to the other track- it’s bending the wrong way from 24 hours out. Even a mirror image wouldn’t be faithful due to its greater radial displacement.

THE POSITION OF THE FRAGMENT IN ORBIT- THE BIGGER PICTURE:

I will acknowledge that when NASA said that the Chebarkul meteor was not following along the same path as 2012DA14 they were right but only in a highly technical sense. Any fragment passing within a radius of a few thousand miles of the trajectory would not have impacted the other side of the Earth. But when considering the possibility meteor showers, you have to think in terms of millions of miles, even for asteroidal showers such as the Geminids and the Quarantids, because the Earth takes days to travel through them. I think NASA was clutching at straws. You have to look at the bigger picture and besides, the proposition as put forward in this comment isn’t played out on a vast scale in solar system terms.

I propose a fragment riding just 200,000 miles above 2012DA14 (north with respect to the solar plane). Just stating that baldly might understandably invite querying as to why they should be related. However, visualising it scaled down, it would be the equivalent of two tiny pieces of rock on an orbit 54 metres round, mirroring each other’s every move in speed, inclination and eccentricity, all the while staying exactly 2 centimetres apart, one directly above the other. I would consider those two pieces as related, one broken off from the other.

When the 65,000 mph prograde element of the Earth’s orbit is removed we get the geocentric element of relative movement between 2012DA14 (along with its hypothetical fragment) and Earth. Gone is the gentle 10 degree inclination with respect to the Earth’s orbit, with the asteroid climbing gently up a slope and sedately past the night side. It’s turned into a precipitous 69 degree climb, skewing round to vertical as 2012DA14 was apparently dragged up from under the South Pole and slung shot vertically above. That does serve a purpose for geocentric calculations and visualisations but it is as well to remember that it helps to plug mentally into the elongated, gentle slope version from time to time so as to get a good feel for what is really happening to the Asteroid and the purported fragment as they pass Earth.

Once the frame of reference snaps to geocentric you see the fragment rising up ahead of 2012DA14 and slightly to one side and they start to look a little disjointed. But when you snap back to solar system view with them both sailing along, rising up alongside Earth, you see that one is directly above the other: the 50,000 mile displacement is really just a 200,000 mile vertical displacement which, when looking down the -69 degree radiant makes them appear to be 50,000 miles apart. That said, there may be a fraction of further displacement to the outside of the orbit track too to allow for the skewing effect. They only ride on different tracks because of their vertical displacement and those two tracks went either side of the Earth. One was too close and the fragment hit (hypothetically). There’s something telling about that vertical nature of the relationship: the proposed fragment is following the exact same track but directly above. If it had been shifted a few thousand miles long ago, perhaps by a small collision, then previous close encounters, passing beneath the Earth would have widened that gap quite dramatically: 0.01mm/sec^2 differentials in gravitational acceleration add up to 4m/sec over a four day encounter within a million miles. That’s tens of thousands of miles per year. 200,000 miles isn’t as far as it seems.

I doubt if its possible but old sky scans might show up the culprit: at 12 million miles it would be 15 minutes of arc displaced from 2012DA14 when looking straight down the 69 degree track and would be offset at around the ’9 o’clock’ mark. For the 2012 pass at 6 million miles it would have been around one degree offset above at about the 12 o’clock mark.

Happy hunting!

Scute

Comments
  1. Scute says:

    Frank,

    I forgot the drop in the z position vector on the 14th that would position the proposed rock in a place commensurate with a two degree inclination, 1.5 degrees lower. I think it’s -33 to 34,000 km in z. Exact figure was 33,690 but there’s some guesswork there on Earth position and gravity well effects.

    Andrew

  2. Frank Davis says:

    assuming Iceland hits are grazers

    They are.

  3. Frank Davis says:

    Andrew,

    Oops!!!

    I didn’t have an impact after all.

    Last weekend, to test an idea of yours, I pulled the rockcloud 4000 km down the z axis to force an impact. I thought I’d removed the bit of code that did this, but it seems that I didn’t. And so the impacts I reported last night were an artefact. The microcloud actually passed about 9600 km from the Earth on 15 Feb 2013.

    Back to the drawing board.

  4. Scute says:

    Frank

    We’re going to make mistakes with this fine-tuning. It’s still a partial success even now. We’ve got a rock sitting in the DA14 rock train that flies 3000km over Chelyabinsk at the correct time a year after close approach. I know I’m always scaling it down to the human scale but I’ll say it again. It’s the same as being 3mm out after travelling 949 metres. Oh, and out on the orbit time by less than 0.01%.

    Drawing board suggestion:

    How about doing that increase in inclination/ drop in z position on 14th Feb 2013 in order to get a feel for what’s happening? You could then send it back to 2012 and see what date it crosses the Earth’s orbit. If it’s within the time window on 16th-17th it would mean that, where it crosses is the place and also the time for the Earth position in the 2012 pass. It may still overfly in 2013 but the 2012 position would be interesting to know so as to get a feel for our working margins.

    This 2 degree inclination is a minimum for a reasonably similar atmospheric altitude to the Chelyabinsk meteor.

    Andrew

  5. Frank Davis says:

    I agree. It’s tantalizingly close. We’re only 3000 km up the z axis from the Earth on 15 Feb 2013.. But going that extra 3000 km seems to be extremely difficult..

    I fooled around with it all a bit more this evening, moving the start position of the microcloud. But all I ended up doing was to just move backwards and forwards along the same orbit, which is more or less in the ecliptic plane.

    What we seem to need is an orbit which has the opposite inclination to DA14, and has negative vz on 15 Feb 2013 instead of positive vz. Rocks with that sort of inclination should have no trouble landing anywhere in the northern hemisphere. Not sure how to construct them, though.

  6. Scute says:

    Frank

    Just an update. I’ve been quite occupied doing some calculations on the specific orbital energy (enery per kg) of DA14 as compared with the Earth so that I can determine the speed of DA14 as it would have crossed the Earth’s orbit on the 15th without the gravity well smudging things. It’s quite illuminating as are some other observations to do with the node positions and perihelion. Trouble is, I’m rather busy for a few days so there’s no time to go into detail now and I still want to redo some bits with slightly more accurate inputs. But I’ll get there.

    Andrew

  7. Scute says:

    Frank

    I was looking through some DA14 bookmarks for something when I came across a page of historical fireballs. Since I think I understand the August node a little better now, I thought I’d look through them for an August fireball. The only one was the August 18th 1783 fireball which travelled a thousand miles from Scotland to SW France and northern Italy just after 21:00 and was witnessed by many fairly reliable people like army types, artists and a natural philosopher on the Windsor Castle terrace. I’m surprised we haven’t heard of this before. And, as you know, August 18th is very close to DA14’s descending node.

    I plugged the date into the DA14 ephemeris plus a few days either side and also did the same for the Earth so as to get radial distance comparisons. I can’t get your SSB state vector version, just sun-centred polar coordinates with distance in AU and relative km/sec to sun. But that served me well enough.

    If you can believe the 230 year DA14 projection down to the last km, the upshot is that it was 4.5 degrees behind the Earth at 21:15 on 18th August 1783. That’s roughly how far it was behind the Cuban fireball of 11th February 2013.

    More importantly, our purported rock train was passing 1 million km above and behind the Earth on the 18th August 1783 (642,000 km in -xy; 866,000 km in +z). I worked this out by sending DA14 forward to the same sun angle as the Earth was at 21:00 on the 18th.

    Also, the year before, 18th August 1782, DA14 itself had been roughly in this 1 million km vicinity because it had a 3.5 day slower orbital period than the Earth at this time. That meant it was trailing a day behind in August 1782 and 4.5 days behind a year later, in August 1783. This means that in 1782 there may have been some action going on in the rock train which would have sped up a few rocks, bringing them in earlier in 1783 and nearer to the Earth instead of 642,000 km on the outside track.

    It should be remembered that DA14 is nowhere near the August node at the same time as the Earth for the better part of a century at a time so it is quite a coincidence that the 1783 fireball happened at the only time it could reasonably have been associated with DA14.

    This seemed like enough circumstantial evidence to delve a little deeper. I found a 1989 paper by Martin Beech that gives an overview of the witness accounts collated by Charles Blagden of the Royal Society at the time of the fireball. It’s linked below and it’s from Harvard.edu which always churns out sensible, detailed papers on these fireballs. Beech notes that Blagden never plotted a trajectory in his account for the Transactions of the Royal Society, which was rather an oversight considering the wealth of detailed sightings. So Beech drew a trajectory based on those sightings and it’s shown in the paper as running south-east from the west coast of Scotland to the sea just off Kent. He didn’t plot it all the way to Italy.

    If I run my cotton across that trajectory on my globe and carry it on round in a great circle, it near as damn it runs through a 67 deg North radiant and 67 south antipode. It crosses the equator around the Uganda/ Kenya border at 35 deg east. If I swivel and tilt the globe to the orientation it would have had at 21:00 on 18th August, this 35 degree east line is about 5-10 degrees west of the midnight line. I measured 6-7 degrees but concede it’s not that accurate. This means that the great circle path of the 1783 fireball is mimicking a DA14 radiant. I presume the inclination and eccentricity of DA14 were similar then even though there were a few moderately close encounters between 1782 and 2013. The sun-centred polar coordinates don’t betray the radiant but I think I can see the typical DA14 behaviour at play, for example, crossing above the Earth’s orbit two days later on the 21st and dropping through the node on the inside track on the 23rd.

    There’s one problem with linking the 1783 meteor to DA14. It’s a grazer but there should only be southern grazers at the August node and northern punches. However, if it was a Southern Ocean bounce event- it would have bounced somewhere around 50 deg south- then any captured fragments would have orbited on that great circle or gone suborbital. The long fireball trajectory down the east coast of Britain and on to Italy would suggest a slowed rock in a shallow trajectory, ‘trying’ to bounce again but doomed. It’s a 1000 mile track. Apollo had a 1084 mile track at 11 km/sec, admittedly with a controlled bounce but I reckon a slightly suborbital DA14 fragment could follow the Earth’s curvature for 1000 miles. That’s 200 seconds, not considering slowing. The Windsor castle witnesses saw a portion of its track for 30 seconds.

    We now know bounce events happen and that they may well have happened in the five-day period from 11th to 16th February 2013. I don’t think it’s too much of a long shot to invoke the possibility for the 1783 fireball when its great circle matches the DA14 radiant so closely and it happened in one of the two or three possible years out of a quasi 70 year cycle.

    http://en.m.wikipedia.org/wiki/1783_Great_Meteor

    http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1989JBAA…99..130B&db_key=AST&page_ind=0&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES

    For anyone who hasn’t heard of Earth grazers (which enter then exit the atmosphere as opposed to grazing then dropping to the surface):
    http://en.m.wikipedia.org/wiki/Earth-grazing_fireball

    Andrew

  8. Scute says:

    The Martin Beech paper link didn’t work. I’ll try again:

    http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?journal=JBAA.&year=1989&volume=..99&letter=.&db_key=AST&page_ind=141&data_type=GIF&type=SCREEN_GIF&classic=YES

  9. Scute says:

    OK, third time lucky for the Martin Beech paper. Try this link and click the button that says ‘send PDF’ under ‘printing options’.

    http://adsabs.harvard.edu/abs/1989JBAA…99..130B

  10. tallbloke says:

    Andy, wordpress won’t parse the groups of full stops in adsabs urls

    Try This

  11. Scute says:

    OK, the best way I can find to access the paper is as follows:

    1) go to the bottom of my main comment about the 1783 Great Meteor (4 comments above).

    2) Click on the Wiki link to the meteor

    3) go to the references section. The first reference is to the Martin Beech paper.

    4) Click the link to the right of the word ‘bibcode’. This sends you to the journal.

    5) scroll down to ‘printer options’ and click on the button that says ‘send PDF’. That should give you the whole paper.

    Andrew

  12. Scute says:

    Another route to the elusive paper:

    Link text seen by others

    [Reply] Heh. See email. 🙂

  13. Frank Davis says:

    Andrew,

    I looked up NASA DA14’s vectors for 18 Aug 1783

    Ephemeris Type [change] : VECTORS
    Target Body [change] : Asteroid 367943 (2012 DA14)
    Coordinate Origin [change] : Solar System Barycenter (SSB) [500@0]
    Time Span [change] : Start=1783-08-12 00:00, Stop=1783-08-25 00:00, Step=1 d
    Table Settings [change] : output units=KM-S; CSV format=YES
    Display/Output [change] : default (formatted HTML)

    and got an x,y,z location for 18 Aug 1783

    1.232869881491631E+08, -8.994665706592803E+07, 3.388674463551950E+06, km

    Doing the same with the Earth, I got x,y,z location

    1.279046312938855E+08, -7.952960278359713E+07, -3.890588840372721E+04, km

    The year before, same date saw DA14 at

    1.287434173132898E+08, -8.070431714595410E+07, 1.526138327810774E+06, km

    and Earth at

    1.286840626329343E+08, -7.883223472825381E+07, -4.984421007358410E+04,km

    Same region of space, but still quite far apart.

  14. Scute says:

    Frank

    Yes, that’s pretty well in keeping with what I could see, 4.5 days behind in 1783, fairly close in 1782.

    By the way, I delved in a bit more by looking at the geocentric ephemeris and DA14 got closer than it was on the 18th August 1782 because it crossed the node on the 21st. At 18:00 on the 21st it made its closest approach of 1.77 million km.

    Your vectors for 00:00 on the 18th August 1782 show a 2.42 million km distance and at 21:00 it was 2.14 million km.

    In fact, DA14 trailed the Earth at an average distance of 2.1 million km or so from the 17th to the 24th inclusive. This corresponds to about 0.09 mm/sec acceleration which amounts to about 7.5 m/sec per day or 60 m/sec over the 8 day period. That would be a minimum because there are additional but lesser accelerations over the days either side.

    The force was directed between roughly 45 deg above the ecliptic to 45 deg below and from 30 deg to the outside of the up range Earth orbit (aft) to 30 degrees to the inside of the up range orbit. This means that the 60m/ sec vector change over those 8 days was acceleration in the prograde direction of DA14 and a direction change that would have reduced inclination faintly with a commensurate increase in xy speed.

    This analysis implies that rocks in the vicinity of DA14 would be perturbed similarly, but if they were a little further along the orbit in 1782, about half a day, they would have been very close to the Earth and perturbed a lot more.

    The main thing is the position of the rock train at the time of the 1783 meteor and the fact that rocks perturbed in 1782 might arrive early and therefore cross the Earth’s orbit earlier, i.e. 640,000 km closer in xy.

    Here are some thoughts related to the above. It reads like facts but, of course, it’s just my supposition based on what your programme has shown so far:

    I believe that with centuries or millenia of Earth and rock train interaction we have not so much a rock train any more but a pulsating cloud with all the different orbits meeting back at the nodes or rather, shooting through a narrow tube at the nodes that is perhaps 500,000 km wide. At the apsides, the orbit ellipses diverge to be 10 million plus km apart, some even further in xy. That is what is happening when you observe the rocks either side of the 2012 breach and folding ‘fireball’ head in 2013. They diverge wildly at the apsides and pulsate back at the nodes.

    After many such close approaches the rocks on these different orbits would be spread right around the sun because of their different sizes and eccentricities and therefore orbit periods but they all pass through or near to the Earth’s Feb 15th and August 21st positions. Most pass through those physical points in space but at other times of the year. But for the Earth it is still like crossing a motorway on those dates, just because of negotiating its way past the rocks that really are coming through at that position at the same time as the Earth.

    As the rocks pass through the narrow tubes at the nodes, some pass near the inside ‘wall’ and some near the outside wall, 500,000 km to the outside track. Because of this, they cross the Earths orbit on different dates, either side of DA14’s node dates. They each therefore have their own distinct node anywhere between 11th to 16th February and 18th to 23rd August.

    I think DA14 is a very insignificant rock in this vast pulsating cloud. This is all the more likely given that two large rocks were discovered last week, one on Sunday and one on Thursday (?) making their close approaches only 12 hours and 2 days, respectively, after discovery. They were discovered by La Sagra which found DA14 in 2012. The astronomer who narrated the La Sagra video that Tallbloke linked said it’s like a bowling alley. I’m not saying these two are DA14 linked but that there are countless millions of small to medium-sized rocks out there, many of which are probably related even though they have seemingly different orbits. If they pulse and meet at the nodes then they are probably related.

    The La Sagra obsevatory discovered these two rocks high up in the northern skies. That’s heartening because any inside trackers perturbed last February will be coming in from that point in the northern night sky, maybe 10 degrees west of the midnight line. If they do come, I suppose it will be between the 18th and 23rd. And if they do, I’ll blame you, Frank, for modelling them. So if you’re at the pub next Sunday afternoon, enjoying a pint and a smoke and you hear a loud bang to the north, you’d better duck under the picnic table, preferably the south side!

    Andrew

    P.S. Correction to last comment: I made a mistake in likening the 1783 situation to the Cuban meteor. In 1783, DA14 was 4.5 days behind in absolute heliocentric travel which put it 11 million km behind the Earth. The Feb 2013 situation, or hypothesised Cuban link, involved the Cuban meteor coming up the geocentric radiant at 6km/sec and DA14 coming up the same radiant 4 days later at 6km/sec so the Cuban meteor was only about 2 million km ahead of DA14. But that doesn’t detract from the bare bones of the 1783 theory of a link.

  15. Frank Davis says:

    I believe that with centuries or millenia of Earth and rock train interaction we have not so much a rock train any more but a pulsating cloud with all the different orbits meeting back at the nodes or rather, shooting through a narrow tube at the nodes that is perhaps 500,000 km wide.

    I see what you mean.

    They’re certainly very interesting things, these rock clouds. Pretty much all the rock clouds that I’ve constructed have had been initialised with the same velocity vectors as the central body (usually DA14). These (usually cubical) clouds gradually spread out along the orbit of the the central body. Sometimes I make them spread quicker by giving the rocks velocities which move them away from the central bodies.

    A week or two back, I put together a new way of making clouds which seemed rather more realistic. I supposed that the central body gradually spawned rocks moving away from it. This could happen when the central body was impacted by some other rock. Or it might happen as a result of thermal expansion or contraction. Or by tidal forces during close approaches.Whichever way, my new method of cloud generation entailed regularly firing rocks off the surface of the central body in some random direction with 10 – 20 m/s relative velocity.

    Whereas the old method of generating rock cloud produced fairly uniform clouds, the new method produced clouds with a high concentration of rocks near the central body. The clouds had a new and distinctive asymmetric shape.

    I used these clouds with high concentrations of rocks round the central body to remodel DA14’s close approach in 2013, expecting to get lots of impacts, but actually getting very few, because the Earth doesn’t pass through the exact centre of the rock train. But, trying it with Apophis’ close approach in 2029, I got lots of impacts, because Earth passes through the centre of the Apophis rock train on 13 April 2029. The main meteor impact zone stretches from Spain to Samoa, although rocks can come down on both poles.

    Underlying these approaches is the supposition that these rock clouds are the result of single asteroids entering the solar system, and being broken up in a variety of different ways. I have no idea how long they might take to disintegrate. But it seems to me that once some asteroid starts to disintegrate, a rock cloud gradually grows up around it, extending in a train fore and aft along its orbit. Eventually it extends round the whole orbit. And this rock gets holes punched in it by close approaches to various planets. At which point the rock train fades away, at least in the sense of ceasing to be a recognizable entity. And becomes what you are suggesting – a diffuse cloud that comes together at the nodes. In time, all the rocks land on one planet or other, and the solar system is swept clean of debris..

    I suppose my interest is less to do with the past than the future. It seems to me that large disintegrating bodies are almost certain to be accompanied by rock trains, and that’s what we experienced with DA14. earlier this year with what certainly seems to have been a distinct spike in fireball sightings. If this is true, then Apophis, which is much larger than DA14, will have a (correspondingly large) rock train in 2029, through the centre of which the Earth will pass. So my guess is that this close approach could produce a really spectacular set of fireballs. Whether this poses a serious threat or not is not something I can’t determine. It depends on the density of the rock cloud, and the mean size of rocks.

    Apophis generated some alarm when it was first discovered. The alarm has since subsided, as it became clearer that it would not impact the Earth, but pass within about 20-30,000 km. Nobody, however, seems to be considering whether Apophis has a rock cloud around it. In my view, the real danger (if there is any) comes from such a cloud.

  16. Frank Davis says:

    Andrew,

    You might like this BBC iplayer documentary about comets.

  17. Scute says:

    Frank

    Interesting comment. Can you tell me how long it took for that 2012 asymmetrical rock train to develop? I realise that’s a more slippery question to answer than for the old rock-spawning clouds because they used to happen in one go at the start date and this new cloud/train spawned one rock at the start date and could have spawned its latest rock 10 minutes ago.

    I’m glad you agree in principle with my notion of pulsating clouds meeting at the nodes. Another way of looking at is like gripping many different sized steel rings in your hand so they all run through the narrow ‘tunnel’ within your fist and then extend out to their respective diameters opposite your grip. And in addition, teasing them apart in the third dimension by loosening your grip ever so slightly, allowing them to criss-cross a tad as they go through your grip and watching them criss-cross back again diametrically opposite but at different radii from the centre due to their different sizes nesting in your grip. Thousands or millions of years ago, these rings would have been one ring constituting one rock. That would have changed to one ring constituting many rocks (a train) for a while shortly after break -up and finally the many different rings representing many rocks and passing through the node (your grip) that disturbed the train.

    Andrew

  18. Frank Davis says:

    Can you tell me how long it took for that 2012 asymmetrical rock train to develop?

    About 15 months. The cloud was larger if the relative velocity of rocks ejected was higher, of course. But even when I wound down the relative velocities to 2 – 3 m/s, I was still getting large clouds that stretched from Earth to Moon. No surprise really, even at 1 m/s a rock will in principle travel nearly 32,000 km in a year.

    Another way of looking at is like gripping many different sized steel rings in your hand so they all run through the narrow ‘tunnel’ within your fist and then extend out to their respective diameters opposite your grip.

    Yes. There were several images I produced of rock paths which showed that.

    Anyway, exactly 6 months on from close approach of DA14 and the Chelyabinsk fireball, I seem to have more or less run out of gas or enthusiasm or whatever. I think I’m going to have to drop the investigation for a while at least.

    But we have a ‘partial success’, as you put it. We have a rock from DA!$’s rock train which comes within 8 or 9 thousand km of the Earth on 16 Feb 2012 which returns to a similar distance from the Earth on 15 Feb 2013, from what seems to be a much more realistic direction for a Chelyabinsk impact.

    In so doing we’ve managed to strengthen the case that the Chelyabinsk rock was a DA14 companion. I don’t think it’s ever going to be possible to prove that it was. But I think that DA14 is arguably the most proximate cause. And it’s more likely that a car windscreen gets broken by a stone that’s kicked up by a passing car (DA14) than by one ejected by a volcano 100 miles away (asteroid belt).

  19. Scute says:

    Frank

    You deserve a rest. Thanks for your huge input. Hope you’ll come back from time to time. I’ll keep posting when I find stuff…such as:

    http://arxiv.org/pdf/1307.7918v2.pdf

    This was buried in the Daily Mail link that Tallbloke linked so H/T to you, TB. That DM article cited this paper, published two days ago. It’s right up your street, especially section 5 on p 4. It vindicates everything we’ve been saying about clouds and trains but for another asteroid. They must be using the video evidence for the speeds which in turn dictates the orbit. But no allowance was made for camera distortion so if the speeds were lower as a result of that, everything these guys say can apply to DA14.

    Andrew

  20. tallbloke says:

    http://english.pravda.ru/science/mysteries/16-08-2013/125408-chelyabinsk_meteorite-0/
    Spanish scientists have determined which celestial body could be the “parent” of the meteorite that caused so much trouble to the residents of Chelyabinsk, Russia, last winter. They believe that the meteorite has likely split from asteroids 2007 and 2011 BD7 EO40 from the Apollo group. The latter is a more likely candidate for the role of the “parent”.

  21. Scute says:

    Frank

    [re my comment on a lunar orbiting dust detector as asteroid cloud detector for the asteroid initiative]

    They’re sending an atmospheric dust detector to the moon anyway. Launch next month (see NASA RSS feed below) It’s collecting dust samples. I doubt if it’s measuring delta v on collection though. I’m sure much of the dust is electrically charged and lofted each day but there was an anomalously high component of fast lateral trajectories near the ground as measured by Apollo missions. I would hope for this mission to answer that question but it requires a delta v measurement.

    ////////

    NASA RSS:

    On Thursday, 22 August 2013, NASA News Releases wrote:
    August 22, 2013
    Dwayne Brown
    Headquarters, Washington
    202-358-1726
    dwayne.c.brown@nasa.gov

    Rachel Hoover
    Ames Research Center, Moffett Field, Calif.
    650-604-4789
    rachel.hoover@nasa.gov

    Keith Koehler

    Wallops Flight Facility, Virginia
    757-824-1579
    keith.a.koehler@nasa.gov

    RELEASE 13-265

    NASA Prepares for First Virginia Coast Launch to Moon

    In an attempt to answer prevailing questions about our moon, NASA is making final preparations to launch a probe at 11:27 p.m. EDT Friday, Sept. 6, from NASA’s Wallops Flight Facility on Wallops Island, Va.

    The small car-sized Lunar Atmosphere and Dust Environment Explorer (LADEE) is a robotic mission that will orbit the moon to gather detailed information about the structure and composition of the thin lunar atmosphere and determine whether dust is being lofted into the lunar sky. A thorough understanding of these characteristics of our nearest celestial neighbor will help researchers understand other bodies in the solar system, such as large asteroids, Mercury, and the moons of outer planets.

    “The moon’s tenuous atmosphere may be more common in the solar system than we thought,” said John Grunsfeld, NASA’s associate administrator for science in Washington. “Further understanding of the moon’s atmosphere may also help us better understand our diverse solar system and its evolution.”

    The mission has many firsts, including the first flight of the Minotaur V rocket, testing of a high-data-rate laser communication system, and the first launch beyond Earth orbit from the agency’s Virginia Space Coast launch facility.

    LADEE also is the first spacecraft designed, developed, built, integrated and tested at NASA’s Ames Research Center in Moffett Field, Calif. The probe will launch on a U.S. Air Force Minotaur V rocket, an excess ballistic missile converted into a space launch vehicle and operated by Orbital Sciences Corp. of Dulles, Va.

    LADEE was built using an Ames-developed Modular Common Spacecraft Bus architecture, a general purpose spacecraft design that allows NASA to develop, assemble and test multiple modules at the same time. The LADEE bus structure is made of a lightweight carbon composite with a mass of 547.2 pounds — 844.4 pounds when fully fueled.

    “This mission will put the common bus design to the test,” said Ames Director S. Pete Worden. “This same common bus can be used on future missions to explore other destinations, including voyages to orbit and land on the moon, low-Earth orbit, and near-Earth objects.”

    Butler Hine, LADEE project manager at Ames, said the innovative common bus concept brings NASA a step closer to multi-use designs and assembly line production and away from custom design. “The LADEE mission demonstrates how it is possible to build a first class spacecraft at a reduced cost while using a more efficient manufacturing and assembly process,” Hine said.

    Approximately one month after launch, LADEE will begin its 40-day commissioning phase, the first 30 days of which the spacecraft will be performing activities high above the moon’s surface. These activities include testing a high-data-rate laser communication system that will enable higher rates of satellite communications similar in capability to high-speed fiber optic networks on Earth.

    After commissioning, LADEE will begin a 100-day science phase to collect data using three instruments to determine the composition of the thin lunar atmosphere and remotely sense lofted dust, measure variations in the chemical composition of the atmosphere, and collect and analyze samples of any lunar dust particles in the atmosphere. Using this set of instruments, scientists hope to address a long-standing question: Was lunar dust, electrically charged by sunlight, responsible for the pre-sunrise glow above the lunar horizon detected during several Apollo missions?

    After launch, Ames will serve as a base for mission operations and real-time control of the probe. NASA’s Goddard Space Flight Center in Greenbelt, Md., will catalogue and distribute data to a science team located across the country.

    NASA’s Science Mission Directorate in Washington funds the LADEE mission. Ames manages the overall mission. Goddard manages the science instruments and technology demonstration payload, the science operations center and provides overall mission support. Wallops is responsible for launch vehicle integration, launch services and operations. NASA’s Marshall Space Flight Center in Huntsville, Ala., manages LADEE within the Lunar Quest Program Office.

    For more information about the LADEE mission, visit:

    http://www.nasa.gov/ladee

    [end of newsfeed email]

  22. Frank Davis says:

    New DEVASTATING Chelyabinsk METEOR STRIKE: ‘7x as likely’ as thought

    NASA’s checked its space rock maths and it’s not good news

    NASA has revealed new research on the Chelyabinsk meteorite that exploded over Russia in February, and the findings aren’t good: not only does it look like the astronomic models about the number of similar-sized things reaching Earth are wrong, but also the damage they can do is much greater than expected.

    “If you look at the number of impacts detected by US government sensors over the past few decades you find the impact rate of kiloton-class objects is greater than would be indicated by the telescopic surveys,” said Bill Cooke, meteoroid environment office lead at NASA’s Marshall Space Flight Center at a press conference on Wednesday.

    “Over the past few decades we’ve seen an impact rate about seven times greater than the current state of the telescopic surveys would indicate.”

    Cooke said that as the current state of asteroid surveys was expanded he expected we would find more meteorites in the vicinity to account for these impacts, but also that the amount of damage they caused was being reassessed.

  23. Frank Davis says:

    Also Daily Telegraph.

    Dr Peter Brown, lead author of one of the studies and physicist at the University of Western Ontario, said the Chelyabinsk meteor was forcing scientists to reassess what they know about asteroids and potential meteors.

    He said: “Existing models predict events like the Chelyabinsk asteroid might hit every 120 or 150 years, but our data shows the frequency may be closer to every 30 or 40 years.

    “When Chelyabinsk happened, I would have never expected to see an event big enough to cause damage on the ground.

    “It’s totally outside the realm of what we thought likely in our lifetimes based on earlier statistics.
    “Our statistics now suggest this type of event likely happens with more frequency.”