Pages

Monday, January 25, 2016

Why Planet Nine might not exist

[or: what keeps me up at night]

As you will see in the next post, I think Planet Nine is really out there. But that doesn’t mean you should think it is out there. You might be skeptical. In fact, I would prefer that you were skeptical. I would prefer that you read the scientific paper, looking for potential flaws, caveats, and places where we might have been led astray. But, OK, I understand that the actual scientific paper is on the weighty side, so, rather than make you wade through it finding the potential piutfalls, instead, I will give you my top list of things that might be wrong.

First, though: what is not wrong.

If there is an approximately 10 Earth mass planet on an extremely elliptical orbit in the outer solar system, it would definitely line up the orbits of Kuiper belt objects with similarly elongated orbits, it would create Kuiper belt objects with orbits twisted by 90 degrees to the planets of the solar system, and it would make objects, like Sedna, which have elongated orbits which don’t ever come close to the rest of the Kuiper belt. These effects we now know from a general mathematical analysis and from detailed computer simulations to double-check the mathematical analysis. This analysis, I am confident to say, is iron-clad. Astronomers will try to reproduce it (I hope), and they will get the same results (I know). There truly is no wiggle room here. A 10 Earth mass planet does exactly all of the things that we are trying to explain.

If I am so confident of this, how could Planet Nine possibly not exist? Just because Planet Nine can explain all of these effects, it doesn’t not mean that there is no other possible explanation. We tried to think of everything that we could, and systematically ruled out alternatives, but that doesn’t mean that someone else won’t come up with an idea that works. Again, I hope that there are skeptical astronomers working right now to come up with alternatives. I am confident that they will not come up with them (because I do actually think we considered everything that could possibly be out there), but, unlike my statement above, I will definitely not say that this one is iron-clad. Aluminum-clad, maybe. Stainless steel, perhaps. I’d be willing to bet a lot of money against the idea that someone will find an alternative explanation for all of the effects that we are seeing. But it is possible I could lose.

There is one insidious way in which we may have been fooled into thinking that Planet Nine exists, however, and it is a problem that permeates all of experimental science. My single biggest worry is that perhaps – just perhaps -- we have been fooled into seeing a pattern where none exists. Humans excel at recognizing patterns, even when they are not there (see: everything single face-on-Mars claim ever, for example). Could we have been similarly fooled? Absolutely (again: I don’t think we have been, for reasons detailed in that next post, but is it possible? Of course). Here’s how:

In our analysis, we show that the six most distant objects that have orbits extending outward from the Kuiper belt all line up within a 100 degree quadrant and all have orbital planes which are tilted away from the plane of the planets by about 20 degrees (and within 6 degrees of each other). From some very simple calculations we can show that the probability of these alignments happening due to chance is only about 0.007%. You could also say that there is a 99.993% chance that the alignments we are seeing in the outer solar system are real, and that we are not simply being fooled into seeing a pattern where none exists.
But, really, if you said that, you’d be wrong. Real statistics don’t work that way. You can’t, for example, flip 100 coins, realize that 10 of them in the far upper right corner all turned up heads and then say “wow; the chances of 10 heads in the far upper right corner is only one in 1024 so something must be happening up there.” And if you flipped all of the coins again, chances are you wouldn’t get 10 heads in the far upper right corner (in fact, chances are 1 in 1024). The real statistical question that you should be asking at the first coin flip is more like “what is the probability that something that seems anomalous will appear just due to chance?” That question is essentially impossible to answer, because it relies on knowing what a human who is looking for anomalous patterns would call anomalous.
There are two good ways to combat these sorts of flawed statistics. The first I just mentioned above: replicate the experiment and look for the same result. Your eye and brain might pick out a random pattern from the noise one time, but the same pattern will not occur again. You might see different patterns, but that just shows you how easy it is to find patterns in data.
How do we replicate the finding that the most distant objects in the outer solar system are unusually aligned? We find more of them. If the alignment was just random pattern finding by easily fooled humans, it will quickly go away when the next half dozen objects are discovered. And while it took 12 years to discover the first 6 aligned objects, the next few should be much faster, as telescopes and surveys continue to get bigger and more powerful. One caveat: our computer simulations do not predict that 100% of the most distant objects will be clustered. Just the vast majority. So finding one or two outside of the cluster is not the end of Planet Nine. But finding the next six objects randomly distributed around the sky would be a pretty clear indication that we fell into the pattern-matching trap and that Planet Nine is a fantasy. The Planet Nine hypothesis makes strong predictions, and these can be used to show that the hypothesis is wrong, if it is.
The second way to combat the flawed statistics of pattern matching is to use your explanation for the pattern that you see to predict something entirely unrelated to the pattern. In our example of the coins above, you could hypothesize that the explanation for all of the coins coming up heads in one spot on the table is that there is a powerful magnetic field in that one location of the table (ok, I’m not sure how that could make things come up all heads, but work with me on this one). You could then make predictions. Perhaps you would predict that a set of ball bearings placed on the table would systematically roll towards that location. Or something. The key is that the prediction is something that you don’t know the answer to ahead of time, is not directly related to your original observation, and has a low probability of occurring on its own. Here you are not replicating the experiment but are instead performing a different experiment and predicting a very specific answer.

Our hypothesis passed this test with flying colors – in my opinion – with the prediction and subsequent realization of the existence of what we call the distant twisted orbits (maybe we need a better term for these; definitely we need a better term for these). But maybe it’s all just a bigger case of pattern matching? Such an explanation begins to get unlikely, but now we have a second set of objects that can be replicated, and we’ll all be watching the results come in.
There is one other more mundane in which we can be “wrong.” Given the small number of objects and our, currently, limited number of computer simulations (“limited” here still means ~6 months of super computer time, but we haven’t had time to precisely explore all of the possible parameters of Planet Nine), it is possible that our estimates are not precisely correct. Maybe Planet Nine js 20 times the mass of the Earth instead of 10. Maybe it is actually a giant terrestrial planet instead of a small gas giant. Maybe it is slightly further away or tilted into a slightly different plane. These tweaks are OK.  We would still say that the Planet Nine hypothesis is correct.
If, however, a planet is found beyond Neptune and it is totally different from what we have described, if it exists, but it fails to cause the basic gravitational interactions that we have discussed, then, quite simply, we are wrong. We are not predicting that there is some planet beyond Neptune, we are predicting that there is this planet beyond Neptune and it is causing these effects on the outer solar sytem.
Now, finally, is what you can tell your friends and family to impress them by your informed skepticism of the Planet Nine hypothesis:
“I worry that they have underestimated the likelihood of finding an intriguing pattern in the orbital data and that they have just been fooled into finding a pattern where there is none. I am waiting for the next few discoveries of distant object to see if they, too, have aligned and twisted orbits like the theory demands. And, for now, I am also running some computer simulations to check some ideas I have about other ways that the patterns can develop. Ask me again in six months.”

101 comments:

  1. Out of curiosity, do you have the simulation code available anywhere?

    ReplyDelete
    Replies
    1. This would be very helpful for both: verification by scientists and a learning experience for people who never even seen simulations like that.

      Delete
    2. We run everything using the very standard mercury N-body simulation code as found, for example, here:
      http://www.arm.ac.uk/~jec/home.html

      Delete
    3. The ninth planet does exist. It already has a name, its Pluto. With the findings of the recent Pluto fly-by Pluto acts more like a planet than some of our other 8 planets. So I guess we are searching for the tenth planet. This planet, should it exist, is so far away that it is in perpetual darkness and unless it has a sizeable hot core its surface is frozen solid as well as the gases, if they are any, of the atmosphere. So Nibiru, it is not. We might call it planet Sitchin if it is finally found because it will be as far out as he was.

      Delete
    4. It is not a pseudoplanet of 'Nibiru'-type (enters the inner system) or 'Nemesis'-type (enters the Oort cloud). In fact, it both fails these ideas yet again and cuts down on their remaining gaps. (Though I must not that using myths on the one hand, and supposed extinction patterns on the other where there are none - see Alroy's autocorrelation analysis of the extinction record - seems failed at the outset. (O.o))

      Nor is it a pseudoplanet of the more conventional "disturbance" type of Vulcan (Mercury)/Planet X (Neptune type). Pluto was one of those, but the very basis for the claim is also gone. It has been proposed to use the observed clearing of the orbit - which is necessary for old planets, but also is seen in systems with remaining disks - to unify definitions of our planets with exoplanets.

      If you insist to call a miniature body for 'planet', it is either not relating to astronomical classifications (astrophysicists do this all the time) or it is for personal sentimental reasons. Go ahead, break a mirror (or whatever astronomers say)! ;-)

      Delete
  2. Great post.
    Are there any two-planet explanations for the behavior of the KBO's?

    ReplyDelete
  3. M42 and our Sun with planets from X aphelia cca 300AU in right scale http://senmut.webs.com/nibiruorbitcarpetplanets.gif
    actually the same is also on: http://senmut.webs.com/nibirubigsenmutchinabig.gif because this is also YGGDRASIL-WORLD TREE from nordic legends,..
    Hi,...finaly it is out,....what I supposed too 12years ago,... http://senmut.webs.com/nibirucrosstext.gif … When I made also simulations in WINORSA nobody wanted to believe,... Pavel Smutny

    ReplyDelete
  4. You can find by me proposed coordinates also in this discussion: http://www.universetoday.com/29083/constraining-the-orbits-of-planet-x-and-nemesis/
    http://www.lulu.com/shop/pavel-smutny/ancient-egypt-and-2012/paperback/product-16951885.html
    maybe my the most big mistake was too big mass of X in simulations,... but not of Nemesis,...

    ReplyDelete
    Replies
    1. Is that 'Nemesis' of the extinction pattern search idea? Alroy rejected that with more fossil data and better statistical methods (autocorrelation analysis) already 2008 (IIRC; a PNAS paper I'm quite sure). Also, see my response to Brig why this makes it so much harder for this type of ideas if Planet Nine is found.

      Names have meaning, so if you don't mean the arguably failed idea of 'Nemesis' you may better stick to "Planet X".

      Delete
    2. http://spaceweather.com/images2016/27jan16/cosmicrays_mar15_jan16.png?PHPSESSID=0eejd9rr5qmf39bhu10h5pab51 isnt it signal that something is closer to perihelia than year ago,..? http://senmut.webs.com/cosmic-ray-hot-spots.jpg
      http://senmut.webs.com/nibirueclipticorion.GIF
      Nobody else gave explanation for where are those cosmic rays hot spots whereas from,..?! Nemesis 26000years orbit time, X 1300-2100years orbital time,... If you can give your explanations for where are those hot spots from Milagro cosmic rays survay from,..

      Delete
    3. I think that it is very important to explain right, where are those cosmic hot spots next to Orion (on both sides) from. Though are those hot spots places where from during mainly Spring and Outumn equinoxes are coming cosmic rays-mainly hi eccelerated protons from (X), or what else? If you want to find something, so it is good to look with telescopes, infrared telescopes on those hot spots. Especially on right hot spot-its prolongation during this Spring eqinox,....
      Pavel Smutny

      Delete
  5. Many thanks for the great teaching on probability and stats, Mike, and on being an exemplar of the scientific method. It's helped me a lot, quite apart from anything to do with Planet Nine.

    Oh, BTW, as your resident proof-reader, for "wade through it finding the potential piutfalls," I suggest, "wade through it finding the potential pitfalls,"
    Just a thought. Unless you feel strongly about piutfalls, which does have a nice ring to it. ;-)

    ReplyDelete
  6. If any scientist were to do a peer review of this paper would they also need 6 months super-computer time to verify the results?

    ReplyDelete
    Replies
    1. (also, I'd like to point out that the paper WAS peer reviewed before it was published, of course!)

      Delete
  7. I have heard some scientists say there wasn't enough gas out there to slow Planet Nine down enough to go into orbit.

    ReplyDelete
    Replies
    1. If I understood it correctly, Planet Nine was first put on a very eccentric orbit by Jupiter or Saturn, not fully ejected. It would have returned into the region of the giant planets, but one of the Sun's sibling stars that was passing by accelerated it enough so its new orbit never went back into the inner system.

      Delete
    2. Being ejected from the inner Solar System to ~1000AU does not require ejection from the outer Solar System (~70000AU). You just need a method to "lift the perihelion point" after being kicked outwards.

      Delete
    3. My interest is astrobiology, so this open question is highly interesting. I hope people will work on the mechanisms and timing until PN can be tested as a planet observation. (Shades of Kepler's "candidate" vs "confirmed".)

      When Batygin hypothesized early ejection, and settling due to other system's influences in Sun's birth cluster rather than drag effects, it puts the question front and center for me. Same as PN there is now a "candidate" fossil that dates to before 4.1 Ga, and Valley's latest zircon review (2015) predicts a habitable ocean before 4,.3 Ga. At the same time that this is in tension with a late bombardment, no zircons older than 3.5 Ga show the typical impact fracture patterns seen at e.g. Vredesfort at ~ 2 Ga.

      If an early ejection - which plays nice with the Nice model - could be tied to the Nice model's Jupiter/Saturn resonance in time, the tension would go away. The early Oort cloud could have been developing and compact for much the same reason that kept Planet Nine in the system. Perhaps the Moon impact record (which hinges on absence of contamination re dating) is integrated over the long tail of the disk clearing. (Someone with impact chops may work on that too! X's fingers.)

      A series of circumstances, but so are the late bombardment mechanism...

      Delete
  8. The problem is that it is now totally impossible to simulate the formation of our solar system and all of the interactions (internal and external) that have occurred since its inception.

    What we can do, however, is begin to consider the idea that our solar system was at least initially part of a binary system, and that the anomalies we observe are in part due to the complexities of binary solar system development.

    All of our mythologies tell us that this was indeed the case (although the twin may no longer be with us). In myth, there is both a 12th/"Benjamin"/"Horus" planet (which could be Brown's "Planet 9" or simply Sedna and its ETNO "followers"), AS WELL AS a failed twin/"Esau"/"Apophis" star that "separated" from our own "Jacob/Atum-Re" star under influence of a large "Laban" star.

    I applaud Mike's efforts to find more objects and for continuing to push the issue despite the lackluster support from his colleagues.

    http://www.domainofman.com/boards/index.php?topic=128.0

    ReplyDelete
    Replies
    1. The solar system wasn't formed, it was created by God about 6,000 years ago. Short period comets prove a young solar system. And there are many other proofs.

      Delete
  9. I would like to see an animation of two objects in an anti-aligned resonant orbit.

    ReplyDelete
  10. I don,t follow all the complex maths but wonder if we can rule out the 20* inclination as being due to pertubation from a passing star or even capture of these distant objects from a smaller star ?

    ReplyDelete
  11. I have been wondering (from a layperson standpoint, not as a scientist) – Sedna and these other objects whose clustering appears to indicate the existence of Planet Nine are all near(ish) perihelion, correct? This, I imagine, is one of the reasons making it easier to discover them, since it’s easier to observe them near perihelion than when further away. However, given the extreme difference between the length of their orbits in comparison to the length of time we had the technology to observe such objects – there is a selection bias towards only observing those objects that are near perihelion.

    Could there be far more objects like this with vastly different orbits, just we haven’t found them yet because they are far enough form perihelion that they are hard to detect? So in a sense – once we have a “complete” picture of these objects, could there appear to be no clustering at all – just the clustering we saw is because of a relatively limited window in time and detection capability?

    Of course, I wondered if there are more of these with orbits all over the place – why aren’t any of them near perihelion now? Which got me wondering about a more complex idea (that is probably entirely wrong, again, I’m not a scientist). :)

    Could it be that all of these distant objects are gathered together in similar but separate clusters? Perhaps with the vastly complex gravitational effects of a large number of these objects, they might self-organize into multiple clusters resonating with each other. So, if the “Planet Nine Cluster” has perihelion at 9:00 radially, then there is another cluster that is near aphelion right now that has perihelion at 3:00, and so on for 6 clusters or 10 clusters, or some such. (I imagine it’s a low number, because too many and some others would be near perihelion as well).

    I know you checked for some self-organizing, but is it feasible/possible that with these objects, they are clustered close enough that their combined gravitational effect (and I will throw in maybe some hand-wavey resonance) creates the observed effect? So maybe there is a significant amount of mass out there in these objects, but it is in separate, small objects away from perihelion (and therefore difficult to see) but clustered somewhat near enough to each other that their gravitational effects can build up. (I’m reminded of pushing kids on a merry-go-round – a lot of little pushes timed right can work as well as fewer, bigger pushes).

    Sorry, that wound up being longer than I expected and if I knew my astronomy better is probably full of holes. But it’s fun to theorize about possibilities. Good luck in being proven right! It is an exciting time.

    ReplyDelete
    Replies
    1. There has been no other responses yet, so from a layman to another, I too considered the potential for a selection bias and so could reference your comment in mine further down the thread.

      So this is for the astronomers, but I think the paper (which I only browsed) claims the Kuiper Belt mass is too small for a clumping making the putative shepherding. Then it is hard to envisage clumping of any kind in the neighborhood, at a guess.

      Delete
  12. Question: Unless I've calculated the wrong thing, a New Horizons range signal for a Planet Nine with mass = 5mE and distance = 1000 AU would be about 500 times stronger than the one predicted for a 0,7mE object in a distance of 4500 AU, so as soon as it is on the correct course without the need of course correction (which would disturb the signal) it should be picked up much faster than the six years needed in Iorio's prediction.

    Am I very wrong here? (And if not, are you already in contact with Iorio?)

    ReplyDelete
    Replies
    1. And would accurately measuring the range signal be possible while New Horizons is still in the middle of sending Pluto system data back to Earth?

      Delete
    2. Mostly I think NH is going the wrong direction. But it is worth looking into.

      Delete
    3. It's near the opposite direction. But it would measure the difference of the effects Planet Nine has on Earth/Sun on one side and New Horizons on the other anyway. I think the worst case would be at right angle, but according to your treasure map Planet Nine would have already been found if it was there.

      Delete
    4. Did some back-of-the-envelope calculation with a simple acceleration formula, and now I get 3 meters after one year (44 EP9 - 41 NHP9) and 12 after two, for 5mE at 1000 AU distance - more if closer or heavier, of course. Still detectable, but not as good and fast as I thought from my shortcut. Hm.

      Delete
  13. Could "Planet Nine" be already found? Could those clustered objects be the remnants of a Planet Nine break-up or collision that happened some many Gyrs ago?

    ReplyDelete
    Replies
    1. Nope; they are clustered in perihelion, but with very different orbits. Not like a collision.

      Delete
  14. I've been studying the Moon with my Canon sr60x. I think I see telescopes there, at least long, cylindrical objects. Some of the telescopes align thus are probably looking at the same thing. Perhaps it is Planet 9 or Niburu? Whatever it is it is not in the planetary plane. It is southwesterly. Check my facebook site at "Life on Mars and the Moon", for a photo of what I am writing about.

    ReplyDelete
  15. If planet IX exists maybe it was ejected with planetesimals and created their various orbits? The planet itself was too big to slow down and stay in the solar system.
    WISE did not find Tyche

    ReplyDelete
  16. The "look elsewhere" effect - which traditionally only look for one pattern, but that is a start for quantifying it - is mooted in particle physics by increasing the quality limit from 3 sigma to 5 sigma. (Or as I just listened on a recent SETI talk, in Kepler planet search, which has some of the same problems, by going to 7 sigma.)

    So this explanation of that adding the 5 distant twisted orbits is pending is good to hear. Meanwhile I tried to estimate by two independent means, which seem to check out. Naively extrapolation puts the combined likelihood of being random data in the neighborhood of the required 1 in a million. And so does a simple binomial yes/no combo of 11 distant orbits with 2 independent orbit parameters. (Say, longest axis and one "twist" angle.)

    [I would love to add the known phase of the orbiting bodies, but as Ken says in a previous comment, it can be a selection bias of observation capability.]

    So I think it could be a real observation, not a result of excessive pattern search.

    ReplyDelete
  17. Thankyou eversomuch for this blog; it's a real privilege to see thoughts and musings from the professional astronomers at the center of the recent news. I for one am hoping that as many telescopes as possible can join the hunt.
    During these early days there are lots of names being suggested... my personal fave is 'Nox' being the Roman equivalent of Nyx, goddess of the night.
    Good luck to all involved.

    ReplyDelete
  18. My thanks too for sharing this moment.

    A paranoid thought: If Mike's P9 suddenly disappeared, snatched at aphelion, how fast would the orbit-clustering of opposing bodies "decay"? And sorry if that was covered in the papers I havent read yet...

    ReplyDelete
  19. This comment has been removed by the author.

    ReplyDelete
  20. Is the new planet at around 358.4 AU from the sun?

    ReplyDelete
  21. Planet nine reminds me the planet of Dumusque in Alpha Centauri B. I wonder if these clustered KBOs are a bias due to the strategy of detection as well.

    ReplyDelete
  22. If, as many believe, something seems to be perturbing the outer planetary objects and it is not Planet 9 and assuming that it cannot be our mythical dead twin-sun `Nemesis’ which as yet has never been found (if indeed it ever existed it perhaps should be a lot further out), then what is the cause – an anomaly with the data or can it be anything else?

    ReplyDelete
    Replies
    1. Nemesis is an obsolete idea from the 1980s. The clustering could be the result of a massive belt of objects even further out. But I still prefer the P9 concept as it is a cleaner explanation.

      Delete
    2. This comment has been removed by the author.

      Delete
    3. Agreed. I also see the logic in the existence of Planet 9 but it is always wise and best practice to eliminate all other possibilities (even the most obvious) and subject the theory to close scrutiny before emotionally accepting the hypothesis. At the moment I also seem to be in the Planet 9 camp - but I'm sure that there is a lot more work to be done...

      Delete
    4. This comment has been removed by the author.

      Delete
  23. This comment has been removed by the author.

    ReplyDelete
  24. Question: What exactly is meant when you say Sedna would be back in the Kuiper belt eventually? An orbit like "Buffy"? Or a closer orbit? Or a still-excentric orbit, just with a much closer aphelion? What did the simulations show?

    ReplyDelete
    Replies
    1. perihelion back int he Kuiper belt.

      Delete
    2. Hmm...I'm a bit skeptical about finding planets 9, right now was found when the largely about Planet X...whether it is a coincidence??? Mr.Mike Brown???

      Delete
  25. So, when planet 9 is finally confirmed, how will that info be released? Here, big press conference....?

    ReplyDelete
  26. Is there a Nineth Planet out there? YES.

    Is this planet exactly as described by astronomers? NO, but completely diffrent. for example: if they said it,s cold, the truth is hot. far away, the truth isn't far away. that's because they try to be smarter than the God.

    ReplyDelete
  27. Grab online thesis help from the experience writers of MyAssignmenthelp.com. Our writers are in huge numbers and all our years of expertise. That is why they know how to prepare student's academic papers. They also prepare their thesis paper as the requirements of student's universities and colleges. Get in touch with us today and enjoy submitting a unique thesis paper.

    ReplyDelete
  28. My Assignment login or Assignment Help Australia are among the many services that Assignment Studio has to offer. The best assignment help in Australia by the in-house qualified and expert writers to the local and international students in Australia, so that scoring top-notch grades does not pose a problem for them

    ReplyDelete
  29. Online Biology Paper Writing Services produces different assignments, including Buy Essay Online Services, to help students deal with the Buy Business Reports challenges they face every day.

    ReplyDelete
  30. Looking for essay help online?. Want essay assignment help? Let’s have a look at our endeavors! MyAssignmenthelp AU have a range of professional writers ready to provide essay assignment help or essay help to the students presenting top quality essays, keeping in mind the instruction provided by their professors.

    ReplyDelete
  31. Planet nine always been a surprise to scientists. Maybe we step on planet nine like moon and other planets. By: Buy dissertation online

    ReplyDelete
  32. Computers have penetrated in our daily life stream and now all our daily operations are dominated by this man made machine. The reshaping of computers has made it possible for ordinary men master his own computer. This is an era of widespread computing, which will be characterized by one individual-to-many computers, dominated by handheld, intelligent, and everyday devices with embedded technology and connectivity. Benefit from professional computer assignment help by our expert writers based in Australia.

    ReplyDelete
  33. our team is professional and do work according the requirement. our team customize the Custom boxes according your requirement and print your logo on the boxes.it will main be helped someone
    lipstick boxes
    cosmetic box packaging

    ReplyDelete
  34. Avail my assignment help Australia service by hiring our expert academic writers who have the knowledge, skills and experience to help college and university students with their research papers, essays, case studies and Thesis projects.

    Online assignment help
    Case Study help
    Urgent Assignment help
    Essay help online
    Assignment help

    ReplyDelete
  35. This online essay writing service gives 24 hours of accessibility to understudies. Through this, the understudies can at whatever point look for help from online associations.
    online homework help
    get online assignment help

    ReplyDelete
  36. This is Arick Jhon from Packaging Mines.I am regular reader of your blog. Your thinking about your topic or a business strategy is absolutely right. I am reading your blog's every line and every point describe in a correct way .Thanks for giving me information. We are offering Cosmetic Packaging
    with product designing by wholesale Prices

    ReplyDelete
  37. Your thinking about your topic or a business strategy is absolutely right. I am reading your blog's every line. This is Jones smith from get instant printing. I am regular reader of your blog. We are both in a same industry and every point describe in a correct way .Thanks for giving me information. We are offering Custom Printed Boxes with product designing by wholesale Prices.

    ReplyDelete
  38. I found this one pretty fascinating, and you should go into my collection also. We provide online statistics homework help services all over the world. I am impressed with your article. We appreciate that please keep writing more content.

    ReplyDelete
  39. Different people have different views about this topic because some people think that there are eight planets in the Universe while some think that there are nine planets because they think that Pluto is included in other planets. What is your opinion about it? Dissertation writing service.

    ReplyDelete
  40. Exactly what i was looking for. It is no secret that people are often charged with more responsibility than what they signed up for in an organisation. At such a time, one cannot argue over the fact that they did not sign up for this. Consequently, universities prepare the students to work with a greater knowledge of Petroleum Engineering. For that, the assignments are targeted in a way that makes students go beyond the classroom knowledge. Get Petroleum Engineering Homework Help

    ReplyDelete
  41. Our service has been very supportive to our customers and especially in solving their problems and providing them with best boxes which are fully credible and worthy of their trust.
    Eyelash Boxes
    Lipstick Boxes
    custom book boxes,
    sock packaging

    ReplyDelete
  42. Hi, this is a nice blog thanks for sharing the Informative blog content. I am Axel Smith from USA. I am working as a full-time academic consultant with Crazy For Study. we providing Physics Solution Manuals services in USA to university or students. I served the stressed students residing in USA for more than 7 years and hold excellent writing skills and provides guidance to academic scholars and students.

    ReplyDelete
  43. Everyone looking at some information ideas forms the different platform, If you shared some creative and informative ideas then the user is very loyal to read your blog. thanks for share highly valuable article with us. Geometry Textbook Solution Manual

    ReplyDelete
  44. I love this post. Thanks for sharing. You can also get custom sock boxes packaging also you visit us.

    ReplyDelete
  45. Nice Post. Thanks for sharing. Keep sharing up
    Socks Boxes Packaging

    ReplyDelete
  46. The way you have described about Custom Packaging, Donut Boxes, Rigid Boxes, Candle Boxes, Shoe Boxes is great, every start up business should try to get Custom boxes for their product.

    ReplyDelete
  47. Swaray, is an independent rapper, singer, songwriter based out of Los Angeles, California. Swaray is giving artists a run for their money with not only his diverse catalog but lifestyle as well.

    ReplyDelete
  48. If I am so confident of this, how could Planet Nine possibly not exist? Just because Planet Nine can explain all of these effects, it doesn’t not mean that there is no other possible explanation. We tried to think of everything that we could, and systematically ruled out alternatives, but that doesn’t mean that someone else won’t come up with an idea that works. https://www.harborcompounding.com/tag/1196-compounding-pharmacy

    ReplyDelete
  49. If I am so confident of this, how could Planet Nine possibly not exist? Just because Planet Nine can explain all of these effects, it doesn’t not mean that there is no other possible explanation. We tried to think of everything that we could, and systematically ruled out alternatives, but that doesn’t mean that someone else won’t come up with an idea that works. A rise in endogenous oxytocin results in an increase of plasma endorphins, natural pain killers that can diminish pain in women who suffer dyspareunia , due to anxiety or lack of trust in their partner during the first stages of their relationship.

    ReplyDelete
  50. Are you looking for ayurvedic consultant then don’t worry we have best Ayurvedic Doctor in Australia

    ReplyDelete
  51. A Kansa wand is simply an answer to balance your body, your pH levels, your chakras and your doshas. Kansa wands have a longer history, associated with Ayurvedic practices. You can easily buy Kansa wand from our website.

    ReplyDelete
  52. This comment has been removed by the author.

    ReplyDelete
  53. This comment has been removed by the author.

    ReplyDelete

  54. Corporate Finance emphasizes on the company's finances, financial position, and increasing the company's profits to clients in order to secure long-term profitability. Our professionals can assist you with corporate finance assignment if you are unable to complete assignment for any reason. In Australia's major cities, we have successfully provided well-written and excellent online assignment services. Visit now:- Corporate Finance Assignment Help

    ReplyDelete
  55. Boostupblog is the best guest post services provider. If you want to promote your business and get organic traffic for your website then Boostupblog is the best platform for you. Write quality content related to your business and you will get good results by using our platform.

    ReplyDelete

  56. We,Kickr Technology transforms mobile apps on various platforms and devices. We have a team of experts who works on various technologies and try to make app most downloadable app of play store.

    ReplyDelete
  57. Thank you for posting such a great article. Keep it up mate. custom packaging

    ReplyDelete
  58. Honda navigation update
    Every user can update the honda navigation system with ease. All you have to do is follow some basic instructions, and you can update the honda Navi by yourself. Most of the time, customers ask whether their updates are free or paid.

    We want to inform you that all Honda Navi updates are free of cost most of the time. A few times, the updates are paid if you have an older honda vehicle. Many times consumers end up paying a good amount of money to the local dealers. We want to inform you that you can get the updates for yourself without paying any additional fees or charges if you can follow some basic steps.

    ReplyDelete
  59. does planet nine really exist? time will tell of it, thanks for sharing. check free nitda scholarship past questions pdf

    ReplyDelete
  60. This comment has been removed by the author.

    ReplyDelete
  61. This comment has been removed by the author.

    ReplyDelete
  62. This comment has been removed by the author.

    ReplyDelete
  63. While the possibility of Planet Nine is intriguing, it's important not to forget about monitoring our own vital signs. Meri Sehat's online medical services offer convenience, accessibility, and certified doctors available 24/7. With affordable rates and patient satisfaction as their top priority, Meri Sehat is a game-changer in the field of online healthcare.

    ReplyDelete
  64. Your post describes all the needed information in a detailed manner. Keep posting more! Thanks for sharing this post! Worried about your online math classes in the US? Hire Someone To Take My Online Math Class at Greatassignmenthelp.com to get assured answers for every subjective query you are dealing with. Our professionals can assist you in completing your all tasks with quality work and improve your academic performance. You just need to use our writing services to obtain immediate assistance from well-experienced writers. Visit us now to know more details!

    ReplyDelete