Mordred

The point being is there is budgets in place for research that doesn't make the news. Simply because we don't see the newsworthy materials doesn't mean budgets, policies, research fundings etc are not going on. Obviously developing a feasible and a reliable infrastructure for massive object deflection is a rather complex undertaking full of hurdles.

That makes a lot more sense thanks for clarifying

correction applied and thanks for catching that

Just in case anyone isn't familiar with time derivatives in the above for example \(\dot{a}\) is the recessive velocity term of expansion. When you see two overdots this is a second order derivative for instantaneous acceleration in usage above the accelerating rate of expansion via \(\dot{a}\) \[\ddot{a}=\frac{dv}{dt}=\frac{d^2x}{dt^2}\]

Please don't bring me into this discussion. The other discussion has nothing to do with this thread. Everyone is entitled to their beliefs and personal opinions. One shouldn't judge others when their opinions or beliefs run into conflict with others. For the record I'm not precisely blameless in that discussion either and fully admit I could have handled it better. Anyways AFIAK it's resolved and we both moved on.

My wife has a relative that worked on NEOSSAT https://www.asc-csa.gc.ca/eng/satellites/neossat/ This is a satellite dedicated to hunting asteroids developed in Canada though the project had numerous problems including overbudget at least it's a step in the right direction. One thing remember there is far more going on than one may realize or that you will find articles and links on. At there are ongoing studies and projects.

Well I agree our government's should push to get better early warning detection as well as contingency plans in place thankfully though some testing has occurred already. A few were mentioned in this thread. The moon idea isn't a bad one by the way. Provided the size of asteroid doesn't cause too significant of damage. Though an asteroid of that magnitude would likely not be able to redirect with our current capabilities.

We don't know it can be finite or infinite we only know our Observable portion is finite. Beyond what is observable is strictly speculation based on what we understand of our Observable portion. Nothing makes sense here you might want to try again with more rigor

To generate heat and outgassing on the surface areas to apply Newtons second and third laws without causing large chunks to separate from the asteroid. Those I suggested may or may not work depending on laser sustainability and ability to reduce the output in case it's needful. This method would well on an icy asteroid possibly a solid rock face not too sure the practicality for a conglomerate surface. The other issue being rotation. I have been wondering the practicality of a single craft with both nukes and lasers the combined weight would also make it a suitable tractor but then a single craft could theoretically be equipped with all three options.

Considering they have now missile defense lasers on US ships if I recall I would say it would be transportable on some craft. Albeit I wouldn't know the power requirements. Something similar to the power requirements here could be workable https://en.m.wikipedia.org/wiki/AN/SEQ-3_Laser_Weapon_System Another options being LaWs https://www.cnn.com/2014/12/11/tech/innovation/navy-laser-weapon

A detail I forgot to mention earlier. You can have an energy density with a non zero value (T_(00) ) component of the stress energy momentum tensor but as long as there is no inherent directional flow (scalar field) you can set the stress tensor to zero it becomes the background energy density which you can set for value zero. This determines geometry. The metric tensor, for the global. When you have permutations ie flow etc you set that in the permutation tensor \( h_{\mu\nu}\) Then you add this to the global metric to establish the local metric. For the FLRW metric you have a non zero global energy density but for purpose of the metric it's set at zero hence the stress tensor is zero. (Also done for conservation laws for symmetry relations) as well as renormalization procedures.

Unfortunately this is rather misleading to understanding the FLRW metric. The FLRW metric has a curvature term K. K can still be zero and still have expansion for a critically dense universe. Expansion isn't curvature though curvature affects expansion. In our current universe the FLRW metric the stress tensor for energy conservation and applying the cosmological principle is as follows. Cosmological Principle implies \[d\tau^2=g_{\mu\nu}dx^\mu dx^\nu=dt^2-a^2t{\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\theta d\varphi^2}\] the Freidmann equations read \[(\frac{\dot{a}}{a})^2+\frac{k}{a^2}=\frac{8\pi G}{3}\rho\] for \[\rho=\sum^i\rho_i=\rho_m+\rho_{rad}+\rho_\Lambda\] \[2\frac{\ddot{a}}{a}+(\frac{\dot{a}}{a})^2+\frac{k}{a^2}=-8\pi Gp\] for \[p=\sum^ip_i=P_{rad}+p_\Lambda\] with conservation of the energy momentum stress tensor \[T^{\mu\nu}_\nu=0\] \[\dot{p}a^3=\frac{d}{dt}[a^3(\rho+p)]\Rightarrow \frac{d}{dt}(\rho a^3)=-p\frac{d}{dt}a^3\] \[p=\omega\rho\] given w=0 \(\rho\propto a^{-3}\) for matter, radiation P=1/3 \(\rho\propto{-3}\), Lambda w=-1.\(p=-\rho\) for k=0 It is the equations of state in the last line that determines expansion and expansion rate. For our current universe we can accurately set k=0 for good approximation. This would actually be a critically dense universe. Our universe however does have a slight curvature term but overall is considered flat. Another way to see the above is FLRW Metric equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. Shown here \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] now here you can see where curvature gets applied \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] In the above expansion rate is determined by the relation of each equation of state (including the curvature term k) to the critical density. That density can be any value it is a calculated density (matter only EFE solution). The actual energy density to critical density ratio is what determines expansion rate. That ratio is affected by the density of matter, radiation and Lambda.

Hrrm I can see these functions could have a broad range of applications. Thanks for sharing this, gives me something new to study myself. I always keep an eye out for useful mathematical methods that I could employ. I will have to look more into the Leal functions. You might this listing handy https://personal.math.ubc.ca/~cbm/aands/abramowitz_and_stegun.pdf There is a section listing transcendental functions. (The article simply has a good listing of various functions for the purpose of quick reference . It doesn't go into any particular details on any of them. I found it handy in the past you might as well. Edit doesn't seem to be a whole lot of information on those functions beyond the links you already posted.

I was always wondering how DRAGON got it's name ISOL was before my time as well. TiSOL was just recently put online a couple of years prior (88-89) was when I was there. Sounds as though you and I were there in a similar time frame. I was able to visit the Synchrotron in Sakatchewan as I had a relative that worked in that facility. It's another impressive facility. It also helped one of my uncles of my father's side was teaching at UBC.

Lol another funny coincidence during my internship TRIUMF was in collaboration with Germany in regards to polarized neutron research using helium-3 as the best candidate for production. They were also in a big push for the TR30 accelerator in conjuction with EBCO Industries. It's amazing what you learn for example one wouldn't think a cyclotron would require a radio license to operate however TRIUMF required one. At that time NORDION a radio pharmaceutical company wanted to purchase the first TR30 for proton therapy.( the replacement for CP42 if I recall correctly). I wasn't too involved on the medical side but they certainly gave lots of lectures on the topic lol. As you mention the real learning comes when you need to apply what you learned. For my MSc my dissertation was on quintessence inflation. I long ago lost my copy due to a fire however it was shown invalid with WMAP findings (I didn't have sufficient e-folds to match observational evidence that came available later). Also didn't help that I was also employing Parker radiation for expanding Cosmology. Lol there's a radiation you don't hear about nowadays in Cosmology. (Though I believe there is a variation of Parker radiation in medical applications don't know if that variation is still used today)

I'm sure you found the instructor to individual time extremely useful. Lol perhaps a bit too much instructor to student time in your case lol. I can certainly understand your class mates sentiment. Good thing physics is useful in a wide range of trades beyond being a physicist.

Nice alternative method list on that link. Several mentioned there that hasn't been mentioned this thread. I did previously mention kinetic impact but no one has spent any examining that option. Didn't know about that particular test though thanks for sharing. @Ken Fabian I particularly like the first article in so far as it included fuel consumption as well as a dollar value given in 1995 roughly. Thanks for sharing that link as well. That low deflection value you gave over time is accurate however as you only need enough deflection to miss the gravitational keyhole the needed deflection only requires 20 days but if process starts in the later on that can change to 135 days or greater explained in the first link.

That's fair nukes are one option. The detail many are missing though is that we're also not restricted to a single 1 ton craft for the towing. The first link you supplied gets deflection in 20 days in the examination it did there. I already posted near the beginning of this thread another paper that uses several gravity tractors to greatly speed up the time. Here is a related statement in the paper relating to nukes vs tractor. "operation as well. Finally it is very critical that neither NASA nor any other agency involved in addressing this challenge underestimate the degree to which the international community, both at the state level and that of the general public, will demand to be involved in and ultimately be satisfied with many of the decisions regarding NEO deflection. Fragmentation of the NEO, uncertainty in the execution and the results, and even nuclear explosions and radiation will be of enormous concern to the world public. Where more certain and benign methods are available to accomplish the deflection such instantaneous but risky approaches will not be acceptable. The Gravity Tractor, where capable of meeting the deflection challenge, is both technologically and societally the most preferable deflection option.". I tend to agree with that quoted section. Particularly since a 1 ton craft is trivial compared to the rocket fuel consumption to reach escape velocity. As we all seem to agree on using Apophis then according to this link we simply need to miss an 800 km gravitational keyhole. https://en.m.wikipedia.org/wiki/99942_Apophis As your first link examines this 20 days that it gives is quite reasonable.

Use the equation of state for a scalar field. The FLRW metric version is a good starting point. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) We already have equations to describe vacuum fluctuations with a pressure term see link. Under GR the stress energy momentum tensor has the pressure terms. This will correspond to how pressure is handled under QFT

Lmao small World indeed. I always thought highly of my time there. Very friendly and supportive environment. Everyone was incredibly helpful.

Precisely when you get right down to it every solution has infrastructure hurdles. I would think it would be far easier to get a gravity tractor solution than it would be convincing every involved government nukes are needed.

No problem quite frankly delivery is a large part of the problem to begin with. We haven't particularly established how much can or can't be reasonably delivered. Obviously we're not firing missiles from Earth to the asteroid so you would need a craft. That craft will determine how big a payload it can deliver.

Yes and AFAIK they still are quite open for internship.

Agreed one of my more memorable moments from my coursing was being able to get some time in TRIUMF. While the university I attended wasn't in partnership of owners we were still able to get a limited access. Got quite a bit more time with the University telescope though. Roughly the same size as the telescope Hubble used. I was able to get more time by being that helpful student with facility maintenance.

Well as I described earlier there's nothing stopping us from loading a craft full of warheads so we really aren't limited in megatonnage.