Mordred

Both the use of nukes and impactor method has the risk of breaking apart the asteroid. Asteroid composition being a factor for the likely hood. Even though you only get the radiation portion and not the kinetic shock waves from the nuke. There is still a risk. One risk is thar if you have non uniform outgassing this can lead to breakage.

Ordinarily if the mass/energy density distribution was non uniform you would get different regions with different time rates as per GR. We see that today with large scale structure formation, galaxies stars etc. However the Cosmological principle of a homogeneous and isotropic uniform mass distribution still occurs at the large size scales. It's like looking at the waves of a lake as you move further from the surface the more uniform the lakes look. The uniform mass distribution becomes apparent on a scale of 100 Mpc (megaparsec) at the time of the CMB that scale is greatly reduced. However we cannot forget that dark matter fills up most of the universe and baryonic matter is only 3 percent of the mass. Gravity itself However only attracts it doesn't expand. We also already take into account the result from matter forming into stars galaxies etc in the matter only solutions of the FLRW metric. This is rather complex to understand but essentially a matter only universe can expand due to structure formation because the global mass distribution reduces due to matter forming those structures on the local scale. So yes the mass distribution does contribute to expansion However that isn't the same as being due to time dilation ( I'm going to assume the time dilation statement is more a poor choice of descriptive for non uniform mass distribution). Now dark energy is not the only contributor to expansion it's the current most dominant contributor.. Expansion also can be caused by matter, radiation (relativistic particles photons etc) spacetime curvature as well as the Cosmological constant. At one point (except the curvature term as k=0 for the near flat universe we see) each of these contributors was dominant. The three eras are radiation dominant, matter dominant and Lambda dominant (Cosmological constant aka Dark energy). In essence yes non uniform mass can cause expansion so you are correct however we already factor that detail in the FLRW metric via the equations of state See here for the equations of state https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)

That answer depends on the model of how the universe started which we do not know. For example if the universe started from nothing then it stayed immediately after T=0. If our universe was due to a bounce from a previous universe then you would have the spacetime from the previous universe ( the portion of the previous universe that bounced to form out universe.) In short we do not know previous to 10^{-43} seconds. We can only accurately extrapolate to that time. Any process prior we can only speculate.

They gradually change as well though interpretations is more the realm of metaphysics which is more philosophy than physics. Truth be told as a physicist I honestly don't waste much time with interpretations. I've always been more concerned with mathematical to observational accuracy. The interpretations particularly those involved in QM and entanglement too often get in the way. Lately I've found metaphysics argument has all too often become a tool for those that try to change physics without understanding the mathematics. So you see far too many posters in Speculations arguing against main stream and we'll tested physics based on personal feelings and interpretations.

The other factor we are missing is that certain universities are better at one program but fall behind in other programs. So depending on the area of study one University that may be top ranked may be behind in the area of study. For example a university that focuses of trade schooling may be lacking in hard sciences.

There is one example of the scientific I can provide with regards to Cosmology. At one time the FLRW metric did not have a cosmological constant term. This went on for roughly 40 to 50 years. Later findings and research found that universe expansion was accelerating. So the FLRW metric was repaired with the new findings. The Cosmologicsl constant term was then added. That's just one example. If later research shows an inaccuracy or a better method then the theory either gets a modification or revamped entirely. Another example is just prior to Higgs at one time the neutrino was considered massless later findings showed it has a miniscule mass term. The Higgs research showed how the neutrino acquires mass. Research and observational evidence will trump any theory or bias once the evidence becomes sufficient

One misconception that's rather common. Science never states something is the truth. Every theory or model is " to the best of our understanding" due to observational and experimental evidence. This includes the various laws such as the above mentions laws of thermodynsmics. The only truth behind them is their success rate to match observational evidence.

You don't get the kinetic energy from a nuke like you do in the atmosphere. What you will get is the radiation components but not the sudden shock waves from instantaneous heating in atmospheric explosions. So composition matters more in how the surface dissipates the heat generated from the radiation. It is this heat dissipation (outgassing) that supplies the push not the kinetic explosion as you don't have an atmosphere. The above applies to surface or above explosions. Obviously this differs if you explode the nuke internally via mining etc.

Ok this is simply useful to understand the FLRW acceleration equation above in terms of the first law of thermodynamics. expansion is a homogeneous and isotropic that is maximally symmetric. This expansion is also adiabatic in thermodynamics if you have a container (system)there is no net outflow of energy with the surroundings. This also describes a conserved system. \(T^{\mu\nu}_\mu\). The first law of thermodynamics for an adiabatic expansion is \[de=pDv=0\] with \(E=\rho V\) and \(V=\frac{4}{3}\pi a^3\) this becomes \[d(\rho a^3)+pda^3=0\] with respect to cosmic time \[\dot{\rho}+3(\rho+p)\frac{\dot{a}}{a}=0\] differentiating the first Friedmann equation in the form \[\dot{a}^2=\frac{8\pi G\rho a^2}{3}-kc^2\] gives \[2\dot{a}\ddot{a}=\frac{8\pi G}{3}(\dot{a}a^2+2a\dot{a})\] substituting \(\dot{\rho}\) from the first law \[2\dot{a}\ddot{a}=\frac{8 \pi G}{3}a\dot{a}(-\rho-3p)\] gives the acceleration equation \[\frac{\ddot{a}}{a}=-\frac{4\pi G}{3}(\rho+3p)\] you can find other forms of the above in different literature its a fairly standard heuristic Newtonian treatment. Its useful to recognize how thermodynamics is used to describe our universe expansion as well as understanding how the equations of state apply which is already above. Hope this helps

Chrome has a ad blocker extension I posted earlier this thread it's still works on my laptop. I could never get a version working for chrome on my phone however the Samsung ad-blocker for Samsung internet browser works.

Your welcome likely tonight I will setup the derivatives of how the equations of state are determined via the ideal gas law relations to help you better understand how thermodynamics are applied.

I would like to clarify one detail. The vacuum can have numerous connotations. For example the Einstein vacuum (devoid of all particles including virtual) which is the vacuum solution. Is different than the way vacuum is applied in the FLRW metric. In the FLRW metric vacuum is the relation between the kinetic energy and potential energy terms of a scalar field using the scalar field equation of state. Example w=-1 for the Cosmological constant. This value specifically -1 describes a constant incompressable fluid with negative pressure. Inflation would have a different value but can slow roll to the value for the cosmological constant (you may see that in the case of Higgs inflation where the cosmological constant term is also considered being due to the Higgs field) Another detail is that curvature can also mean slightly different things. For example extrinsic and intrinsic curvature. You can also have curvature independent of coordinate or coordinate choice or curvature that has a coordinate dependency. An example of the latter. Is the localized curvature term due to gravity. It is dependent on the location. (Localized anistropy)

Ideally yes but as we saw in this discussion no single idea works in every situation.

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.