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[LordBaal]

It think magnetism wouldn't be strong enough to deviate the orbits in any meaningful way. But I'm no astrophysicist so I couldn't really told.

[Starver]

It think magnetism wouldn't be strong enough to deviate the orbits in any meaningful way. But I'm no astrophysicist so I couldn't really told.

Neither am I, but my gut feeling is that the differences between a fluorescent/magnetic sun and a non-fluorescent/magnetic black-hole would be fairly minimal and would have a 'new equilibrium' of orbits (at least beyond Mercury, but we'd have to look at what changes the concentrated alteration in Frame Dragging might do to that, perhaps) of a not dissimilar nature.

Naturally, the current solar system is not actually in a perpetual equilibrium at the moment (though I think they've proved that, left to its own devices, it'll last largely unchanged for a highly significant amount of time in the future).  And if the Sun gets swapped out with its equivalent Black Hole replacement when a planet or two are on their 'upstroke' or 'downstroke' in their already slightly eccentric orbits, or when other perturbations from planetary neighbours are at their most prominent, the sudden lack of solar effects (wind outwards, magnetism whichever-which-way) could provide a nudge that sends a body or two out of their narrowly-predicted future orbits just enough to start something chaotic...  But it wouldn't be instant disaster.  If it takes as little as a 1000 or so orbits to change any element enough to cause it (and thence the others) significant orbital shift, I'd be surprised.  (Although it'd need calculating.)

The lack of solar heating would cause us problems though.  (There's a What-If on roughly that subject, IIRC.)  As would any less-than-seemless method for giving us a black-hole focus to the solar-system.  (I'm not sure what the scenario actually is you're discussing...  There's a song about it, you say?)

[wierd]

Ah. So you've never actually tried putting any numbers on that.

More, I was at work at the time, and had duties to attend to besides hunting down data for you.

But, to get an idea of how large the magnetic flux of a star is, remember that gravity falls off at the inverse square of distance, while electromagnetism falls off at the inverse CUBE. With that in mind, the strength of the sun's magnetosphere at the heliopause is sufficient to deflect interstellar cold plasma in front of the star, as it plows its way through that medium in its orbit around Sagittarius A. While not very dense at all, that medium does represent a not inconsiderable quantity of mass, given the volume impacted-- though not all of that volume can be attributed to magnetic flux alone. (The solar wind pressure will also be at work, and will likely contribute the lion's share of the deflection pressure.)

However, I was not kidding about flux tube formation stripping off chunks of atmosphere-- It is a significant part of the theory behind why mars lost its atmosphere.

http://onlinelibrary.wiley.com/doi/10.1029/2009GL038209/pdf

Without this combination of magnetic flux tubes and solar particle wind, Mars would have a significantly thicker atmosphere, as would Venus, and the Earth-- meaning these objects would have greater masses, and thus different orbital periods and stable orbital radii from the central mass.

[Il Palazzo]

Weird, I wasn't asking you to 'hunt data' for me. I was asking you to do some calculations to see for yourself, and indeed show us, how significant the effect you're talking about really is. Like taking the density of local interstellar medium and calculating how much orbital energy would a planet the size of Earth (or whatever) plowing through it over 5 billion years lose.

[wierd]

That too is likewise difficult to do while caring for a geriatric resident in an adult care facility, and would have to wait until after I had finished my shift and come home to provide.

In either case, expecting an immediate answer is irrational.

[Il Palazzo]

I wasn't.

[wierd]

Good.

For the first scenario, we have a "naked" (as in, "not with accretion disc", and not "Lacks event horizon") black hole, that gives off no magnetosphere, because any field lines will be trapped behind the event horizon.

This object has the same mass as our star.  However, our planets forming in stable orbits around this object (let's presume that "somehow", the extremely improbable scenario of this object passing through a sufficiently dense interstellar dust cloud occurred, and that the action of this black hole on the cloud was sufficient to cause clumping and planetary formation consistent with the formation of our existing solar system planets. The early turbulence of this system would be pretty similar to the high radiation output of our star's early existence, though this scenario would provide a healthy abundance of X-ray and gamma radiation. For the sake of argument, we will say that this scenario results in the remainder of the cloud being consumed in totality by the singularity, and the resulting mass of the singularity equals sol's mass. This leaves a "naked" singularity at the center of a planetary system.) would not be exposed to the continued, and sustained solar wind and magnetospheric interactions our existing planets have endured while in orbit around an active star.

Depending on exactly 'when' the singularity stops having an active accretion disc, would vastly color any computation I could derive for the impact of this occurrence, as being blasted by hard X-rays and gamma rays would be pretty nasty for a planet's atmosphere. (1 AU from an active accretion disc would be vastly more energetic than at the same location from our star! Much more energetic fusion reactions would occur inside the mid-structure of the accretion disc than can ever possibly occur inside our star.) Again, an active accretion disc would introduce a very powerful plasma torus source for a "stellar" magnetosphere. The resulting magnetosphere would be powered by far more powerful flow currents than happen inside a normal star, and would be closer to being like what you would encounter near a magnetar than what we encounter now near sol. This means that the flux tube atmosphere ripping action, as described by the previous paper, would happen with much greater intensity while the black hole is still actively feeding.

So, without knowing exactly when the accretion disc stops being present, I cannot even begin to calculate what the impact will be.

[Il Palazzo]

So, without knowing exactly when the accretion disc stops being present, I cannot even begin to calculate what the impact will be.

Sure you can. The question, and your responses that followed, concerned the effect the lack of solar magnetosphere would have on planetary orbits. You can disregard the accretion disc and its influence, since we're interested in the upper bound for the effect.
And even if you're concerned with atmospheric stripping, it shouldn't pose a problem to do the same calculations for an Earth-like planet without an atmosphere. In fact, it may be enlightening to show how much (or how little) losing an atmosphere affects orbital motion in this case.

[wierd]

In other words, "Imagine spherical cows", no matter how un-lifelike that would be?

The question is if I really want to invest that much energy and source-hunting (because any such computation would be worthless without grounding the math in observed science) into a hypothetical of this nature?

The answer to that is "Probably not."  I dont particularly enjoy math.  It WOULD be interesting to see the derivation though, I do agree.

However, the last question is likely easily answered.  A good portion of the mass of the earth is tied up in the form of liquid water, which ceases being liquid when pressure drops below a certain threshold. (see for instance, water sublimation on surface of mars, due to lack of atmosphere.) This creates a catch 22.  When there is sufficient atmospheric pressure, water is a liquid on the surface, and contributes quite significantly to earth's total mass. (a good portion of the mantle is presumed to be hydrated silicates, which can only happen with a surface ocean that is humongous, like ours.) If you strip away the atmosphere, you remove not just the mass of the surface oceans, (because they will sublimate into gas, and likewise be blown off), you will also lose a significant portion of the mass of the mantle, because internal heating in the mantle, coupled with the lack of a heavy ocean introducing water into the mantle via subduction of crust, meaning a good portion of the mantle's mass will be blown out by volcanism into the thin atmosphere, and be blown away.)

You will end up with a dry, shriveled raisin of a planet, instead of the earth-- and that planet will have significantly less mass afterwards.

[Starver]

meaning these objects would have greater masses, and thus different orbital periods and stable orbital radii from the central mass.

Noting that the mass of an object in orbit doesn't affect the object's orbit.

Thought it does affect the counter-pull on the orbited body, or rather shift the effective barycentre of the orbitting/orbitted bodies such that, for a large enough 'orbiting' body, the 'orbited' body can no longer be assumed to be stationary and if you continue it'd become a binary pair mutually orbiting a point between both bodies.

...but the effect of an Earth-sized body (being plus or minus a thicker atmosphere) around a Sun-sized (or '-massed') body wouldn't matter to any useful degree.  [ETA: and if the mass is blown off the Earth, it's still likely somewhere within the Sun's 'system', so still exists as mass outside of the Sun when it comes to gravitational calculations between the Sun's system and nearby/not-so-nearby stars.]

Also, we're talking about it about-face.  The Earth at is has a significantly thinner atmosphere than it might have if solar flux/whatever had not stripped some away, given the nature of the Sun.  Replacing the Sun with a non-stripping object, right now, would not make our atmosphere thicker (all else being equal), it would just stop it being further stripped (also by the action of solar energy allowing wisps of atmosphere to gain enough energy to escape the planet on their own, where a frozen atmosphere would do less so, even before the action of the other pressures).

But how much blown-outwards solar (and occasionally Venusian?) material does the Earth collect?  Probably not so much (being so energetic, it'd go straight past and/or billiard-ball some of our own tentative atmosphere outwards at the cost of its own ability to get back out past the atmospheric shell), but I suppose we wouldn't have that, any more, either.

Anyway, compared with however many megatonnes of solid(/molten) Earth there is, the change in the mass of the atmosphere also seems insignificant except in such sufficient long-runs that we're possibly even subject to a big surprise along the lines of an unheralded Bellus/Zyra-type problem zooming through and creating a game-changer...

[Il Palazzo]

I dont particularly enjoy math.

Eh. How can you know what you're saying has any relation to reality then? Because, you see, no matter how much you may deride spherical cows, even that approximation gives you a better handle on how big a barn you must build than pure guesswork could ever provide.

[Starver]

Eh. How can you know what you're saying has any relation to reality then? Because, you see, no matter how much you may deride spherical cows, even that approximation gives you a better handle on how big a barn you must build than pure guesswork could ever provide.

At least once you solve, once and for all, the Spherical Packing Problem.

[origamiscienceguy]

Or how about we just assume that the Sun will never collapse into a lack hole?

[wierd]

Clarification-- I find math USEFUL, but I dont ENJOY math.  I do not discount the value of math, it is simply not something I decide to do for "fun."

Given the improbable nature of the question, I do not see sufficient motivation, (in terms of satisfaction gained over effort expended) to attempt to frame, and then compute the necessary expressions to answer the question satisfactorily.

If I was designing a universe, sure, I would consider this kind of question very valuable, and worthwhile to explore. It would give me the necessary grounding I would need to produce a good, consistent universe.

I however, do not design universes, nor even do I design orbital habitats. The math is not particularly useful to me outside the scope of idle curiosity. Again, the reward of satisfaction is not sufficiently great (for me), that I would be willing to undertake the rigorous exercise.

The even more generalized parts of my brain already have values that can be loosely compared (such as the strength of magnetism found near a white dwarf star vs that of our yellow dwarf sun, vs that of a magnetar, as derived by observations conducted by other people) and the knowledge of how those forces would interact with more mundane matter, and of how the delicate balance of the triple point affects the compositional character of our planet-- to determine that throwing a big monkey wrench in there like that would result in a planetary system vastly different from the one we have now.

[Il Palazzo]

and that planet will have significantly less mass afterwards.

vastly different from the one we have now

See, those are the kind of qualifying statements that require something more than just 'feelies' to support. Is it really significant? In what way? How do you know? Why should we believe you? Why not check it before saying something like that and risk sounding silly?

Myself, and it's fine if you don't care, I've lost all respect for your opinions - you've never shown any deeper understanding outside how to use google. Dodging relatively simple mathematical exercises like they're the equivalent of performing genesis doesn't help.

Anyhow, I'm outta here. Take what I said as you will - use it or lose it.