[TML] White Dwarfs, Black Holes & 100 Diameters

[Jerry W Barrington]

On 10/28/07 3:20 PM, Leonard Erickson wrote:

> On 23 Oct 2007 at 14:53, Jerry W Barrington wrote:
> 
>> On 10/22/07 8:12 AM, Leonard Erickson wrote:
>> 
>>> The *real* rule is how strong the tidal forces are (which is
>>> equivalent to saying "how sharply space is curved").
>>> 
>>> If that is the case, then the limit depends solely on mass, and for
>>> black holes, neutron stars and white dwafs will be about the same as
>>> any star of similar mass. An AU or so.
>> 
>> I don't remember if you caught my post on this a few months ago, but using
>> tidal force also means the safe distance should also depend on the size of
>> ship.  Tidal force is difference in gravity between parts of the object
>> acted on.  :)  Could be a reason to limit practical ship size.
> 
> No. Tidal force depends on the distance from the center of mass of
> the body the forces are applying to. You could think of it as "gees
> per meter". It's also different in different directions (the late Dr.
> Robert Forward has a nice diagram with formulas in his book
> "Indistinguishable from Magic")

Hmm.  The definition I'm used to of tidal force is the difference in the
gravitation caused by one object between various points of the other object
as compared to the average gravity (at the center of a sphere).  Thus, the
side of the Earth closest to the Moon is pulled more than the far side of
the Earth.  That effect is proportional to the size of the object being
"tided", proportional to the "tiding" mass, and inversely proportional to
the cube of the distance between centers (altho that is only an
approximation, it is valid for the distance being much larger than the
size).

I may need to dig Dr. Forward out of storage, as I have that book.  :)
(Excellent author BTW, and the Rocheworld series is very interesting.)

> But since for jump drives, one would assume that the factor in
> question is the curvature of space (which is what tidal force
> reflects) then the size of the ship drops out anyway.
> 
>> Unless you literally mean space curvature, in which case I'm not sure
>> planet/objects's mass is probably a good approximation.

Actually, I somehow lost a common here after "not sure", and in fact
intended to agree with you.  :)

> What do you think is *causing* the curvature?

True, but that doesn't *necessarily* mean a direct proportionality, as
opposed to a powered or rooted proportionality...

> Tidal forces are a consequence of how sharply space is curved. And
> the fact that they are different (in both strength *and* direction)
> in different axes is because of the way the space is curved.
> 
> Consider the usual "trumpet mouth" depiction of a gravity well. The
> curvature is convex along the line running thru an object to the
> planet. But it's concave in the direction at right angles. The convex
> curvature stretches the ship. The concave curvature compresses it.
> 
>> Gravity drops as you move inside the object, thus so would tidal force.
>> 
>> I doubt the clod would work, for that reason.  If it were the mass of the
>> Sun, it would have the same tidal effect from it's center, but only outside
>> it's radius.  The tidal effect would drop off internally, so right at the
>> edge would be the max effect, and that's more than 100 Solar diameters...
> 
> Tidal effect varies with the *cube* of the distance from the center.
> 
> Which is why it or something like it fits the 100 diameter rule.
> 
> Double the radius of a planet and the mass goes up by a factor of 8.
> but the "100 diameter limit" only goes up by a factor of two.
> Gravitational acceleration at the 100 diameter limit is doubled. But
> "tidal force"/curvature of space is the *same*.

That works, if we assume curvature is proportional to tidal effect, and thus
mass over (distance cubed), and that mass is proportional to radius cubed.
But the planet generation methods I prefer (like the old World Builder book)
allow for different density planets, and a star's density is way different
from a planet's, so we can't assume mass proportional to radius cubed.

In any case, I spent a couple hours research and couldn't get a good handle
on how curvature of 3-space or 4-space/time is measured and calculated.  It
gets in to vectors and tensors and such, which are hard to compare the way
scalar values can be.  For 2-spaces, a simple measure of excess or deficit
of circumference around a point works...

Still I think my point stands, that a molecular cloud would likely be larger
than the 100D size of an equal mass star, and thus wouldn't disrupt Jump.



> That's *not* a trojan point even though it is a resonance orbit.

My point was that the are only *2* exact Trojan points (leading and
trailing) and that only in the ideal circular 3-body solution.  Obviously,
the hundreds of "Trojan asteroids" can't all be in those 2 exact points, if
any are.  They are in fairly stable orbits *around* the approximate points,
and the further out from the point, the odder the orbit gets.  At the
extreme, it becomes a horseshoe orbit.

As for the equilateral triangle, refer to my other post about *any* 3 masses
& equilateral triangles.  I had been misled by the way Dr. Forward phrased
his description of Rocheworld, where he referred to 90 degree separation.
Which is accurate, measured from the barycenter, which of course is centered
between 2 equal masses.  :)