Electric Universe Conference 2016
Well, hello everyone! I'm really happy to
be here for the second time and for this
I'm grateful to Dave Talbott and Susan
Schirott; I feel a lot of personal support
on their side and I'd also like to thank
Mark Span and Michael Goodspeed, it's
always a pleasure talking to you guys, and I'd
also like to thank all of the people from the
EU community in general, all the people
present here in this audience and people
watching us live and in the recording later..
It's just so much fun to be around you
guys, exploring our beautiful electric
universe. So, but what I'm going to talk
about today? Now, for the title of my talk;
you might actually notice, it's quite
weird, but talking about those cognitive
aberrations and other kinds of effects
like that, I just noticed that people
tend to notice and memorize things that
they actually don't like, things that
make them mad, things that they consider
stupid, so I figured that this is the
kind of title that I need. And in your
programs it's even better, even better
fits my purpose,
I hope. OK so, but first I want to make
some advertisement of sorts, tomorrow
during lunch time I'll be giving another
talk in the breakout room, so keep an eye
on this one if you want to hear it. It's
going to be about atmospheric vortices.
But what I'm going to talk about today
is, first of all I'm going to talk about
the motivation for my research, why do I
consider cometary research interesting.
Then I'm going to do, to briefly review the
basics of orbital mechanics so that
everyone would understand what the
parameters are, what is the
thing that I'm talking about. Then I'm
going to briefly outline the electric
comet idea and propose my own, really
simplified, version of it that actually
might lead to some predictions that we
might then compare to the population of
comets that we do have in the solar
system. So, I'm not going to talk about
any individual comet but I'm going to
talk about kind of the population of
comets as a whole. Then I'm going to
propose a few points for a discussion,
just some random thoughts maybe. So, to
start off, why do I consider cometary
research interesting?
First of all it's because the comets are
pretty close to us, they're our neighbors
in our solar system, they're not so far
away like some distant galaxies or
something.
There's an ever growing field of
observational data, so every year some
comet, almost every day actually some
comet gets discovered. We get more and
more data on the comets that we
already know. Then, it is possible to
perform what is called the in-situ
studies. For example, in situ means in
place, so we can actually go there and
study the comet, kind of, where it is
in its natural habitat, so to speak. So
this is the image of the Rosetta probe
of course. The comet 67P. And well, here
you can see this dark spot, it's
actually the shadow of the Rosetta probe
itself so it's just there to illustrate
that we can go there as close as to see
our own shadow on this object and it's
really cool in my opinion. So, then
laboratory experiments are theoretically
possible, at least in the electric comet
model and not only can we do stuff
like SAFIRE, probably already does, I'm
not sure, but I also would like to
propose an idea for a possible
experiment which is not a very close one
in terms of resources but still
theoretically possible. We can take, for
example, a near-Earth asteroid that
has a more or less circular orbit, that
is more or less easy to reach. And we
can put an engine on it and just
decelerate it thus that its orbit
would turn elliptical, and to
see if it might initiate a discharge.
Of course it's not a thing that we can
initiate today but maybe some time in the
future. And the comets were always
considered mysterious
bodies and their behavior is highly
non-trivial, indeed. And so, I think
that there's a lot of potential for
discovery in this area. So, to sum up,
I think that it's an excellent
area for new research initiatives. So, as
I've said, I'm going to review the basics
of orbital mechanics. First of all, some
agreements. I'm going to consider the
usual orbital motion as it is considered
in classical mechanics. So, I'm going to
consider only, like, gravitational force.
I'm going to use it as a black box, pretty
much as Newton did, I'm not going to
concern whether it is related to
electromagnetism or not, it might be true
it may be not. But I'm not going to be
questioning those things. I'm
also going to consider laws of Newton
and Kepler as being true. I'm going
to use the Keplerian laws, actually,
you'll see them later. And I'm also going
to use this simplification that the mass
of the central body is much bigger than
all the other bodies, meaning that
the Sun does not rotate around the
common barycenter with a comet, because
its mass is enormously big with respect
to the mass of the comet. So, it's quite a
straightforward approximation. So, well, in,
theoretically the orbital motion, if you
put it simply, it's just a freefall but
if you might imagine if you just, kind of,
switch on the gravity, it would just fall on
the central body and that's it. But to
move in an orbit means to have some
sideways velocity so that as you fall,
you actually also get shifted sideways.
So as this picture might suggest, to move
in an orbit means to fall free on the
central body but always miss. So, you never
actually hit the surface of the body, you
kind of always go somewhere near it,
never actually fall. So, the laws of
Kepler, the first law of Kepler is that
all planets move in elliptical orbits
with the Sun at one of the foci (focuses).
Here we have, f1 is the Sun. In just a
couple of random orbits,
might not be real, but under the Keplerian
laws it's, it could have been true. So
the second law is that the line that
connects a planet to the sun sweeps
out equal areas in equal times. It's
actually a direct consequence of the
angular momentum conservation but as you
look at those triangles A1 and A2, they are
equal in their area if the time
intervals are equal. And the consequence
of this is that the farther we are out
from the Sun, the slower we are going and
the closer we are, the faster we are
going. So, the biggest velocity is
achieved at perihelion, which is the
closest distance, and the smallest
velocities at aphelion, which is the
farthest distance. And the third law is
that the square of the period of any,
I mean, the orbital period of
any planet is proportional to the cube
of the semi-major axis of its orbit. So
it directly relates the orbital period
to the size of the orbit. So, the bigger
the orbit is, the longer it takes for a
body to go around and vice versa. So,
already, I should make a correction that
Kepler considered only periodic orbits,
so those are indeed elliptical, but we
also might consider non periodic orbits;
they are possible, such as parabola
and hyperbola. So, as I've said, you
need to have certain sideways velocity,
so it's not just the fall on the body but
actually to move in an orbit. And we
might consider putting, like an, engine
on your body and if you would accelerate,
your orbit would become more and more
elliptical and then, as you reach the
so-called escape velocity, it turns into
parabola so you just go away and
never return. And if you would increase
the velocity even more, your orbit would
become hyperbolic. And for an infinite
velocity, you would just get a straight line.
So this means that you're going so fast
that the body cannot even change
your orbit, even the slightest bit. And
it, kind of, relates to the eccentricity
although I've talked about velocity. So
only the elliptical orbits are closed ones
and for them the eccentricity is less
than one. Here we
have an example with 0.5; eccentricity
equal to 1 is parabola and everything
more than 1 is hyperbola. And so parabola
is sort of a limit case, sort of a border-
line between hyperbolas and ellipses.
There's an infinite number of elliptical,
of kinds of ellipses, infinite number of
kinds of hyperbolas, only one parabola in
between them. So, some of (the) orbital
parameters that are used to describe the
orbits; a - semi-major axis is the half of
the horizontal, in this case horizontal size
of this ellipse.
b - is the semi-minor axis, the
vertical one; then we have c - the focal
length, it's the displacement of the
focus which is the Sun in our case from
the center, the geometric center of
the ellipse. So, you might consider this
actually being a definition of
eccentricity, although usually it's quite
different but you might consider this
one because, as you can see, c is equal to a
times e, where e is the eccentricity and a
is the semi-major axis, I've already said.
So the bigger the eccentricity is, the
bigger displacement is, the more kind
of, squeezed the orbit becomes and so for
zero eccentricity we get obviously
zero displacement and just a circular
orbit. And then we have other parameters
like distance to the apoapsis or periapsis,
in our case it's
aphelion and perihelion. We have the
dynamical parameters that change, v is the
velocity and theta, angle between the
direction to the perihelion
and the current position of the body. So
those two, velocity and theta, they change
along the orbit. And as for the name:
true anomaly is just a historical name,
it doesn't have any real significance. So
just for you to, kind of, feel those kinds of
orbits, I've plotted several ellipses with
the same semi-major axis but different
eccentricities, so here we have a zero
eccentricity as I've said, it's just a
circle and as it increases, the orbit gets
kind of squeezed while remaining at the
same, kind of, linear size - the
horizontal one. Here we have a highly
eccentric orbit, these are just those plotted
together. This point is of course the
position of the Sun with respect to the
orbit that you would have at certain
eccentricity. So, those two parameters,
for example perihelion and aphelion
distance or semi major axis and
eccentricity, they describe the orbit in
its plane. But to describe the orbit in
the three dimensions we also need
to know how this plane is oriented, so to
do that we need a few more parameters. In
particular, this is the inclination of
the orbit, plane of the orbit, so it's
just called an inclination. Then we
have, the orbit might be rotated around
the vertical axis and it might be
determined through this longitude of
ascending node parameter. And then the
orbit might be rotated in the plane of
its own and it's going to be determined
by the argument of periapsis
parameter. So we need at least three more
parameters to determine the position of
the orbit in three dimensions. And the
orbit itself is static, but the object
moves in it and to determine the
position of the object in its
orbit, we need one more parameter, it
might be time or it might be the true
anomaly for example, this angle between
the current position and the perihelion,
and it defines the current
position of the object completely. So, as
I promised, a sort of, really simplified
version, maybe someone would disagree with
how do I perceive this but it's the way
that I propose you to look at it. So, the
idea is that the source of cometary
phenomena is in the interaction of the
comet nucleus and, later, coma and tails,
when they are already developed, with
electromagnetic field associated with
the Sun and the solar wind. So, the
internal composition of the object is
secondary. It might play
some role, it might not.
This isn't
actually covered here. So, what Iam
interested in is to try to
derive some sort of quantitative
description, so to put it simply, to just
write down some equations and to compare
what do we acquire from this, with
real data. So, I'm going to be interested
in trying to derive a probability
density function for comets based on
those assumptions that I would propose a
little bit later. So the probability
density means I'm going to find a
function, well, just to put it shortly;
I would have a couple of assumptions,
from them I would derive some function
which would tell me how many comets
should I have at the orbit with a given
eccentricity. And then I would look at
how many comets are actually there at,
with such orbits,
moving in those orbits with such an
eccentricity. So some fudge factoring
might be necessary, we'll see later.
So here are my really naive
considerations that the Sun is a point
positive charge, spherically symmetric,
and the probability of an object to
undergo a discharge, cometary-like
discharge, is proportional to the
potential difference between the
perihelion and aphelion of its orbit. So
if the object moves in an orbit of a,
positively-charged, positive charge, then
at perihelion, when it's the
closest to the central body, the
potential would be the highest and as it
moves to the aphelion at the farthest
point, the potential is the lowest. This
is quite the straightforward idea that
maybe this potential difference is what
governs the probability of this
discharge to going on. And I'm, again, I
want to reiterate, I'm talking about
probabilities, so it's not a very
deterministic thing, but since we have
some quantity of comets, we can
actually consider this like that in my
opinion. So really simple formulas, just the
electric potential phi is equal to k/r;
r is the distance that we've already
encountered but k contains pretty much
all the constants, all the fudge
factoring, everything that we would
would like, maybe, to insert later, some
nonlinearity,
some things like the charge of the Sun,
constants of interactions, Debye
screening factor, things like that
would all go to there, but I
wouldn't be interested in this right now,
I'm only interested in the dependence on r.
So for perihelion and aphelion I
just substitute the r with the
respective distances and I take the
difference of those two and I apply
the formula (4), really nothing complex
here. Then I use the known expressions
for ellipses, substitute the aphelion
and perihelion, taking their dependence
on semi-major axis which
determines the size of the orbit, and
eccentricity which determines the shape.
So I substitute it to there and then get
the formula (5). So according to my
hypothesis, the probability of this
discharge P is proportional to this
Delta of potentials which is k2e over
a(1-e squared). So as you might notice,
here we have the semi-major axis appearing
and, well, a kind of physical in the
denominator so the more semi-major axis
is, the less the probability and, well, the
physical reason for this is because, as
we move farther away from the Sun, the
field kind of gets less dense, it's very
tightly packed with the potential
difference and the, kind of, energy
density as we are closer to the Sun, and
it gets more relaxed as we are farther
away. So it's harder to sustain a
discharge. And I'm not even going to be
interested in this, I'm going to talk
about, only about eccentricities
today, so I'm only interested in this
part that contains the letters e. 2e
over (1 minus e squared). And here I've got
this graph plotted, of this function with
respect to e. So you can disregard the
numbers at the y axis, it's not actually
like a probability, as I've said
it's pretty much arbitrary. I'm only
interested in the shape of the curve and
the,
kind of, the functional dependence itself,
not the absolute height of it. And you
might see that as eccentricity is equal
to 1, we actually move to infinity, which
is quite bad actually, but we would need to
introduce, probably, some fudge factor in
order to normalize our probability to
unit value which is a fairly standard
procedure. So we would have to introduce
something later here. But anyway, we
already have something to work with and
I've compared this to the data on
real solar system cometary
population and here is the source of my
data. So just a couple of quick facts. We
have more than 700,000 asteroids known,
more than 3,000 comets and actually as
I've said, almost every day a new object
is getting discovered, so this
data is already obsolete. Now ninety
percent of asteroids have orbits with
quite a low eccentricity, less than
0.25. Ninety percent of
comets have orbits with eccentricity
of more than 0.5 so they're quite in
eccentric orbits. What's quite
important in my opinion is that no
asteroids have parabolic or
hyperbolic orbits, so all the asteroids
that we know about actually move in
periodic orbits, but all the stuff that
kind of, as you can see, 1800 parabolic
and 300 hyperbolic comets, so the
majority of comets actually are
non-periodic so they, kind of, go from
somewhere out there and never return.
But actually there's a problem with the,
a slight problem is that
there are almost 1,000 objects that
are considered parabolic comets,
when in fact they're not quite.
Those are the so-called Kreutz comets,
Kreuz is a cross in German, that's the
last name of the guy who, kind of, worked
on the theory about them. So they are
actually elliptical and they have
a period of about the 750 years, but
their perihelion is almost equal to
the radius of the Sun, so they never
survive a single orbit.
I don't know why are they considered
parabolic, but it's
just a fact. The community somehow
considers them being parabolic and
I'll show you later that they actually
kind of spoil the statistics in a pretty
major way.
But anyway, interesting is that no
asteroids are on parabolic or
hyperbolic orbits, meaning that all the
stuff that goes from somewhere outside
the system actually is a comet. It never,
it cannot be an asteroid. So in electric
comet it's of course something to be
expected because if something is, goes
from far far away it should experience
a discharge anyway. So here's the graph that
I've plotted. I'm actually going to show
you only the lowest part now so that we
could see actual kind of dynamics, what's
going on there because it's not a very
easy thing to analyze with his huge
spike at 1. So here's the lowest
part blown up. So, this is the
graph that I've shown in the preview
of my talk but it was probably not the
best idea because this graph is integral,
which means, it shows the number of
comets that has an eccentricity of this
value and all the ones that were
before, so for 0.4 for example
eccentricity, I plot on the y-axis
the number of comets that have
eccentricities of 0.4 plus all that were
before like 0.1, 0.2, 0.3; so
this graph cannot fall, it can only rise
or be horizontal at best. So it's probably
not the best option and what.. At
first what I did was to analyze it. I was
interpolating this graph. The first part
kind of looks like a, let me show you,
this part kind of looks like a parabola,
this part kind of looks like a linear
function, this part kind of looks like a
exponential. So I took the derivative
out of those, just to get the
differential graph and parabola of
course which would turn, just into
a straight line. The straight line would
turn into horizontal and exponential
would remain exponential but then I
decided to work in another way and I've
just plotted the differential graph
itself so, I extracted it from
the initial data and here what I have
got and again, this is only the lowest
portion of, so that we could see what's
actually going on in here because at 1
we have a very powerful spike of,
like, fifteen hundred or even more, so
I've only given the lowest part. So you
can see certain spikes here and there.
This is the quite a noticeable spike at 0.7,
I'll talk about this a little bit later,
it might be important in my opinion. But we
don't actually observe, what we observe is a
strong growth at 1 but as I've said;
I'm not going to be interested in the
number of comets but rather in the
probability of an object to be a comet.
And it means that I'm going to take a
ratio of number of comets to the
number of all the small bodies that are
out there. So maybe there's just no small
bodies at all at certain orbits, right?
So I'm going to be interested in this
ratio of number of comets divided by; number
of comets plus number of asteroids, to
determine, roughly at least, the
probability of a randomly chosen object
to be a comet. So the more comets there
are, the less asteroids, the bigger the
probability. I hope this is quite
clear.
So, in order to do that, of course, I need
the number of asteroids too. So I looked
at the number of asteroids, this is again
the integral graph, looks kind of like a
charging capacitor but I don't think
there's a physical meaning to this
analogy. But here's the differential
graph. It shows exactly how many
asteroids have orbits with this exact
eccentricity. So we can see that the absolute
majority have less than 0.3 or something
like that. But even for quite a big
eccentricities like the 0.9, there are
some asteroids with such,
with such orbits now but there
aren't many of them. So here I have the
graph that I've promised you, sort of this
ratio I took for every given eccentricity,
I took the ratio of number of comets divided
by; number of comets plus number of
asteroids. And we can compare this to the
data that I've shown you, that's my
prediction of sorts. From my really
simplified assumptions. Again we can see
the spike at 0.7, I'm going to talk about
this in a minute and another spike which
is kind of close to 1, this one. It's
actually only one data point. It just
happens that there are no
asteroids at this measure of
eccentricity, so it's maybe not that
important. But anyway, just as a reminder,
this is what I've got from my assumptions
and here's the comparison. So well, in my
opinion looks, well, maybe not very well
but kind of acceptable,
maybe. So as I've promised, this 0.7 thing,
I actually think it might be important.
I mean this spike over here. Because well it’s
just my intuition, sort of, but 0.7 might
be important number because remembering
Steve Crothers' talk about numerology,
from last year, like 0.7 might be for example
like square root of 2 divided by 2, or it might be
square root of 3 minus 1, or it might be the
base of natural logarithm e minus two. So
there might be a relatively easy way to
reproduce this spike but I'm not sure,
this is just my, kind of, hypothesis
so to speak. This is pretty much the
main picture I wanted to show you today,
but now I'm going to show you some more
data. Maybe you were wondering what kind
of inclinations the cometary orbits have
and I was actually quite surprised when
I saw the real data because it looks
like this; So you have a, well, first
of all let me explain what is shown
here. The length of the spike
shows the number of comets. You can see
that it is in negatives sometimes
but you should take the length as
through Pythagoras’s theorem. You
would get the number of objects,
number of comets, but the angle between
the spike and the x-axis determines the
inclination. So the horizontal spike
there means zero inclination and the
inclination rises, then 90 degrees mean
polar orbit and as we move more than
90 degrees it means the
retrograde motion. So the orbits
backwards, sort of, with respect to the
planets at least. So you see this insane
spike at around 145 degrees, so it's 35
degrees retrograde motion. And its
the mentioned Kreutz comets that I have
told you about.
So it just so happens that, well, at least the
theory states of those Kreutz comets that
once there was a very big comet and it
fragmented and gave birth to, like, well,
we know at least of 1,000 or something like
that, Kreutz comets. So and it, kind of,
oversaturated its orbit with comets, just
out of nowhere and it's quite a big
drawback of my method, of my approach,
because, as we see, there, kind of, should
have been only one comet but there are
actually almost 1000 and it's not a very
good thing. And we should try and, kind
of, filter out the cases like that. Maybe
those other spikes that you can see
to the right, they have a nature
similar to that. This is the lowest part,
again blown up, so you could see the
more fine structure. And well, in general
I would say that it looks more or less
kind of homogeneous. There are kind of
more populated prograde sector, maybe the
collisions were more frequent in this area,
well, due to obvious reasons. And then the
retrograde sector is less populated
because the objects were destroyed
due to frequent interactions with,
like, major planets. I don't know, it's
an interesting thing to look into in
more detail,
probably. Again, I want to see
a percentage, so I look also at
asteroids. So you can see that the
absolute majority of asteroids have
prograde orbits, so kind of normal
regular orbits with relatively low
inclination. There are retrograde
asteroids, some of them, but you can see
them here, they are come completely
overwhelmed by the prograde ones. So
here's the percentage and, as you
can see, the prograde sector,
I mean the percentage of comets at
orbits with given inclination. So you can
see the prograde sector is really low
on comets, relatively speaking,
but as we move to retrograde, there's
more and more comets being
there. So the retrograde sector is
dominated by comets. Here is the only
graph that shows the semi-major axis
dependence. It's quite hard to obtain the
data because it's very time-consuming.
The semi major axis is horizontal, it
goes from 1 to 32 astronomical units.
That's all that I could have obtained.
And from, kind of, the vertical one is the
eccentricity, so it goes, kind of, into the
plane of picture. And the surface
shows the number of comets
with those kind of parameters. So we can
see a huge asteroid belt spike, some
spike nearby, probably
related to it but we also see kind of a
hyperbolic fall as we move to bigger
semi-major axis. It might be related to
what I've shown you because my formula, kind
of, "predicts" that, because the semi-major
axis is in the denominator so, as we move
farther away we need more and more
and more eccentricity to sustain the
same discharge. We see also two stripes
between the orbits of major planets and
two, kind of, dead zones where, again, the
orbits of major planets lie. So
unfortunately this is all that we could
see here.
Just a couple of points for discussion
now; apophenia means to see patterns where
there are actually none. So the possibility
here, we should always consider this
as a possibility because we might just,
kind of, try to derive patterns were it's,
kind of, well, either there are none or
maybe they are not the way we think they
are, sorry for this. Then we might have
possible observational issues and biases.
We obviously don't know, probably, the
majority of bodies, we only know the
biggest ones and it's probably the
minority in our system. So the whole
statistics might be, kind of, different
then, from what we know. Then other
hypotheses are possible ..not even.. and I'm
talking about, for example, the electric
comet framework hypotheses for example.
You might look at radial velocities, how fast
the object is moving to or from the Sun, this
is the thing that I actually looked into
and get similar results. But that's not
the topic of my talk now. Even a dirty
snowball hypothesis might theoretically
reproduce the same results. I haven't looked
into it but it's a possibility that if
we are to approach this scientifically
we should look into this too. And, well,
other kinds of hypotheses are also
possible. Internal structures, I've said,
it's a kind of secondary factor in an
electric comet approach but it might be
important, we might have, we might like
to look into the spectroscopic
data, maybe there are various kinds of
discharges, changing like the surface
chemistry, influencing this
spectroscopic data that we might
actually have the real data about. Active
asteroids are sort of, kind of,
intermediate case between the asteroids
and comets and they are, of course, very
important thing to look into because,
well, because they are kind of,
there might be some experimental cruces
here, so to speak, because they are, as I
said, the intermediate case between the
asteroids and comets. And actually, what I,
I have
an idea that, as I've said, I'm working
with probabilities so, well, let's draw an
analogy. For example we have a piece of
radioactive material and every atom has
a certain possibility to decay,
certain probability, but over time more and
more atoms get decayed so maybe the same
thing could be observed with comets, maybe
more and more asteroids kind of spark
up as time goes on and maybe, I don't
know, how many years more and more
comets would appear just out of
some regular asteroids.
Well this is the idea that I had. The
density thing; we know from Philae data
that the density of 67P's material is
almost the same as the density of
asteroid material but it's the high
porosity that makes it so light in, kind
of a, in a bulk, in general. So it's also a
thing to look into, especially related to
active asteroid thing. We should look
into what kind of densities do they have.
Maybe, actually, the mass of the object
is changing. It's quite an outrageous
idea from the mainstream-
gravitational kind of approach but, well,
who knows? As I've said, comets are pretty
mysterious objects. So, a couple of other
quick points. Solar activity, of course,
might be a factor.
I had another idea, that there might
be a quantizing, of sorts, of cometary
quantity as we move.
I mean with the solar periods, as the
orbital periods go like, 11, 22, 33 etc;
maybe there are some like a step-like
function. I don't know, I haven't actually
looked into this as I've said, I haven't
actually looked into the semi-major axis
nor the orbital period. So the
orientation of orbit with respect to stars
might be important, aphelion distance,
time spent in outer solar system. As I have
said, ther are many many things possible here
but to, kind of, conclude my talk I think
that naive "electric" considerations
are moderately successful to describe
the distribution of comets that we do
observe. Some additional hypotheses might
be required. Data might be
corrupted, just as the Kreutz comets
demonstrate. We should always be very
careful with our analysis. It is good that
we have falsifiability, that we actually
have more and more means to actually
interact with the object that we're
looking into. Orbital parameters, surface
composition, various chemistry,
might be important. It's always a thing to
look into. But the bottom line is that,
as I've said in the introduction, that
the cometary research is interesting and
potentially fruitful topic and I hope I
was able to communicate this to you.
Thank you
