[extropy-chat] SPACE: How many planets?

[Alan Eliasen]

   I like the idea of a roundness criterion, but it's always the vaguest one
when planets are brought up.

   If we're going to use a "roundness" definition, it has to be quantifiable,
otherwise it will be a completely subjective measure as to whether it's "round
enough" or not, and every single person will have a different answer.  It
becomes vaguer than a minimum radius question, or almost any other criterion
used.  So let's try to come up with one.  There are lots of subtleties to this.

   I have some questions below if you or others want to nail down a "round
enough" criterion.  Or, if someone has an equation as I originally requested,
you can ignore the questions and we'll discuss the equation.

> --- Alan Eliasen <eliasen at mindspring.com> wrote:
>>   As I recall, that discussion dwindled off just as it started to
>>get
>>interesting.  Nobody ever defined what "roundness" meant and how it
>>was to be
>>defined.
>>
>>   After all, Sedna is probably a lot "rounder" than Jupiter, which
>>has an equatorial radius of 71492 km, and a polar radius of 66854 
>>km.  It's all squished.

Mike Lorrey wrote:
> Atmospheric squishing from angular velocity or tidal influence is not
> an issue here.

   What about surface *liquid* deformation?  So when is it an issue and when
is it not an issue?  How do we determine that a body is non-spherical due to
angular velocity vs. due to tidal influence vs. due to not having enough mass?
 We have to be able to calculate the expected shape of the body under
gravitational and accelerational forces to calculate the deviation of its
actual "roundness" from this theoretical ideal condition.  What if the body
doesn't even have a well-defined surface (like the gas giants?)

   Put another way, if something is the exact same shape as Jupiter, is it a
planet too?  What if it has 1/10000 the mass?  What if it does or doesn't
rotate?   What if it's made of iron?  Largely liquid?  Why *doesn't* rotation
influence this decision?

> It is assumed that any planet of any significant size is
> going to be tidally influenced by other bodies in a similar way, as the
> Earth is influenced by the Moon and vice versa.

   If tidal influence isn't an issue, I guess I don't understand the point of
this paragraph.  Bodies like Sedna, if it has no moon, probably experience
near-undetectable tidal forces, especially because, as you probably know,
tidal force is inversely proportional to the *cube* of distance, not the
square.  We *do* need to know if there are any significant tidal effects,
though, to see if the object is actually relativistically round.

> Roundness is a matter of distinguishing the fact that some bodies have
> enough gravity and resulting internal pressure and heat to cause their
> material to have enough fluidity so as to become round, as opposed to
> an oblong or an otherwise accreted misshapen pile of rubble.

   So is any sphere of liquid automatically a planet?  It forms into a sphere
because it has enough internal pressure and heat to do so.  Even a glob of
water orbiting in, say, the space shuttle, tries to (and rapidly does) achieve
a spherical shape.  Is that a planet?  What if it's bigger?  What if it forms
a shell of ice adequate to keep its contents in place?  As a corollary, does
buffeting from micro- and macro-meteors affect its planet status?

>>   So what is the equation that quantifies "roundness," and what is
>>the line that differentiates planets from non-planets?
>  
> Take its average internal temperature and pressure at different points
> over the life and compare against the average elastic strength of the
> material the body is made up of. If it is hot and high pressured enough
> to cause some significant majority of the material to flow into a ball,
> at some point in its evolution, then it is 'round'.

   I guess I really don't understand this.  If you can rephrase as an
equation, that would be unambiguous.

   When you say "different points over the life" do we need to know the
history of the object for a million years to make the determination?  One
year?  A billion?  What does the history of an object have to do with its
current roundness?  What if it melted into a round shape due to being heated
by collisions or heating from a star or internal radioactivity?  Does it
really not count as being a planet?  What is the typical amount of heating a
body receives by loss of gravitational potential energy, as opposed to, say,
kinetic energy from collisions or heating from the sun or internal radioactivity?

   When you say to compare temperature, pressure, and "elastic strength," how
do we do compare those things which have different dimensions?  Would any body
in the solar system hold together if its gravity went to zero?  How small
would the average piece size get over time?  Is the average piece size
increasing or decreasing right now, and has this trend always been this direction?

   Again, a sphere of any liquid with some cohesion would almost always
qualify as being a planet.  How do you differentiate between the effect of
gravity and the electromagnetic force?

   Can you quantify "some significant majority?"  If so, how do you choose
(and calculate) that number?  Does the shape of the non-round minority affect
your metric?  Like if it was a lollipop shape with an almost-perfect sphere
but carrying a big stick?

   When you say, "at some point in its evolution," if it's temporarily round,
but then diverges from that, (say, by a large impact,) is it still round?  If
it achieves roundness by some other type of heating or forming, does that make
it *not* a planet?  Do we give points for age?  Is a younger body allowed to
be rougher?  Or expected to be hotter and smoother?  Is an older body
penalized for being old and frozen and not able to re-form into sphericality
as well from a severe impact?  Or do we penalize it for the opposite--for the
hills not eroding enough to the level of the valleys?

   Roundness is an extremely fuzzy concept.  Without being able to quantify it
by some (perhaps arbitrarily-chosen) metric, this is every bit as non-rigorous
as just saying "it's a planet if I say it is."

   I have my own quantifiable metrics in mind, which I've hinted at above, but
I know what *I* think.  Maybe someone else will come up with a quantifiable,
rigorous definition that we can argue.  And then try to come up with some
vaguely-reasonable but probably still utterly arbitrary line to distinguish
"round enough" bodies from "not round enough" ones.

   That's the problem.  This line *will* probably always be as arbitrary as
any one of the other metrics used to distinguish planet/non-planet.

   I apologize if this discussion isn't on-topic for this list.  If so, let me
know and I'll withdraw it, but it is an interesting physics problem.

-- 
  Alan Eliasen                 | "You cannot reason a person out of a
  eliasen at mindspring.com       |  position he did not reason himself
  http://futureboy.homeip.net/ |  into in the first place."
                               |     --Jonathan Swift