## How many jellybeans are in this jar?

The cosmos at our fingertips.
BDanielMayfield
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### How many jellybeans are in this jar?

I like big numbers, and I like planets, so a question I’d like to discuss is: How many planets does the universe contain? It’s kind of an ultimate, guess the number of jellybeans in a jar question.

Of course in practical and exact terms this question is un-answerable. Nevertheless, the effort to approximate a reasonable answer should be both interesting and informative. For instance, consider definitions. For the question to be meaningful what is meant by “planet” and “the universe” must be clearly defined.

Let’s define the “jar” first. Some think that the universe is infinite, truly unbounded. If the universe really is infinite in the ultimate mathematical sense of the word then the number of galaxies, stars, and planets inside it would also be infinite, and the problem ends there, with a an admittedly big, although somewhat ambiguous answer. So let’s add the qualifier “observable” to limit the size of the jar to more manageably stupendous proportions.

But since when we look across vast intergalactic distances we are also looking backward across billions of years of universal history we need to address the question of timing. Adding “now” to the end of the question, as in “How many planets are in the observable universe now?” still seems ambiguous. I say this because galaxies at the extreme limit of the currently observable universe have “now” receded far beyond our ability to see them forevermore. I welcome suggestions as to how to set a reasonable temporal boundary for this question.

Then there is the endlessly debated but (to me at least) ever entertaining question of how to define the word “planet”. Do we dare include the diminutive dwarf planets? I like big numbers and this is my question, so on the grounds that a dwarf planet is still a planet I’m inclined to say yes, let’s let ‘em in. This adroitly avoids the problem of where to draw the line between “real” planets and the dwarfs. Unfortunately, we still have an even bigger problem of where or how to make the cut between dwarf planets and lesser bodies. Any suggestions?

On similar grounds I would also include starless “rouge” planets too. Does a planet stop being a planet just because it goes rouge? It wasn’t its fault. Why demote it from planet status simply because other bigger bodies bullied it about? So I’m inclined to let the rouges in too, but contrary opinions are fun to consider and so are welcome as well.

Timing comes up again, as in WHEN is a planet a planet? I’m not fond of the part of the IAU’s definition that requires planets to have cleared their orbits of other bodies. A consequence of this rule would be that “planets” could technically never collide. But early in our solar system’s history a Mars sized body named Theia collided with a Venus sized proto-Earth, producing the Earth/Moon system. Where Theia and the proto-Earth planets before the collision? I would argue that they were. Therefore in my opinion once an object is big enough to be a planet, it’s a planet, unless …

… it’s a moon, which is an object orbiting a planet. But if two objects are big enough to both be considered planets if they weren’t in a mutual orbit, are there two planets, or one? Since such a dual object can also be known as a double planet, and the “planet” part of the term is sigular, I would say one planet. (This is spliting hairs, but not planets.) You might think that such objects would be rare, and maybe they are, but in our solar system the Earth/Moon system is sometimes called a double planet, and Pluto and Claron have been as well (before the Deplanitization Decree). If the Moon was orbiting the Sun instead of the Earth it would be known as a dwarf planet. (Adding up the number of planets in the Sun’s domain will be important in this discussion, so this paragraph is not as unimportant as it may have at first seemed.)

So how do Brown Dwarfs enter in to this question? Planets have been found orbiting BDs, and these orbiters are always called planets, so BD orbiting objects in the right mass domain are in, IMO. BDs themselves should be out, because these are “failed stars”, not planets. But if a planet sized body orbits a BD that in turn orbits a star, is it a planet, or is it a moon? Any opinions?

And then there’s the question of the how or where to draw the line between a BD and a massive planet. Very recently MargaritaMc informed us of a breakthrough in distingushing bewteen the smallest stars and BDs, in this topic: http://asterisk.apod.com/viewtopic.php?f=31&t=32575 In that discussion Ann provided this comment about the division between BDs and planets which prompted me to post this question in the first place:
Ann wrote:This is beginning to look like old news now, but I have been thinking about it, and it is really so interesting. In particular, the relation between mass and radius in planets and brown dwarfs is very interesting.
http://en.wikipedia.org/wiki/Brown_dwarf#Distinguishing_low-mass_brown_dwarfs_from_high-mass_planets wrote: A remarkable property of brown dwarfs is that they are all roughly the same radius as Jupiter.

At the high end of their mass range (60–90 Jupiter masses), the volume of a brown dwarf is governed primarily by electron-degeneracy pressure,[11] as it is in white dwarfs; at the low end of the range (10 Jupiter masses), their volume is governed primarily by Coulomb pressure, as it is in planets. The net result is that the radii of brown dwarfs vary by only 10–15% over the range of possible masses. This can make distinguishing them from planets difficult.

Gas giants have some of the characteristics of brown dwarfs. For example, Jupiter and Saturn are both made primarily of hydrogen and helium, like the Sun.

Saturn is nearly as large as Jupiter, despite having only 30% the mass.
Isn't it remarkable? Jupiter is a sort of sub-stellar/brown dwarf/gas giant standard when it comes to radius and volume. However, Jupiter appears to be larger than the smallest stars. I googled the mean radius of Jupiter (69,911±6 km), and the radius of the Sun (695,500 km), and even though the uncertainty seems to much greater when it comes to the radius of the Sun than when it comes to the radius of Jupiter, I nevertheless used these two figures to conclude that the raidus of Jupiter appears to be pretty much 10% the radius of the Sun. However,
http://www.noao.edu/news/2013/pr1311.php wrote: Dr. Todd Henry, another author, said: “We can now point to a temperature (2100K), radius (8.7% that of our Sun), and luminosity (1/8000 of the Sun) and say ‘the main sequence ends there’ and we can identify a particular star (with the designation 2MASS J0513-1403) as a representative of the smallest stars.”
So the smallest hydrogen-fusing star may have a radius 8.7% that of the Sun, but Jupiter may have a radius 10% that of the Sun. Then again, this is without a very reasonable margin of error.

It might be more correct to say that Jupiter is, for all intents and purposes, the same size as the very smallest M-type stars.

This makes me wonder how large a gas giant planet can be. Several massive gas giants have been found among exoplanets. I remember having read about hot Jupiters whose atmospheres have been puffed up from the intense radiation of their suns, so that the planets were very large. But when it comes to gas giants at greater distances from their suns, how large can they be? Is Jupiter once again a sort of gold standard of the size of small stars, brown dwarfs and gas giant planets?

Ann
So you can see that this is a multi-facited question. The answer is beyond our reach, but the path toward the answer should be interesting and informative.
Just as zero is not equal to infinity, everything coming from nothing is illogical.

Beyond
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### Re: How many jellybeans are in this jar?

How many planets does the universe contain
Simply put...

Not too many
and not too few,
discounting the ones that cycle through.
IF you count them
the way i do...
not too many
and not too few.
To find the Truth, you must go Beyond.

Ann
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### Re: How many jellybeans are in this jar?

This is a fantastic question to ponder, Bruce. To some extent it is philosophical, but we can make a few educated guesses.

Just a thought, though. I think that the term "the universe" should be defined as the observable universe. That means that galaxies that can be spotted at high redshifts should considered parts of the observable universe, even if they are "now" beyond our horizon.

However, we should not assume that the galaxies that we can spot at high redshifts necessarily contain the same "relative number" of planets as nearby galaxies. Very young galaxies are often (but not always!) very metal-poor, and it could be that they don't contain enough planet-making materials to make a lot of planets.

But when it comes to the Milky Way, it could well be that planetary system similar to our own are the norm rather than the exception. (I'd like to qualify that: I personally don't believe that "well-ordered" planetary systems with planets in near-circular orbits are necessarily the norm at all.) But do we have any special reason to believe that Milky Way stars typically have fewer planets than our own Sun? Personally, I don't think we do.

So let's assume that the average star in the Milky Way has 5-10 planets. Let's assume, too, that there are 400 billion stars in the Milky Way. If we multiply that number by 5, we get 2 trillion planets in the Milky Way. If we multiply it by 10, we get 4 trillion.

However, we should bear in mind that some of the stars in the Milky Way are metal-poor, and they may not have formed so many planets when they were born. So it might be overly optimistic to think that the average star in the Milky Way has 10 planets. Let's settle for 5.

There may be very many "rogue" planets in the Milky Way, though. Who knows, maybe there are enough of them to boost the number of planets back to 10 planets for every star, even if half of the surviving planets have wandered away from their parent stars.

But how big does a cosmic object have to be to qualify as a planet? Consider Enceladus, the active moon with water ice jets in the Saturnian system. It is very small, which can be seen in this picture comparing the size of Enceladus with the size of the United Kingdom.

And what about Pluto? Maybe it is big enough to be a planet, but if it is, shouldn't the Moon be considered a planet, too? The Moon is bigger than Pluto. Should large moons be disqualified as planets just because they orbit a still larger body? Can we really say that Pluto should be considered a planet but Ganymede and Titan should be regarded as moons?

I think we can't really talk about planets until we have a firmer definition of what we mean.

Still, the question you have raised is most fascinating, Bruce!

Ann
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BDanielMayfield
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### Re: How many jellybeans are in this jar?

Beyond wrote:How many planets does the universe contain
Simply put...

Not too many
and not too few,
discounting the ones that cycle through.
IF you count them
the way i do...
not too many
and not too few.
Thanks Beyond, but I was looking for a somewhat more analytical approach …
Just as zero is not equal to infinity, everything coming from nothing is illogical.

Chris Peterson
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### Re: How many jellybeans are in this jar?

Ann wrote:This is a fantastic question to ponder, Bruce. To some extent it is philosophical, but we can make a few educated guesses.
I'd say it's not even slightly philosophical. It's an entirely scientific question, that simply lacks sufficient evidence (for now) to answer with any sort of precision.
Just a thought, though. I think that the term "the universe" should be defined as the observable universe.
This is a good point, that generally applies most of the time. Since we have no idea at all how large the actual universe is, an awful lot of questions are best restricted to the observable universe.
However, we should not assume that the galaxies that we can spot at high redshifts necessarily contain the same "relative number" of planets as nearby galaxies. Very young galaxies are often (but not always!) very metal-poor, and it could be that they don't contain enough planet-making materials to make a lot of planets.
Here's where we need to be a bit careful. What we observe as very young galaxies are, in fact, very old. In the same way that the actual distance of these objects is much farther away than their light travel time, we need to consider just what we are actually asking. After all, most young galaxies are actually outside the observable universe now. Do we include them? When we ask how many planets are in the observable universe, do we mean now, or as we could observe them?

There are no right or wrong answers here, but we do need to be very careful with our definitions.
But how big does a cosmic object have to be to qualify as a planet?
Again, no right or wrong answers. But it's a definition that has to be provided before the question can be answered.

Personally, I'd probably define a planet as a substantially spherical body that formed in orbit around a protostar. But I'd count separately the number of planets in orbit around stars from the number that are rogue, since both numbers are interesting, and you need to know both to really understand planet formation in the universe.
Chris

*****************************************
Chris L Peterson
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BDanielMayfield
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### Re: How many jellybeans are in this jar?

Ann wrote:This is a fantastic question to ponder, Bruce. To some extent it is philosophical, but we can make a few educated guesses.
Thanks Ann, and I’m glad you like the question. Yes, educated guesses are the best we can do. You go on to make many interesting points in the rest of this comment, which I will get back to when I have more time.

At this point though I would like to respond to this question you raised from your earlier comment re the BD/planet distinction:
This makes me wonder how large a gas giant planet can be. Several massive gas giants have been found among exoplanets. I remember having read about hot Jupiters whose atmospheres have been puffed up from the intense radiation of their suns, so that the planets were very large. But when it comes to gas giants at greater distances from their suns, how large can they be? Is Jupiter once again a sort of gold standard of the size of small stars, brown dwarfs and gas giant planets?
I remember reading a Sky & Tel. magazine article a few years ago about Jupiter to Super-Jupiter masses planets, and the main point was that regardless of mass, planets in this mass range should all be about the same radius, except for puffed up hot planets in tight orbits. In fact as revealed by the finding in the topic MargaritaMc started about the boundary between the smallest stars and the most massive BDs, the most massive BDs are also the smallest of this class. Yes, Jupiter is about as big as gas giants get, unless their surfaces are heated greatly by close proximity to a star.

But since so many planets are being discovered in close orbits, and since even Jupiter is bigger that the smallest stars, size cannot be used to discriminate between giant planets, the smallest stars, and brown dwarfs. Consider this from the Wikipedia article on Brown Dwarfs:
Distinguishing low-mass brown dwarfs from high-mass planets

A remarkable property of brown dwarfs is that they are all roughly the same radius as Jupiter. At the high end of their mass range (60–90 Jupiter masses), the volume of a brown dwarf is governed primarily by electron-degeneracy pressure,[11] as it is in white dwarfs; at the low end of the range (10 Jupiter masses), their volume is governed primarily by Coulomb pressure, as it is in planets. The net result is that the radii of brown dwarfs vary by only 10–15% over the range of possible masses. This can make distinguishing them from planets difficult.

In addition, many brown dwarfs undergo no fusion; those at the low end of the mass range (under 13 Jupiter masses) are never hot enough to fuse even deuterium, and even those at the high end of the mass range (over 60 Jupiter masses) cool quickly enough that they no longer undergo fusion after a period of time on the order of 10 million years. However, there are ways to distinguish brown dwarfs from planets:

X-ray and infrared spectra are telltale signs. Some brown dwarfs emit X-rays; and all "warm" dwarfs continue to glow tellingly in the red and infrared spectra until they cool to planetlike temperatures (under 1000 K).

Gas giants have some of the characteristics of brown dwarfs. For example, Jupiter and Saturn are both made primarily of hydrogen and helium, like the Sun. Saturn is nearly as large as Jupiter, despite having only 30% the mass. Three of the giant planets in the Solar System (Jupiter, Saturn, and Neptune) emit much more heat than they receive from the Sun.[12] And all four giant planets have their own "planetary systems"—their moons. Brown dwarfs form independently, like stars, but lack sufficient mass to "ignite" as stars do. Like all stars, they can occur singly or in close proximity to other stars. Some orbit stars and can, like planets, have eccentric orbits.

Currently, the International Astronomical Union considers an object with a mass above the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 Jupiter masses for objects of solar metallicity) to be a brown dwarf, whereas an object under that mass (and orbiting a star or stellar remnant) is considered a planet.[13]

The 13 Jupiter-mass cutoff is a rule of thumb rather than something of precise physical significance. Larger objects will burn most of their deuterium and smaller ones will burn only a little, and the 13 Jupiter mass value is somewhere in between. The amount of deuterium burnt also depends to some extent on the composition of the object, specifically on the amount of helium and deuterium present and on the fraction of heavier elements, which determines the atmospheric opacity and thus the radiative cooling rate.[14]

The Extrasolar Planets Encyclopaedia includes objects up to 25 Jupiter masses, and the Exoplanet Data Explorer up to 24 Jupiter masses. Objects below 13 Jupiter-mass are sometimes studied under the label "sub-brown dwarf".
So this boundary is rather ambiguous, isn’t it? It would be nice if there was a clean distinction here like has now been found at the star/BD boundary, but that seems unlikely. For the purposes of this discussion about overall planetary numbers I think the “13 Jupiter-mass cutoff rule of thumb” should be used, since objects over this mass begin fusion reactions they more generally fit the BD definition, and they are therefore not planets.

Bruce
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### Re: How many jellybeans are in this jar?

This particular type of problem tends to leave me feeling Googolplexed

orin stepanek
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### Re: How many jellybeans are in this jar?

I'd say a few quadrillion; + or = a few trillion or two! Just guessing!!!
Orin

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### Re: How many jellybeans are in this jar?

I'll have a (mildly) tongue-in-cheek go at it.

First, some definitions...

Universe - as much as we can see of it, but extrapolated so that all of it exists "now". That is, the galaxies we see by the light they emitted millions or billions of years ago have matured in a reasonable manner over their lifetime, just as our galaxy has. In other words, I'm taking an omniscient, god-like view. (The Great Donut in the Sky.)

Planet - whatever looks like a planet to our eyes, whether inhabitable or not. That is, not moons, not asteroids, not Oort Cloud objects, etc. (It doesn't matter if we can't agree on this, because our disagreement will fall well within the error bars.)

Assumption: the Milky Way is somewhat larger than the average size of all galaxies.

Bearing in mind that my definition of Universe means I am absolutely guessing here, since I can't know for sure how those distant galaxies actually matured, here's my calculation:

5 planets per stellar system x 100 billion stellar systems per galaxy x 100 billion galaxies (based on the Hubble Deep Field containing about 10,000 galaxies in its tiny area) = 5 x 1022 planets, or in round figures, a lot.

Rob

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### Re: How many jellybeans are in this jar?

rstevenson wrote:I'll have a (mildly) tongue-in-cheek go at it.

First, some definitions...

Universe - as much as we can see of it, but extrapolated so that all of it exists "now". That is, the galaxies we see by the light they emitted millions or billions of years ago have matured in a reasonable manner over their lifetime, just as our galaxy has. In other words, I'm taking an omniscient, god-like view. (The Great Donut in the Sky.)

Planet - whatever looks like a planet to our eyes, whether inhabitable or not. That is, not moons, not asteroids, not Oort Cloud objects, etc. (It doesn't matter if we can't agree on this, because our disagreement will fall well within the error bars.)

Assumption: the Milky Way is somewhat larger than the average size of all galaxies.

Bearing in mind that my definition of Universe means I am absolutely guessing here, since I can't know for sure how those distant galaxies actually matured, here's my calculation:

5 planets per stellar system x 100 billion stellar systems per galaxy x 100 billion galaxies (based on the Hubble Deep Field containing about 10,000 galaxies in its tiny area) = 5 x 1022 planets, or in round figures, a lot.

Rob

Sure,
And I was just about to say 50 Sextillion (50,000,000,000,000,000,000,000)

BDanielMayfield
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### Re: How many jellybeans are in this jar?

rstevenson wrote:I'll have a (mildly) tongue-in-cheek go at it.

First, some definitions...

Universe - as much as we can see of it, but extrapolated so that all of it exists "now". That is, the galaxies we see by the light they emitted millions or billions of years ago have matured in a reasonable manner over their lifetime, just as our galaxy has. In other words, I'm taking an omniscient, god-like view. (The Great Donut in the Sky.)

Planet - whatever looks like a planet to our eyes, whether inhabitable or not. That is, not moons, not asteroids, not Oort Cloud objects, etc. (It doesn't matter if we can't agree on this, because our disagreement will fall well within the error bars.)

Assumption: the Milky Way is somewhat larger than the average size of all galaxies.

Bearing in mind that my definition of Universe means I am absolutely guessing here, since I can't know for sure how those distant galaxies actually matured, here's my calculation:

5 planets per stellar system x 100 billion stellar systems per galaxy x 100 billion galaxies (based on the Hubble Deep Field containing about 10,000 galaxies in its tiny area) = 5 x 1022 planets, or in round figures, a lot.

Rob
This is a good first aproximation attempt for bound planets Rob.

I like your definition of "the jar". I think it can be stated as "all the galaxies that we could possibly see now, as they are now."

Bruce
Just as zero is not equal to infinity, everything coming from nothing is illogical.

rstevenson
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### Re: How many jellybeans are in this jar?

Thanks Bruce.

I left out unbound planets because we really have no Earthly idea how many of them there might be. Besides, to my way of thinking they're not really planets any more. That is, my definition of a planet would include being bound gravitationally to a star.

Rob

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### Re: How many jellybeans are in this jar?

You could possibly take the estimate of total matter, subtract the matter estimated to exist as stars, dark matter, black holes, etc. and then have the remaining matter to divide into planets and come up with a guess in that way. My idea of a planet definitely includes the rogues so that would cover that aspect.
Just call me "geck" because "zilla" is like a last name.

neufer
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### Re: How many jellybeans are in this jar?

geckzilla wrote:
You could possibly take the estimate of total matter, subtract the matter estimated to exist as stars, dark matter, black holes, etc. and then have the remaining matter to divide into planets and come up with a guess in that way. My idea of a planet definitely includes the rogues so that would cover that aspect.
Our own solar system consists of ~1.0014 solar masses
... and that ignores dark matter, gas, dust, black holes, etc.

Do you still think that your scheme would be feasible
Art Neuendorffer

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### Re: How many jellybeans are in this jar?

You didn't even use scientific notation. You'll have to use a smaller fraction to scare me away from the idea.
Just call me "geck" because "zilla" is like a last name.

BDanielMayfield
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### Re: How many jellybeans are in this jar?

geckzilla wrote:You didn't even use scientific notation. You'll have to use a smaller fraction to scare me away from the idea.
Good for you for not being intimidated Geckzilla, and for thinking outside the box.

You’d actually only need to know three numbers to make your method work: (1) The total mass of the observable universe’s normal baryonic matter, (2) The percentage of that matter contained in all the planets in said universe, and (3) the average planetary mass.

Bruce
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### Re: How many jellybeans are in this jar?

geckzilla wrote:
You didn't even use scientific notation.

You'll have to use a smaller fraction to scare me away from the idea.
Sir Karl Popper: The Tradition of Bold Conjecture and Free Criticism

<<"Anaximander criticizes his master and kinsman [Thales], one of the Seven Sages, the founder of the Ionian school. He was, according to tradition, only about fourteen years younger than Thales, and he must have developed his criticism and his new ideas while his master was alive. But there is no trace in the sources of a story of dissent, of any quarrel, or of any schism.

This suggests, I think, that it was Thales who founded the new tradition of freedom-based upon a new relation between master and pupil and who thus created a new type of school. He seems to have been able to tolerate criticism. And what is more, he seems to have created the tradition that one ought to tolerate criticism.

Yet I like to think that he did even more than this. I can hardly imagine a relationship between master and pupil in which the master merely tolerates criticism without actively encouraging it. It does not seem to me possible that a pupil who is being trained in the dogmatic attitude would ever dare to criticize the dogma (least of all that of a famous sage) and to voice his criticism. And it seems to me an easier and simpler explanation to assume that the master encouraged a critical attitude – possibly not from the outset, but only after he was struck by the pertinence of some questions asked, by the pupils perhaps, without any critical intention.

However this may be, the conjecture that Thales actively encouraged criticism in his pupils would explain the fact that the critical attitude towards the master’s doctrine became part of the Ionian school tradition. I like to think that Thales was the first teacher who said to his pupils: ‘This is how I see things-how I believe that things are. Try to improve upon my teaching’ (Those who believe that it is ‘unhistorical’ to attribute this undogmatic attitude to Thales may again be reminded of the fact that only two generations later we find a similar attitude consciously and clearly formulated in the fragments of Xenophanes.). At any rate, there is the historical fact that the Ionian school was the first in which pupils criticized their masters, in one generation after the other. There can be little doubt that the Greek tradition of philosophical criticism had its main source in Ionia.

It was a momentous innovation. It meant a break with the dogmatic tradition which permits only one school doctrine, and the introduction in its place of a tradition that admits a plurality of doctrines which all try to approach the truth by means of critical discussion.

It thus leads, almost by necessity, to the realization that our attempts to see and to find the truth are not final, but open to improvement; that our knowledge, our doctrine, is conjectural; that it consists of guesses, of hypotheses, rather than of final and certain truths; and that criticism and critical discussion are our only means of getting nearer to the truth. It thus leads to the tradition of bold conjectures and of free criticism, the tradition which created the rational or scientific attitude, and with it our Western civilization, the only civilization which is based upon science (though of course not upon science alone).

In this rationalist tradition bold changes of doctrine are not forbidden. On the contrary, innovation is encouraged, and is regarded as success, as improvement, if it is based on the result of a critical discussion of its predecessors. The very boldness of an innovation is admired; for it can be controlled by the severity of its critical examination. This is why changes of doctrine, far from being made surreptitiously, are traditionally handed down together with the older doctrines and the names of the innovators. And the material for a history of ideas becomes part of the school tradition.

To my knowledge the critical or rationalist tradition was invented only once. It was lost after two or three centuries, perhaps owing to the rise of the Aristotelian doctrine of epistémé, of certain and demonstrable knowledge (a development of the Eleatic and Heraclitean distinction between certain truth and mere guesswork). It was rediscovered and consciously revived in the Renaissance, especially by Galileo Galilei."
>>
Art Neuendorffer

BDanielMayfield
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### Re: How many jellybeans are in this jar?

I wanted to respond to Ann and to Chris, who already addressed some of her interesting comments.
Chris Peterson wrote:
Ann wrote:This is a fantastic question to ponder, Bruce. To some extent it is philosophical, but we can make a few educated guesses.
I'd say it's not even slightly philosophical. It's an entirely scientific question, that simply lacks sufficient evidence (for now) to answer with any sort of precision.

Yes, the question is purely scientific. The answer may have philosophical implications to some, but that’s not why I posed the question. Since “the answer” will be so uncertain the path toward an answer can be as or even more interesting than the result.
Just a thought, though. I think that the term "the universe" should be defined as the observable universe.
This is a good point, that generally applies most of the time. Since we have no idea at all how large the actual universe is, an awful lot of questions are best restricted to the observable universe.
Good. As in my comment to Rob, I think “the observable universe” in this question can be defined as ‘all galaxies within our present limits of observation, as they are at the present.’ Thus for the purposes of this discussion we can consider the entire observable universe to be of the same age, and we wouldn’t have the complication of needing to consider earlier conditions.
There are no right or wrong answers here, but we do need to be very careful with our definitions.
Which is why I’m spending so much time on these definition issues. Thank you for pointing out the importance of this Chris.
But how big does a cosmic object have to be to qualify as a planet?
Again, no right or wrong answers. But it's a definition that has to be provided before the question can be answered. Personally, I'd probably define a planet as a substantially spherical body that formed in orbit around a protostar.
I like the way you make the cut between dwarf planets and lesser bodies, using round shape and avoiding a specific numeric limit. This would include any stellar orbiter or rogue object that is in hydrostatic equilibrium. But like Ann I wonder, how big would an object need to be to meet this test? I know that it depends both on mass and on composition, but wouldn’t this definition cause there to be a large number of “planets” in our solar system? (Not that that’s a problem, we all know how to count higher than 10.)
But I'd count separately the number of planets in orbit around stars from the number that are rogue, since both numbers are interesting, and you need to know both to really understand planet formation in the universe.
This is a very good suggestion. It lets us break the problem down into its two main parts, so we have

Total Universal Planets = Total Bound Planets + Total Unbound Planets

Thanks for adding some gravitas to this discussion Chris.

Thank you Ann also. I enjoyed the photo of Enceladus over the UK, and that’s a wonderful example of a small but completely round body, but don’t worry about bodies orbiting planets. Moons are out in this discussion. If you want to include them you could ask another question after this one plays out: “How many Worlds does the universe contain?”

Bruce
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### Re: How many jellybeans are in this jar?

geckzilla wrote:You could possibly take the estimate of total matter, subtract the matter estimated to exist as stars, dark matter, black holes, etc. and then have the remaining matter to divide into planets and come up with a guess in that way. My idea of a planet definitely includes the rogues so that would cover that aspect.
Good idea. However, some stars may have debris disks where most of the mass consists of dust, gas and "space gravel" as well as (small) asteroids and comets. Beta Pictoris might be an example of such a star.

Anyway, how much mass is there in the Kuiper Belt and Oort Cloud in our own solar system? Is that mass negligible compared with the mass of the planets? If moons don't count as planets, we need to take their mass into account as well. How much of the non-solar mass of our own solar system consists of planets, and how much consists of something else?

Rob, I like your estimate. It sounds pretty good to me.

Ann
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### Re: How many jellybeans are in this jar?

BDanielMayfield wrote:Good. As in my comment to Rob, I think “the observable universe” in this question can be defined as ‘all galaxies within our present limits of observation, as they are at the present.’ Thus for the purposes of this discussion we can consider the entire observable universe to be of the same age, and we wouldn’t have the complication of needing to consider earlier conditions.
The term "observable universe" is already defined. We should use it properly, or pick a different expression. The observable universe is not what we are able to observe given our technology, but what is actually observable in principle. It is defined by the horizon created by space moving away from us at greater than c. Although we can see nearly to this horizon, there still remains a narrow zone that we can't see (for technological reasons) and in which we would expect planets to exist.

My point with age is that we don't see the entire universe as having the same age. We observe very distant galaxies as they were when very young. As Ann pointed out, these are metal poor, and may not have any planets. But those exact same galaxies still exist now, and are no longer metal poor, and certainly are full of planets. That's why we need to be careful in our count. Is the question "how many planets are observable" or "how many planets are in the observable universe"? Because these will yield very different values.
But like Ann I wonder, how big would an object need to be to meet this test? I know that it depends both on mass and on composition, but wouldn’t this definition cause there to be a large number of “planets” in our solar system? (Not that that’s a problem, we all know how to count higher than 10.)
Actually, the composition isn't very important (outside of some exotic special cases). Any body that masses about 1020 kg will assume an approximately spherical shape. There are about 40 such bodies observed in the Solar System, and perhaps 150 or so which can be assumed to exist based on statistical arguments. Personally, I have no problem considering them all planets.
Chris

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### Re: How many jellybeans are in this jar?

rstevenson wrote:I left out unbound planets because we really have no Earthly idea how many of them there might be.
I know what you mean Rob, and yes we (as in you and I, at the least) have no good idea how many unbound planets exist. However, these guys; Louis E. Strigari, Matteo Barnabe, Philip J. Marshall and Roger D. Blandford are from the Earth, and they did have an idea about this question. About two years ago they published a paper entitled “Nomads of the Galaxy” available at: http://arxiv.org/abs/1201.2687 Here’s its abstract:
We estimate that there may be up to ~10^5 compact objects in the mass range 10^{-8} -10^{-2} solar mass per main sequence star that are unbound to a host star in the Galaxy. We refer to these objects as nomads; in the literature a subset of these are sometimes called free-floating or rogue planets. Our estimate for the number of Galactic nomads is consistent with a smooth extrapolation of the mass function of unbound objects above the Jupiter-mass scale, the stellar mass density limit, and the metallicity of the interstellar medium. We analyze the prospects for detecting nomads via Galactic microlensing. The Wide-Field Infrared Survey Telescope (WFIRST) will measure the number of nomads per main sequence star greater than the mass of Jupiter to ~ 13%, and the corresponding number greater than the mass of Mars to ~25%. All-sky surveys such as GAIA and LSST can identify nomads greater than about the mass of Jupiter. We suggest a dedicated drift scanning telescope that covers approximately 100 square degrees in the Southern hemisphere could identify nomads as small as 10^{-8} solar mass via microlensing of bright stars with characteristic lightcurve timescales of a few seconds.

I wasn’t a member of this forum back when this news hit the fan, er, press, so I don’t know how y’all oldtimers here took this news, but surely some of y’all must have heard of it. The notion that up to 10^5 or 100,000 rogues per star roam the galaxy was viewed with great skeptism by commenters on S&T’s blog. Was this a topic rasied here?
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### MicroFUN?

BDanielMayfield wrote:
Louis E. Strigari, Matteo Barnabe, Philip J. Marshall and Roger D. Blandford are from the Earth, and they did have an idea about this question. About two years ago they published a paper entitled “Nomads of the Galaxy” available at: http://arxiv.org/abs/1201.2687 Here’s its abstract:
We estimate that there may be up to ~10^5 compact objects in the mass range 10^{-8} -10^{-2} solar mass per main sequence star that are unbound to a host star in the Galaxy. We refer to these objects as nomads; in the literature a subset of these are sometimes called free-floating or rogue planets. Our estimate for the number of Galactic nomads is consistent with a smooth extrapolation of the mass function of unbound objects above the Jupiter-mass scale, the stellar mass density limit, and the metallicity of the interstellar medium. We analyze the prospects for detecting nomads via Galactic microlensing. The Wide-Field Infrared Survey Telescope (WFIRST) will measure the number of nomads per main sequence star greater than the mass of Jupiter to ~ 13%, and the corresponding number greater than the mass of Mars to ~25%. All-sky surveys such as GAIA and LSST can identify nomads greater than about the mass of Jupiter. We suggest a dedicated drift scanning telescope that covers approximately 100 square degrees in the Southern hemisphere could identify nomads as small as 10^{-8} solar mass via microlensing of bright stars with characteristic lightcurve timescales of a few seconds.

I wasn’t a member of this forum back when this news hit the fan, er, press, so I don’t know how y’all oldtimers here took this news, but surely some of y’all must have heard of it. The notion that up to 10^5 or 100,000 rogues per star roam the galaxy was viewed with great skeptism by commenters on S&T’s blog. Was this a topic rasied here?
http://en.wikipedia.org/wiki/Gravitational_microlensing wrote:
<<Microlensing is based on the gravitational lens effect. A massive object (the lens) will bend the light of a bright background object (the source). This can generate multiple distorted, magnified, and brightened images of the background source. Microlensing is caused by the same physical effect as strong lensing and weak lensing, but it is studied using very different observational techniques. With microlensing, the lens mass is too low (mass of a planet or a star) for the displacement of light to be observed easily, but the apparent brightening of the source may still be detected. In such a situation, the lens will pass by the source in a reasonable amount of time, seconds to years instead of millions of years. As the alignment changes, the source's apparent brightness changes, and this can be monitored to detect and study the event. Thus, unlike with strong and weak gravitational lenses, a microlensing event is a transient phenomenon from a human timescale perspective.
Unlike with strong and weak lensing, no single observation can establish that microlensing is occurring. Instead the rise and fall of the source brightness must be monitored over time using photometry. This function of brightness versus time is known as a light curve.

Most focus is currently on the more unusual microlensing events, especially those that might lead to the discovery of extrasolar planets. Although it has not yet been observed, another way to get more information from microlensing events that may soon be feasible involves measuring the astrometric shifts in the source position during the course of the event and even resolving the separate images with interferometry.

In practice, because the alignment needed is so precise and difficult to predict, microlensing is very rare. Events, therefore, are generally found with surveys, which photometrically monitor tens of millions of potential source stars, every few days for several years. Dense background fields suitable for such surveys are nearby galaxies, such as the Magellanic Clouds and the Andromeda galaxy, and the Milky Way bulge. In each case, the lens population studied comprises the objects between Earth and the source field: for the bulge, the lens population is the Milky Way disk stars, and for external galaxies, the lens population is the Milky Way halo, as well as objects in the other galaxy itself. The density, mass, and location of the objects in these lens populations determines the frequency of microlensing along that line of sight, which is characterized by a value known as the optical depth due to microlensing. The microlensing "optical depth" is, roughly speaking, the average fraction of source stars undergoing microlensing at a given time, or equivalently the probability that a given source star is undergoing lensing at a given time. The MACHO project found the optical depth toward the LMC to be 1.2×10−7 or about 1 in 8,000,000, and the optical depth toward the bulge to be 2.43×10−6 or about 1 in 400,000.

In 1986, Paczyński proposed using microlensing to look for dark matter in the form of massive compact halo objects (MACHOs) in the Galactic halo, by observing background stars in a nearby galaxy. Two groups of particle physicists working on dark matter heard his talks and joined with astronomers to form the Anglo-Australian MACHO collaboration and the French EROS collaboration. In 1991 Mao and Paczyński suggested that microlensing might be used to find binary companions to stars, and in 1992 Gould and Loeb demonstrated that microlensing can be used to detect exoplanets. In 1992, Paczyński founded the OGLE microlensing experiment, which began searching for events in the direction of the Galactic bulge.

The first two microlensing events in the direction of the Large Magellanic Cloud that might be caused by dark matter were reported in back to back Nature papers by MACHO and EROS in 1993, and in the following years, events continued to be detected. The MACHO collaboration ended in 1999. Their data refuted the hypothesis that 100% of the dark halo comprises MACHOs, but they found a significant unexplained excess of roughly 20% of the halo mass, which might be due to MACHOs or to lenses within the Large Magellanic Cloud itself. EROS subsequently published even stronger upper limits on MACHOs, and it is currently uncertain as to whether there is any halo microlensing excess that could be due to dark matter at all. The SuperMACHO project currently underway seeks to locate the lenses responsible for MACHO's results.

Despite not solving the dark matter problem, microlensing has been shown to be a useful tool for many applications. Hundreds of microlensing events are detected per year toward the Galactic bulge, where the microlensing optical depth (due to stars in the Galactic disk) is about 20 times greater than through the Galactic halo. In 2007, the OGLE project identified 611 event candidates, and the MOA project (a Japan-New Zealand collaboration) identified 488 (although not all candidates turn out to be microlensing events, and there is a significant overlap between the two projects). In addition to these surveys, follow-up projects are underway to study in detail potentially interesting events in progress, primarily with the aim of detecting extrasolar planets. These include MiNDSTEp, RoboNet, MicroFUN and PLANET.>>
Art Neuendorffer

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### Re: How many jellybeans are in this jar?

Chris Peterson wrote:
BDanielMayfield wrote:Good. As in my comment to Rob, I think “the observable universe” in this question can be defined as ‘all galaxies within our present limits of observation, as they are at the present.’ Thus for the purposes of this discussion we can consider the entire observable universe to be of the same age, and we wouldn’t have the complication of needing to consider earlier conditions.
The term "observable universe" is already defined. We should use it properly, or pick a different expression. The observable universe is not what we are able to observe given our technology, but what is actually observable in principle. It is defined by the horizon created by space moving away from us at greater than c. Although we can see nearly to this horizon, there still remains a narrow zone that we can't see (for technological reasons) and in which we would expect planets to exist.

My point with age is that we don't see the entire universe as having the same age. We observe very distant galaxies as they were when very young. As Ann pointed out, these are metal poor, and may not have any planets. But those exact same galaxies still exist now, and are no longer metal poor, and certainly are full of planets. That's why we need to be careful in our count. Is the question "how many planets are observable" or "how many planets are in the observable universe"? Because these will yield very different values.
Thanks for your help in carefully framing this question. I would want to use the correct, scientifically understood definition of “observable universe.” I’m glad to have my understanding of this term improved.

I understand that we cannot literally “see” the entire universe as having the same age, but on the grounds of the Copernican principle can’t we assume that all that “is actually observable in principle” can be expected to have evolved along the same path as our local region of the universe has? Can’t we then use the local density of galaxies as a representative sample of the galactic density everywhere inside our observable radius?

Since my goal was to seek an approximation for ALL the planets that might reasonably be in existence I would want to phrase the question as “How many planets are in the observable universe?” and not “How many planets are observable?”
But like Ann I wonder, how big would an object need to be to meet this test? I know that it depends both on mass and on composition, but wouldn’t this definition cause there to be a large number of “planets” in our solar system? (Not that that’s a problem, we all know how to count higher than 10.)
Actually, the composition isn't very important (outside of some exotic special cases). Any body that masses about 1020 kg will assume an approximately spherical shape. There are about 40 such bodies observed in the Solar System, and perhaps 150 or so which can be assumed to exist based on statistical arguments.

This is great information Chris, providing a definable lower limit for planets in this discussion, namely round bodies with masses of more than approximately 10^20 Kg. Of those figures, about how many are moons, since by definition moons aren’t planets?
Personally, I have no problem considering them all planets.
Agreed. Let ‘em in. The more the merrier.

Bruce
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### Re: How many jellybeans are in this jar?

BDanielMayfield wrote:I understand that we cannot literally “see” the entire universe as having the same age, but on the grounds of the Copernican principle can’t we assume that all that “is actually observable in principle” can be expected to have evolved along the same path as our local region of the universe has? Can’t we then use the local density of galaxies as a representative sample of the galactic density everywhere inside our observable radius?
Generally, I think so (but "local" may still need to be quite a large volume to account for the odd structure of the Universe on a large scale). If we ask the question this way, we are essentially ignoring our observations of distant galaxies and simply assuming that any given volume of the Universe (which may be the observable universe, or it may be anything else) currently contains X planets. I actually like this approach, as a density seems more useful than an absolute count.
This is great information Chris, providing a definable lower limit for planets in this discussion, namely round bodies with masses of more than approximately 10^20 Kg. Of those figures, about how many are moons, since by definition moons aren’t planets?
19 of the bodies are satellites. Maybe a few more given that there's a gray area in terms of bodies that were once in hydrostatic equilibrium but are no longer. But in any case, the vast majority orbit the Sun and presumably formed in orbit around the Sun (or the proto-Sun).
Chris

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### Re: How many jellybeans are in this jar?

Chris Peterson wrote:
BDanielMayfield wrote:I understand that we cannot literally “see” the entire universe as having the same age, but on the grounds of the Copernican principle can’t we assume that all that “is actually observable in principle” can be expected to have evolved along the same path as our local region of the universe has? Can’t we then use the local density of galaxies as a representative sample of the galactic density everywhere inside our observable radius?
Generally, I think so (but "local" may still need to be quite a large volume to account for the odd structure of the Universe on a large scale). If we ask the question this way, we are essentially ignoring our observations of distant galaxies and simply assuming that any given volume of the Universe (which may be the observable universe, or it may be anything else) currently contains X planets. I actually like this approach, as a density seems more useful than an absolute count.
This is great information Chris, providing a definable lower limit for planets in this discussion, namely round bodies with masses of more than approximately 10^20 Kg. Of those figures, about how many are moons, since by definition moons aren’t planets?
19 of the bodies are satellites. Maybe a few more given that there's a gray area in terms of bodies that were once in hydrostatic equilibrium but are no longer. But in any case, the vast majority orbit the Sun and presumably formed in orbit around the Sun (or the proto-Sun).
Thank you again Chris. So now let me rephrase my question now that I have more precise definitions in mind:

How many bound and unbound planets are contained in the entire known universe?

By “bound” I mean in orbit of a brown dwarf, a star, a stellar remnant or a multiple system of such stellar objects.

“Unbound” means formerly in orbit of a stellar or proto-stellar system. (Or, is it possible that some unbound planet sized bodies may have formed on their own outside proto-stellar systems?)

“Planet” means a natural astrophysical body in hydrostatic equilibrium which is not in orbit of a similar body in the mass range from 10^20 kg up to 13 Jupiters.

By “entire known universe” I mean everything that is observable in principle. (How large would this radius be, btw?)

Bruce
Just as zero is not equal to infinity, everything coming from nothing is illogical.