# BAFact Math: Jupiter is big enough to swallow all the rest of the planets whole

By Phil Plait | August 22, 2012 9:46 am

[BAFacts are short, tweetable astronomy/space facts that I post every day. On some occasions, they wind up needing a bit of a mathematical explanation. The math is pretty easy, and it adds a lot of coolness, which I'm passing on to you! You're welcome.]

Today’s BAFact: Jupiter is so big you could fit every other planet in the solar system inside it with room to spare.

Volume is a tricky thing. Our brains are pretty good at judging relative linear sizes of things: this thing is twice as long as that thing, for example. But volume increases far more rapidly than linear size. Take a cube where each side is one centimeter. It has a volume of one cubic centimeter (cc). Now double the length of each side to 2 cm. It looks twice as big, but its volume goes up to 8 cc! The volume of a cube is a the length x width x height, so there you go.

Spheres are the same way: the volume increases with the cube of the radius. Specifically, volume = 4/3 x π x (radius)3. So one sphere might look slightly larger than another, but in fact have a lot more volume.

Such is the way of Jupiter. I see pictures of it compared to the other planets, and honestly Saturn looks only slightly smaller – Saturn’s radius is about 60,000 km compared to Jupiter’s 71,000. But that turns out to make a huge difference in volume!

Here’s a table I created to compare the planets. The first number column is the planet’s equatorial radius in kilometers (the biggest planets aren’t perfect spheres, but as you’ll see this doesn’t matter). The second number column is the volume in cubic km based on that radius. The third is the volume of the planet divided by the volume of Jupiter (so that ratio = 1 for Jupiter itself). The last column is the same, but rounded to two decimal places to make it easier to read.

The big conclusion here is pretty obvious when you look at that last column. Even though Saturn is only a little smaller than Jupiter, it only has 60% of the big guy’s volume! Uranus and Neptune together are only another 9%. If you combine all the planets in our solar system, they add up to only about 70% of Jupiter’s volume. That leaves a lot of room left over for all the moons and asteroids in the solar system, too!

So Jupiter really is a monster. There’s a half-joke astronomers say: The solar system consists of the Sun, Jupiter, and assorted rubble. As you can see, that’s really not that far off from the truth!

Image credit: NASA

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MORE ABOUT: BAFacts, Jupiter, math, Saturn, volume

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1. Jamie

Jupiter has enough volume to fit the sum of the volumes but I don’t think you could fit the planets themselves in there simply due to Saturn + Neptune (or Uranus) radius > Jupiter radius.

2. a_lex

It will fit only if you destroy the planet first. There is not much space left if you put Saturn as a sphere.

3. Kkozoriz

Jupiter would have to chew up the other planets. It couldn’t swallow them whole.

4. There’s a half-joke astronomers say: The solar system consists of the Sun, Jupiter, and assorted rubble.

Could be mistaken but wasn’t that an Isaac Asimov quote originally?

5. Alan

So we’re including Pluto, then, in that list of planets.

6. Gus Snarp

So if the planets were thin shells filled with liquid, then all the liquid in the other planets could fit inside Jupiter if it were just the shell. Or you could chop all the planets up and fit them inside a hollow Jupiter. But you couldn’t actually fit them all in whole at once, right?

7. Nick D

As they’ve stated before, that wouldn’t work. In order to do that, Saturn and Neptune would have to touche horizontally. Their added radii exceed that of Jupiter’s.

8. Daniel

You’d have difficulties shoving them all “in” Jupiter whole if every planet was rocky…but they arent. I’d say it’s quite likely that all the planets could be physically pushed together and fill a space no larger than Jupiter’s size.

9. Reminds of a pig´s entrails. The whole pig (meat that is) will fit in it, making a nice ausage.

10. Brian

Messier Tidy Upper:

The Asimov quote that you’re thinking of was slightly different, if memory serves. As I remember, it was: “The solar system consists of four planets (plus various bits of rubble).” His point was more that the terrestrial planets are so different in nature than the gas giants, it’s not clear that they should be identified with the same word.

11. Gridlore

Good thing we appease Jupiter with the occasional sacrificial comet!

12. Blaise Pascal

If you dump all of the other planets and dwarf planets into Jupiter, it would only be 20% larger in diameter.

However, it would be much brighter in the sky, since the Earth would be in it.

13. Chris

And the Sun could hold 920 Jupiters!

14. Chris

I hate to add this but all the terrestrial planets would fit inside Uranus, at least according to this http://space-facts.com/the-planets-to-scale/

15. Infinite123Lifer

@Chris – I was looking for that. I went to Wolfram Alpha and typed in volume of sun/volume of jupiter and its said 990. Curiously even number that is. So I tried using 1.409 x 10^18 km^3 for the Sun and 1.43128 x 10^15 km^3 for Jupiter and using Wolfram again got 984.4335 . . . So I thought there surely has to be some play in the volumes so I checked the NASA Facts & Figures pages, the volume is listed as Metric: 1,409,272,569,059,860,000 km3 (Sun) and Metric: 1,431,281,810,739,360 km3(Jupiter) . . . simply dividing those two numbers yields 984.6227 . . .

So would it be more like 980 Jupiters? Or is there some play being allotted here somewheres?

16. It seems the solar system actually consists of the Sun .. and some assorted rubble

17. Thomas Siefert

Sometimes a sight, sound or smell triggers a distant memory and reminds you of something completely unrelated.
This one is straight forward, I feel like playing Pacman now.

18. Manimal

Interestingly (at least to me), the combined volume of Mercury, Venus, and Mars exceeds that of Earth by only (approximately) 6%.

Combined volume of Mercury, Venus, and Mars: 1.153e+12
Volume of Earth: 1.09e+12
Ratio: 1.0578

19. Valdis Kletnieks

Actually, there’s 2 things to consider:

1) Since the definition of “planet” includes “enough gravity to form itself into a sphere”, that *also* implies that if you put 2 of them next to each other and touching, they’d probably collapse and form a bigger sphere (unless you get something *really* bizarre like Robert Forward’s Rocheworld). So if you put Saturn right next to Uranus, you’d get one big sphere with (0.60+0.05) the volume of Jupiter.

2) Jupiter is actually about as big as a planet can get – if you were to dump Saturn in there, you’d *not* get a bigger planet with (1.0+0.6) times the Jupiter volume. That’s because the added mass will cause greater pressure in the core, and it will compact down even further while keeping the same volume. That holds true until it gets massive enough to start fusion at the core, at which point the fusion energy will push back and allow a larger radius again.

20. ND

My mom always said to stay away from Jupiter. “Don’t get anywhere close to that planet. Nothing good will come of it.”

21. Dragonchild

3. Kkozoriz Says:
“Jupiter would have to chew up the other planets. It couldn’t swallow them whole.”

Probably the best way to put it. If Jupiter was a hollow shell it could hold all the other planets, but it’d have to chew before swallowing.

It’s also more massive than all the other planets combined, and IIRC in this case it’s not even close.

22. Cat

And when you consider mass alone, Jupiter’s ‘superiority’ is even greater still – by a ratio of about 317 to 130, or 41% using the same metrics as in the volume comparison.

23. mike burkhart

Ok but the Sun is big enough to swallow all the palnets and Jupiter and have enough room for the Asteroids,miniplanets,and a few Comets.Of couse the Sun would fry all this so it would never be full.

24. Prof. Hubert Farnsworth

@Chris, (#15) I’m sorry, but they changed the name back in the 2600s to put an end to that stupid joke, once and for all. It’s now called “Urectum.”

On a slightly less foolish note, Valdis, I thought I’d seen our Phil state that fusion starts at around eighty times Jupiter’s mass. If so, you’d need, what, a hundred-thirty Saturns?

25. rompompom

@mike (#24) The Sun is 99,8% of the mass in the Solar System… there would be a lot of free space left even if you add every single grain from it.

26. Mark Joseph

@Phil, #4, #10:

The quote from Asimov, with source (courtesy of Wikiquote):

“Outside intelligences, exploring the Solar System with true impartiality, would be quite likely to enter the Sun in their records thus: Star X, spectral class G0, 4 planets plus debris.”
“By Jove!” in View from a Height (1963); often misquoted as “Jupiter plus debris”.

27. amphiox

re @19;

So if you add the moon, earth wins?

re @20;

You know what #2 implies? That the smallest stars and largest planets (and all brown dwarfs) will all be roughly the same size!

Just imagine observing a transit of a system with a Jupiter mass planet around a 80J red dwarf!

28. Gary Ansorge

“There’s a half-joke astronomers say: The solar system consists of the Sun, Jupiter, and assorted rubble”

Yes, but it’s such USEFUL rubble. We could build another 3000 earths with that “stuff”…So much room for dolphins and whales and bears…oh my…

Gary 7
Oh yeah, and people too…

29. Infinite123Lifer

Man Jupiter is epic. I was just thinking about how Jupiter was so close to becoming a star but never made it. Then I started thinking maybe some day in the astronomical future Jupiter might have its chance to become a star. So I started a quick look around and I am kinda hoping to find out if anybody knows of any books fiction or non-fiction that have been written about the distant future of our solar system.

http://en.wikipedia.org/wiki/Formation_and_evolution_of_the_Solar_System

I scrolled down to “Timeline of Solar System evolution”. If the solar system can survive the merger with Andromeda I like the idea of Titan becoming habitable. Life can be so cool! I mean sure, we could have had like x amount of like earths in our own system but to have Mars, essentially like a kick-starter planet and massive Jupiter and the different moons . . . well, some coincidence. I guess you might think to find well evolved planets like the Earth in places that were far from anywhere but when your in space whats anywhere? Well, others have pondered the future and the times more poetically.

30. Nigel Depledge

Jamie (1) said:

Jupiter has enough volume to fit the sum of the volumes but I don’t think you could fit the planets themselves in there simply due to Saturn + Neptune (or Uranus) radius > Jupiter radius.

However, if you were to place Saturn and Neptune in atmosphere-to-atmosphere contact, their mutual gravitational attraction would cause them to merge and form one slightly larger planet. And this amalgamation would indeed fit within Jupiter’s diameter.

31. Infinite123Lifer

Compared to Earth, Jupiter’s equatorial circumference is approximately 11 times larger but the surface area of Jupiter is approximately 120 times more.

32. amphiox

Man Jupiter is epic.

Thinking seriously about how stupendous Jupiter is boggles the mind. And then you realize that there are exoplanets out there that are 10 times more massive and behemoths 2-5X more massive are are not that rare, and the boggle gets boggled.

I was just thinking about how Jupiter was so close to becoming a star but never made it.

Well, not really that close. Getting only to 1/80th of the way, via a formation mechanism that probably never gave it a chance of getting that much bigger anyways, isn’t really THAT close….

Then I started thinking maybe some day in the astronomical future Jupiter might have its chance to become a star.

That will take intelligent intervention. And assuming that the Monolith builders of 2001 don’t actually exist, it will have to be us humans….

33. Messier Tidy Upper

@27. Mark Joseph : That’s the quote I meant. Cheers!

@10. Brian : Yep.

@12. Blaise Pascal : Very True. LOL. Although given how cloudy it’d make our skies as a consequence – not to mention toxic and inflammable – it’d be hard to see it!

34. Infinite123Lifer

“and the boggle gets boggled.”

Me goggles are fogged, wait that’s better, um okay, well If you took Jupiter and you doubled it or tripled up until the point where we began to obtain a low mass star (my understanding of the following:

http://exoplanet.eu/catalog/all_fields/

http://en.wikipedia.org/wiki/Brown_dwarf

) then that number of Jupiter’s is somewhere around 80Mj (I take it that is Jupiter Masses). . . where we get a mass high enough to sustain hydrogen-1 fusion core reactions.
This fusion reaction in the core is a characteristic of a possible low mass star. I say possible because we are currently a bit unaware as to whether a planet will phase in and out of the hydrogen to helium fusion? At which point a brown dwarf may become a star. One thing to consider with this hypothetical experiment is that I have 80 Jupiter’s and not a mix of 80 different worlds with different make-ups, though I don’t claim to know if that is that important.

I see deuterium does fuse at amphioximately 13 Mj and lithium somewhere around 65 Mj in some brown dwarfs or giant planets. How to distinguish between planets and stars?

The idea that to become a star . . . assuming the planet is struggling to make its way to becoming a star and not just raging with conditions (density, mass, material) sufficient for h fusion, assuming that this planet is roiling, spinning, collapsing and pushing out on itself in its attempt to find equilibrium in becoming a star or resisting the starry Life that at the point of fusion it just might not turn right on . . . the planet being in an immense struggle to collapse on itself and to fuse hydrogen that maybe a tug-o-war between fusion and collapse begins thus giant planets sometimes have to mature awhile maybe. We have this giant planet – going – star.

And now we have to go to the Hertzsprung-Russell diagram? Ok to see the main sequence we have to look at this plot. A plot of 22,000 stars and it is named Hertzsprung-Russell? So

http://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram

So this diagram of some stellar evolution shows us some things which right now I am thinking how long am I going to have to contemplate this diagram in order to understand it but a quick analysis has me guessing that all different types of sizes planets form into stars many many different ways at different points in their lifetime. Well, I guess that is what I would expect, an unbelievably believable set of criteria which form magnificent stellar objects and do big things. Skimming around I see all the labels from the graph. Labels are good.

Argh, me goggles are foggin

“Well, not really that close. ”

Yup, I guess about 80 Jupiter’s is about the lowest for hydrogen fusion at the core and I wonder if that changes with differently layered gas giants…if they are layered at all. I wonder how long it takes for the surface go through its evolution to a star…I am guessing they need material to continue.Even at 80 Jupiter masses we are still close to 1/900 of the Sun or somewhere in there. It is interesting to think an object that much smaller than the sun might become a star and or die as one. How
could you not love this stuff.

And amphiox I am going to “intervene” on Jupiter approximately how? Though when it comes to stars Jupiter has a long ways to go compared to us humans . . . well, maybe jus’ maybe an intervention will be inline…in 10 billion years or so when we are not even the milky way galaxy anymore and the dust from this screen has been reused in more ways than I have keyboard skills to explain, possibly in Jupiter I suppose that is one way humans might intervene on Jupiter, although I don’t think the solar system evolution models show it happening that way.

35. JOel

This is why I unexpectedly run out of TP, isn’t it?

36. Jonathan Ray

Smushing Uranus and Neptune into different shapes is sort of cheating. Either one’s diameter plus the diameter of Saturn is bigger than the diameter of Jupiter.

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