# How much does a cubic AU of the Solar System weigh? **URL:** \ **Category:** Factual Questions\ **Created:** [March 1, 2000, 7:37pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030 "2000-03-01T19:37:00Z")\ **Posts on this page:** 19\ **Page:** 1
**Author:** ![Ursa\_Major](https://avatars.discourse-cdn.com/v4/letter/u/a88e57/32.png) [@Ursa\_Major](https://boards.straightdope.com/u/Ursa_Major)\ **Post date:** [March 1, 2000, 7:37pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/1 "2000-03-01T19:37:00Z")
Okay, I know this is a silly question but I made a rash statement about how “empty” most of the Solar System is. Without any evidence I stated that, with proportional representation, you could fit the mass of one cubic AU of the Solar System into a child’s balloon. I further pontificated that the balloon would float (in 1G), because so much of the Solar System is hydrogen and helium. Unfortunately, I got called on it. Apparently my bullshit isn’t as edible as it once was, because someone said, “Prove it!” I’m guessing that to prove this I need to first figure out how many cubic AUs there are in the Solar System, then find out how much mass there is, and how much of that mass is lighter than air…and then comes the math…and I suck at math. Is there anybody out there who will take pity on a know-it-all and come up with some numbers? ---
**Author:** ![Nen](https://avatars.discourse-cdn.com/v4/letter/n/c5a1d2/32.png) [@Nen](https://boards.straightdope.com/u/Nen)\ **Post date:** [March 1, 2000, 7:51pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/2 "2000-03-01T19:51:00Z")
Ursa Major, lucky for you I’ve got all the numbers to work with and education to use 'em, but the numbers are at home. I’ll get the figures tonight. ---
**Author:** ![gEEk](https://avatars.discourse-cdn.com/v4/letter/g/ed8c4c/32.png) [@gEEk](https://boards.straightdope.com/u/gEEk)\ **Post date:** [March 1, 2000, 8:42pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/3 "2000-03-01T20:42:00Z")
Ok, here we go: ``` Mass of the solar system: Sun = 1.99x10^30 kg Mercury = 3.3 x10^23 kg Venus = 4.9 x10^24 kg Earth = 6 x 10^24 kg Mars = 6.4 x 10^23 kg Jupiter = 1.9 x 10^27 kg Saturn = 5.7 x 10^26 kg Uranus = 8.7 x 10^25kg Neptune = 1 x 10^26kg Pluto = 1.3 x 10^22 kg Total = 1.993 x 10 ^30kg We could have ignored everything but the Sun, but hey, let's try to be accurate. Volume of the Solar System: Let's use the maximum distance from Pluto to the Sun as the radius of the Solar System: 39.53AUs ``` So the volume of the Solar System assuming it’s spherical is: ``` 259000 cubic AUs So, the average density of the solar system is: 1.992x10^30kg ------------------ = 7.69x10^24 kg/cubic AU 259000 cubic AUs Oops, I don't think we can fit 7.69x10^24 kilograms in a balloon. ``` Ok, so let’s be generous and use the distance to the Oort cloud as the radius of the Solar System. That distance is 40,000 AU so the volume becomes: ``` 2.68 x 10^14 cubic AUs So now the average density is: 7.43 x 10^15 kg/cubic AU ``` Not much better. ``` I think a retraction may be in order. gEEk ``` ---
**Author:** ![Ursa\_Major](https://avatars.discourse-cdn.com/v4/letter/u/a88e57/32.png) [@Ursa\_Major](https://boards.straightdope.com/u/Ursa_Major)\ **Post date:** [March 1, 2000, 9:18pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/4 "2000-03-01T21:18:00Z")
Damn! Does anybody know how big the largest balloon in the world is? There must be some way I can weasel my way through this delemma without admitting I don’t know what I’m talking about. (Note to self: Stick to the social sciences from now on!) ---
**Author:** ![douglips](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@douglips](https://boards.straightdope.com/u/douglips)\ **Post date:** [March 1, 2000, 10:36pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/5 "2000-03-01T22:36:00Z")
Ursa, you are wrong in so many ways. Even if you wanted to be talking about the empty part of the solar system (i.e. just the solar wind & dust) you are completely off the mark. This site ([http://itss.raytheon.com/cafe/qadir/q1734.html](http://itss.raytheon.com/cafe/qadir/q1734.html)) gives a density of 10 atoms per cm\3\ of space. Let’s assume it’s all hydrogen. 6.022x10\23\ is Avogadro’s number, the number of atoms that weigh n grams where n is the atomic number of the atoms. So, for hydrogen, 6.022x10\23\ atoms weigh 1 gram. **How many atoms in a cubic AU?** [ul][li]1 AU\3\ = (9.3x10\7\ )\3\ miles\3\ = 8x10\23\ miles\3\.[/li][li]1 mile = 1609 meters, so 1 mile\3\ = 4.2x10\9\ m\3\.[/ul][/li] Do you see how badly this is going for you? [ul][li]1 AU\3\ = 3.36x10\33\ m\3\.[/li][li]1 m\3\ = 1x10\6\ cm\3\.[/li][li]Thus, 1 AU\3\ = 3.36x10\39\ cm\3\[/li][li]So, at 10 atoms per cm\3\, that’s 3.36x10\40\ atoms per AU\3\.[/ul][/li] **How much mass is that?** [ul][li]Getting back to Avogadro, that means there are 5.4x10\16\ moles of atoms per AU\3\.[/li][li]Assuming hydrogen, that’s 5.4x10\16\ grams.[/li][li]That’s 5.4x10\13\ kg.[/ul][/li] **What does that mean to me and my balloon analogy?** [ul][li]For scale, let’s take 5.4x10\13\ kg of water. That’s 5.4x10\13\ litres.[/li][li]This site ([http://shookweb.jpl.nasa.gov/validation/US/LakeTahoe/Default.htm](http://shookweb.jpl.nasa.gov/validation/US/LakeTahoe/Default.htm)) gives a volume of 156 km\3\ for Lake Tahoe.[/li][li]156 km\3\ is 1.56x10\11\ m\3\. There are 1000 litres in 1 m\3\, so that’s 1.56x10\14\ litres.[/li]Your balloon needs to be about 1/3 the size of Lake Tahoe.[/ul] ---
**Author:** ![douglips](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@douglips](https://boards.straightdope.com/u/douglips)\ **Post date:** [March 1, 2000, 10:37pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/6 "2000-03-01T22:37:00Z")
Doh! All my superscripts are totally broken. Sorry 'bout that. The conclusion is still valid, though. ---
**Author:** ![Ursa\_Major](https://avatars.discourse-cdn.com/v4/letter/u/a88e57/32.png) [@Ursa\_Major](https://boards.straightdope.com/u/Ursa_Major)\ **Post date:** [March 1, 2000, 10:41pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/7 "2000-03-01T22:41:00Z")
That’s okay, Doug. I understood the “1/3 the size of Lake Tahoe” part. What’s the best way to cook crow? ---
**Author:** ![MrKnowItAll](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrknowitall/32/87_2.png) [@MrKnowItAll](https://boards.straightdope.com/u/MrKnowItAll)\ **Post date:** [March 1, 2000, 10:45pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/8 "2000-03-01T22:45:00Z")
I’ve always preferred breaded and fried, with a nice lemon sauce. * * * _When someone annoys you it takes 42 muscles to frown. But it takes only 4 muscles to extend your arm and whack them in the head._ ---
**Author:** ![AHunter3](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ahunter3/32/368_2.png) [@AHunter3](https://boards.straightdope.com/u/AHunter3)\ **Post date:** [March 1, 2000, 10:49pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/9 "2000-03-01T22:49:00Z")
You could claim that you did not (of course) mean to be including the sun itself, that you were referring to the collection of things that orbit it and the space in between them. That brings your average density down to a mere 7.4626 x 10^12 kg/AU^3, relying upon gEEk’s figures for radius and mass. Hmm…hope you’ve got some awfully durable mylar on hand. * * * Disable Similes in this Post ---
**Author:** ![SoulFrost](https://avatars.discourse-cdn.com/v4/letter/s/f07891/32.png) [@SoulFrost](https://boards.straightdope.com/u/SoulFrost)\ **Post date:** [March 1, 2000, 11:25pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/10 "2000-03-01T23:25:00Z")
Ahhh, Ursa–you know you’re right. All you have to do is assume that the Crystal Spheres theory was correct after all, and _viola!_ you have a balloon the size of the solar system. Ummm…wait–that way lies Phaedrus… I guess that slow-roasting might tenderize that crow. -David ---
**Author:** ![WallyM7](https://avatars.discourse-cdn.com/v4/letter/w/b5e925/32.png) [@WallyM7](https://boards.straightdope.com/u/WallyM7)\ **Post date:** [March 1, 2000, 11:49pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/11 "2000-03-01T23:49:00Z")
A good Zip program can reduce the volume by at least 50%. * * * I’m the poster you’d most like to meet. Please don’t tell me why. ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [March 1, 2000, 11:52pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/12 "2000-03-01T23:52:00Z")
I would fall back on the “prove I’m wrong” defense, and while they’re busy with their pocket calculators, make a quick dash for the exit. When people later remind you of the conversation, deny ever having said anything on that subject. ---
**Author:** ![Lord\_Jim](https://avatars.discourse-cdn.com/v4/letter/l/ecccb3/32.png) [@Lord\_Jim](https://boards.straightdope.com/u/Lord_Jim)\ **Post date:** [March 2, 2000, 2:20am UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/13 "2000-03-02T02:20:00Z")
It would seem to me, that with the help of a co-operative Black Hole, you could hang your balloon on the tail end of it and suck the whole solar system up and cram it in the balloon. Now, you are going to need some help carrying the thing around, but it should fit. You’ll have to back down on the floating part, though. ---
**Author:** ![The\_Ryan](https://avatars.discourse-cdn.com/v4/letter/t/7feea3/32.png) [@The\_Ryan](https://boards.straightdope.com/u/The_Ryan)\ **Post date:** [March 2, 2000, 5:34am UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/14 "2000-03-02T05:34:00Z")
Was this on this message board? You could be a total weasel and claim that the hacker used your password to impersonate you. ---
**Author:** ![Ursa\_Major](https://avatars.discourse-cdn.com/v4/letter/u/a88e57/32.png) [@Ursa\_Major](https://boards.straightdope.com/u/Ursa_Major)\ **Post date:** [March 2, 2000, 5:44am UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/15 "2000-03-02T05:44:00Z")
> [@](#): > > Was this on this message board? No, I made this comment to co-workers, in real life. I’ve already 'fessed up. They were very magnanimous; they didn’t make me eat the beak. ---
**Author:** ![MrKnowItAll](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrknowitall/32/87_2.png) [@MrKnowItAll](https://boards.straightdope.com/u/MrKnowItAll)\ **Post date:** [March 2, 2000, 6:18am UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/16 "2000-03-02T06:18:00Z")
Hey! I’ve got it! Like any good know-it-all, MrKnowItAll may have a way out. Okay. The nearest system to us is Alpha Centauri, right? If I recall correctly (remember, I’m a musician, not an astronomer) AC is 4 lightyears away. _That gives the solar system a sphere with a 2 light year radius!_ Now, doing a little math… (Someone else, I mean. I’m already up too late.) * * * _When someone annoys you it takes 42 muscles to frown. But it takes only 4 muscles to extend your arm and whack them in the head._ ---
**Author:** ![MrKnowItAll](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrknowitall/32/87_2.png) [@MrKnowItAll](https://boards.straightdope.com/u/MrKnowItAll)\ **Post date:** [March 3, 2000, 12:09am UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/17 "2000-03-03T00:09:00Z")
Okay. Since no one else has had a go at this, I’ve given it a shot. It’s probably wrong, but I come up with a mere 11 grams of mass per cubic AU, if you extend the system out to 2 LYs. If that’s right, it should fit in a ballon, no problem, though I don’t think it will float. As previously stated, I’m a musician, not a mathemetician. * * * _Now with 1000 posts of pure wisdom!_ (or something) ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [March 3, 2000, 1:43pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/18 "2000-03-03T13:43:00Z")
> [@](#): > > Originally posted by Ursa Major: > **Without any evidence I stated that, with proportional representation, you could fit the mass of one cubic AU of the Solar System into a child’s balloon.** Along with a list of other errors, let’s look at your basic premise! A cubic AU is a measurement of volume - period. How do you propose to fit (93 million miles)^3 into a child’s balloon? Must be BIG baby! Talk about ebing “larger than life”! When this BABY sits around the house…whoa! * * * “They’re coming to take me away ha-ha, ho-ho, hee-hee, to the funny farm where life is beautiful all the time… :)” - Napoleon IV ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [March 3, 2000, 1:44pm UTC](https://boards.straightdope.com/t/how-much-does-a-cubic-au-of-the-solar-system-weigh/8030/19 "2000-03-03T13:44:00Z")
Oops! My apologies! I goofed and read too fast! I missed the key word “mass” and made a big mass of myself! :o * * * “They’re coming to take me away ha-ha, ho-ho, hee-hee, to the funny farm where life is beautiful all the time… :)” - Napoleon IV