I'm trying to work out the best way of expressing the rate of energy generation in the Sun.
As you may know, the average rate of energy generation per cubic metre on the Sun's core is less than that generated in a well maintained compost heap; and the reason the sun glows is because it's really big.
But how big? In numerical terms the core generates from a volume that's about 10^25 m³ so
is it better to say
Ten trillion trillion
or
Ten thousand billion trillion
or
Ten million million million million
or what?
Re: Big numbers..
Posted: Sun Sep 10, 2023 10:54 pm
by dyqik
Solar luminosity is the number you are looking for, at 3.83 10²⁶ W, or 91 billion Megatons TNT per second.
And the best way to write the volume is as 10²⁵ m³.
The next best is as 1.3 million Earth volumes.
Re: Big numbers..
Posted: Mon Sep 11, 2023 7:05 am
by Boustrophedon
.
That's 1029 bananas.
Re: Big numbers..
Posted: Mon Sep 11, 2023 7:24 am
by tenchboy
For the beloved memory of Carl Sagan the correct expression Is Billions of Billions of Trillions.
1 cubic km is 1 billion cubic metres. So 1025 m3 is 1016 cu km. At least 10,000 trillion cubic km can be spoken. But I don't think it aids comprehension. I can't easily envision a volume like that.
I think it is easier to understand that the sun's core is a sphere with diameter approx 300,000 km or radius of 150,000 km. If you want a comparator for that, the earth-moon orbital system is useful, as the moon orbits with an average radius of about 380,000 km. So it's about 40% (linearly) of the sphere implied by the Earth-Moon orbital disk, though only about 5% of the volume of that because that's what happens when you cube things.
The compost heap comparison requires averaging the output over the whole volume of the sun.
Someone was saying that they had a problem envisioning a compost heap of 1 cu km. I was standing on a fjord bank about 1000m above the fjord in Norway about 3 weeks ago. It's about 1km from my house to the end of the road. OS maps have 1km squares printed on them. So I think I can picture sizes like 1 sq km and 1 cu km. Darn sight more easy than acres which are 640 to the sq mile.
Re: Big numbers..
Posted: Mon Sep 11, 2023 7:02 pm
by KAJ
"the best way of expressing" depends on the audience. Most people here are happy with power notation. I guess most of the general population are not.
I mean with the cubic metres, you're getting most of the way to a mole of cubic metres which is just a silly use of Avogadro's number
A mole of moles would only be about the size of the moon - clicky.
From that clicky, "a mole is ... really just a number". Wish I'd known that when I was 14, newly introduced to chemistry. The teacher would continually rattle through the formal definition of a mole whenever someone asked, and it just came over as word salad (though I did notice it always seemed to be the same quantity). Because of this I was relieved I soon had the opportunity to give up this awful subject with its arbitrary rules.
I mean with the cubic metres, you're getting most of the way to a mole of cubic metres which is just a silly use of Avogadro's number
A mole of moles would only be about the size of the moon - clicky.
From that clicky, "a mole is ... really just a number". Wish I'd known that when I was 14, newly introduced to chemistry. The teacher would continually rattle through the formal definition of a mole whenever someone asked, and it just came over as word salad (though I did notice it always seemed to be the same quantity). Because of this I was relieved I soon had the opportunity to give up this awful subject with its arbitrary rules.
Of course, I'm slightly contradicting myself because if he'd simply said a mole is <this big number> then that would have been even more apparently arbitrary than a definition. Even so, I always felt chemistry was an arbitrary subject because it seemed so unpredictable (add X to Y and it's self-evident that you get Z, but if you add Y to X then obviously get something else entirely etc.). Maybe the last straw was his response to a homework answer: Spoiler: