Big numbers..

[Gfamily]

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?

[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.

[Boustrophedon]

.
That's 10²⁹ bananas.

[tenchboy]

For the beloved memory of Carl Sagan the correct expression Is Billions of Billions of Trillions.

[Grumble]

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.

The way the volume renders in my browser it looks like 10 squared to the power of 5

[science_fox]

Is it any more sensible in cubic km?

[dyqik]

.
That's 10²⁹ bananas.

Next question: how close do you have to stand to the sun to receive a radiation dose equal to 10²⁹ bananas?

[dyqik]

The astronomical way of writing the power (mass) density of the sun is 1.

In units of L_sun/M_sun

[Gfamily]

Is it any more sensible in cubic km?

I can imagine a 1 cubic metre compost heap, I can't imagine a 1 cubic km compost heap.

Though I like the idea of saying "think of a compost heap the size of the earth - now think of 10,000 of them" *

* reduced from 1.3M because only considering the core of the Sun.

[dyqik]

Is it any more sensible in cubic km?

I can imagine a 1 cubic metre compost heap, I can't imagine a 1 cubic km compost heap.

Though I like the idea of saying "think of a compost heap the size of the earth - now think of 10,000 of them" *

* reduced from 1.3M because only considering the core of the Sun.

I think the compost heap thing is only true for the whole volume of the Sun: 3.8 10²⁶/1.4 10²⁴ is 270 W/m³.

The core is 60-125 times smaller in volume, so has a power density of ~25 kW/m³ if all the power is generated there.

The continued existence of my garage confirms that my 1 cu yd compost heap doesn't reach 25 kW/m³

[IvanV]

Is it any more sensible in cubic km?

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.

[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.

[dyqik]

"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.

Yes. However, some numbers are so unbelievably vast that power notation is the only unambiguous option. Otherwise you end up describing things like a peanut in Reading, etc. (©D. Adams)

[jimbob]

"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.

Yes. However, some numbers are so unbelievably vast that power notation is the only unambiguous option. Otherwise you end up describing things like a peanut in Reading, etc. (©D. Adams)

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

[Gfamily]

"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.

Yes. However, some numbers are so unbelievably vast that power notation is the only unambiguous option. Otherwise you end up describing things like a peanut in Reading, etc. (©D. Adams)

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

Oh no! I've got moles of my compost bins!

[monkey]

"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.

Yes. However, some numbers are so unbelievably vast that power notation is the only unambiguous option. Otherwise you end up describing things like a peanut in Reading, etc. (©D. Adams)

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.

[dyqik]

"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.

Yes. However, some numbers are so unbelievably vast that power notation is the only unambiguous option. Otherwise you end up describing things like a peanut in Reading, etc. (©D. Adams)

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

There's about 3 billion moles of moles of hydrogen in the sun, and 65 million moles of moles of helium.

[Grumble]

Yes. However, some numbers are so unbelievably vast that power notation is the only unambiguous option. Otherwise you end up describing things like a peanut in Reading, etc. (©D. Adams)

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

There's about 3 billion moles of moles of hydrogen in the sun, and 65 million moles of moles of helium.

When you say hydrogen are you counting deuterium? I heard (on SGU) that the majority of fusion is hydrogen > deuterium

[Brightonian]

Yes. However, some numbers are so unbelievably vast that power notation is the only unambiguous option. Otherwise you end up describing things like a peanut in Reading, etc. (©D. Adams)

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.

[Brightonian]

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:

?

</rant>