Stealth said:

HELP, my 7yo old wont’ go to sleep because he is doing that “thinking” thing. As much as I tell him nothing good will ever come from thinking, and it will do him no good, he persists. So I need to check my answer before telling him (as the only thing worse than not answering, is giving a child the wrong answer)

7yo Question

What size piece of paper is needed to wrap the earth? And the sun?

Now he knows that A0 is1m^2. He therefore assumes That A-1 is 2m^2. It is also the minimum amout of paper being asked, not what size sheet is wrapped to fully cover.

I have answers but I hope to check their validity before providing him the answer.

Also, is there any substance that could be used to wrap the sun?

PM 2Ring said:

The surface area of the earth is about 5.1E14 m^2, according to Wikipedia.
As you son knows, the A scale works on powers of 2.

So we need to solve 2^x = 5.1 × 10^14
Taking logs,
x * log(2) = log(5.1 × 10^14)
x = log(5.1 × 10^14) / log(2)

Using Google Calculator,
log(5.1 × 10^14) / log(2) = 48.8574905755

2^48.857 ~=5.1000333e+14
2^48 = 2.8147498e+14
2^49 = 5.6294995e+14

So we need A-49 to wrap the Earth; we’ll have a fair bit of paper left over.

Bubblecar said:

Also, is there any substance that could be used to wrap the sun?

Dark Matter.

I reckon you would need a sheet of paper equivalent to A -49 to be able to wrap the Earth.

I just did that figure in my head so I may be off a tad.

Doh, I allowed for 10,000m^2 in 1km^2. But when two great minds like PMs and Sibeen(cough, cough) both get the same answer, if worth checking your own working.

For the sun, I get
Area = 6.0877E12 km² = 6.0877E18 m²
log(6.0877E18) / log(2) = 62.400602973

The “surface” of the Sun (to be precise, the photosphere) has an effective temperature of 5778 K, quite a bit higher than what any normal solid can cope with.

From Wikipedia

Binary compounds such as tungsten carbide or boron nitride can be very refractory. Hafnium carbide is the most refractory binary compound known, with a melting point of 3890 °C. The ternary compound tantalum hafnium carbide has one of the highest melting points of all known compounds (4215 °C).

The corona of the Sun is much hotter, around 5 megakelvin.

PM 2Ring said:

For the sun, I get
Area = 6.0877E12 km² = 6.0877E18 m²
log(6.0877E18) / log(2) = 62.400602973

The “surface” of the Sun (to be precise, the photosphere) has an effective temperature of 5778 K, quite a bit higher than what any normal solid can cope with.

From Wikipedia

Binary compounds such as tungsten carbide or boron nitride can be very refractory. Hafnium carbide is the most refractory binary compound known, with a melting point of 3890 °C. The ternary compound tantalum hafnium carbide has one of the highest melting points of all known compounds (4215 °C).

The corona of the Sun is much hotter, around 5 megakelvin.

So, how to get past the corona?

So, how to get past the corona?
——————
I never go past a Corona.

roughbarked said:

PM 2Ring said:

The corona of the Sun is much hotter, around 5 megakelvin.

So, how to get past the corona?

With great difficulty.

The corona has very low density, so the amount of heat energy per unit volume isn’t actually as bad as the temperature makes it sound. So you might be able to get a multi-layered spacecraft through it by allowing most of the craft to boil away. But it’s not just the heat you need to worry about: it’s very active magnetically.

From https://en.wikipedia.org/wiki/Corona

If you get caught by one of those loops, you’re history. And I doubt we’d be able to make any sort of electronics that’d survive the magnetic environment of the corona.

Won’t anyone think of the trees?

Sobs

Time for bed. My eyelids have turned to concrete.

Damn – and now I’ve got the wromg frigging thread to boot.

The earth has a complex shape with many peaks and valleys and its surface area is poorly defined but let us assume that we don’t need to wrap it too snugly.

The surface area of an oblate spheroid the size of the earth is 5.1 × 10^14 m^2. To wrap it we’d need to get over some peaks and ranges, but let’s assume that the presence of major mountain ranges doesn’t make a sig dif to this.

log_2(5.1 × 10^14) = 48.86, so A-49 would have enough area, with a 10% margin

But that doesn’t mean we can necessarily wrap the earth with an A-49. I’ll grant that it does mean we can wrap the earth with pieces of paper with a total area of an A-49, for instance by cutting it into strips or suitable squares, but is that within the bounds of the question?

If the paper has to remain intact, and can only be folded or creased (as is usually the case when wrapping something), then you might struggle to do it with that 10% margin. Consider: could you wrap a ball 13.5 cm in diameter using an A4?

On the other question, the sun could be wrapped by gases or plasma.

dv said:

On the other question, the sun could be wrapped by gases or plasma.

I’ll pay that.

dv said:

The earth has a complex shape with many peaks and valleys and its surface area is poorly defined but let us assume that we don’t need to wrap it too snugly.

Actually, even if the earth is considered to be a perfect sphere, then wrapping it in a sheet of paper is the same as diffeomorphically mapping a curved surface onto a flat surface, which is impossible. In practice, it means that the wrapping will introduce creasing in the paper.

KJW said:

dv said:

The earth has a complex shape with many peaks and valleys and its surface area is poorly defined but let us assume that we don’t need to wrap it too snugly.

Actually, even if the earth is considered to be a perfect sphere, then wrapping it in a sheet of paper is the same as diffeomorphically mapping a curved surface onto a flat surface, which is impossible. In practice, it means that the wrapping will introduce creasing in the paper.

Not if one cuts pieces out of the paper and glues it down.

roughbarked said:

KJW said:

dv said:

The earth has a complex shape with many peaks and valleys and its surface area is poorly defined but let us assume that we don’t need to wrap it too snugly.

Actually, even if the earth is considered to be a perfect sphere, then wrapping it in a sheet of paper is the same as diffeomorphically mapping a curved surface onto a flat surface, which is impossible. In practice, it means that the wrapping will introduce creasing in the paper.

Not if one cuts pieces out of the paper and glues it down.

there is always one smartarse at playgroup

Riff-in-Thyme said:

roughbarked said:

KJW said:

Actually, even if the earth is considered to be a perfect sphere, then wrapping it in a sheet of paper is the same as diffeomorphically mapping a curved surface onto a flat surface, which is impossible. In practice, it means that the wrapping will introduce creasing in the paper.

Not if one cuts pieces out of the paper and glues it down.

there is always one smartarse at playgroup

Well we don’t want to waste too much paper. I’d guess that we have run out of existing paper making materials by now.

Bubblecar said:

Also, is there any substance that could be used to wrap the sun?

A solid, not permanently, but I figured out a while back that by making a sufficiently thick layer of tungsten aerogel (not all aerogels have excellent thermal insulation, use one that does) you could wrap the Sun at a distance of 1 Solar radius from the surface for as long as you like. The inner layer of this would be continually evaporating but the outer surface would be protected.

A bit expensive making it of tungsten, second best would be carbon which is relatively inexpensive. A good source of carbon is paper, so by choosing a paper microstructure to give maximum thermal insulation you could wrap the Sun in it for a while, until it evaporates.

Also, is there any substance that could be used to wrap the sun?

A Dyson Sphere, though it depends on how closely you define ‘wrapping’.

get a terry’s chocolate orange

unwrap the covering and then scale the earth and the covering to earth

wookiemeister said:

get a terry’s chocolate orange

unwrap the covering and then scale the earth and the covering to earth

not worth it unless it turns the Earth into a chocolate orange

I’ll grant that it does mean we can wrap the earth with pieces of paper with a total area of an A-49, for instance by cutting it into strips or suitable squares, but is that within the bounds of the question?
————————————————————-

Not If you cut strips and follow the contours… then you would use more paper than if you covered it like a lolly.

And of course the smaller the strips the greater amount of paper needed…