I bet you've walked on these spots of light all summer.
They don't look like much but they can actually provide us with some amazing information.
By making 3 measurements with these spots, we can determine the density of the Sun.
You know what I'm talking about: when one of 2 objects of a same volume is heavier, it's the denser one;
the lighter one is also the less dense one.
If we just look at the sun spots (without knowing the Sun's mass or anything),
we can find out the density of the Sun.
Firstly we have to understand what these spots even are.
They are all circular and they are produced under a rather thick foliage
that only lets a little bit of sunlight through.
I reproduced the type of area that the foliage lets through by making a round hole in a piece of paper.
We can see that this stencil produces a round spot when placed under the sunlight.
I made more stencils, this time cutting triangular and square shapes into the papers.
And when placed under the sunlight, we still get... round spots.
It's quite surprising to see that the spots' shape doesn't depend on the shape of the holes they originate from.
But it is coherent with the foliage:
foliage never forms perfect rounds and yet we always end up seeing round spots on the ground.
The reason for this is that the spots are actually a picture of the Sun.
You literally walk over pictures of the Sun.
This property is made use of in the basics of photography with the pinhole camera.
Pinhole cameras are very simple: they are an empty box with a small hole in one end.
As we can see here despite the blur, the pinhole camera's picture is upside down.
When Mr. Head is exposed to the light, the light rays he reflects are sent into every direction.
(I'm simplifying the drawing with only two points of origin).
On a receiving screen, no image can be formed because the light rays are just superimposed.
By using a blocking screen with a hole, we let a few light rays through without them getting on top of each other.
Mr. Head's picture is reproduced... upside down.
We don't only walk over pictures of the Sun; we walk over pictures of the Sun that are *upside down*.
If you're still not convinced that the spots are actual pictures of the Sun, I have one last element of proof.
During a solar eclipse, look down instead of up.
The spots won't look round this time; instead they will illustrate the progression of the Moon over the Sun.
That is ultimate proof that the spots are pictures of the Sun.
Now let's go back to figuring out the density of the Sun.
We're gonna need 2 things:
1. The definition of the mass which involves density and volume.
The equation of the circle lets us know that the circle's diameter is linked to the distance between Earth and the Sun and to the angle of the light ray.
2. We also need Kepler's 3rd Law that describes how much time a planet takes to make one revolution around the Sun,
depending on the Earth-Sun distance, the Sun's mass and the gravitational constant.
Let's combine our equations to isolate the Sun's density:
we get a new equation that only involves the gravitational constant
(which is a fixed number),
the period (365 days),
and the light ray's angle.
We can find the value of the angle by using Pythagoras' Theorem by measuring 3 things:
the spot's diameter;
the angle at which the spot looks circular compared to the floor;
and the distance between the spot and the hole it originates from.
With all this data and several measurements, I managed to calculate the density of the Sun
but with a margin of error of about 30%, which is rather high.
It isn't very easy to get the measurements right anyway:
it's often hard to tell where exactly the spots look their most round
or where the spot even originates from in a messy foliage.
I am sure that with the right tree and a little bit of practice,
we can get very close to the actual value of the Sun's density.
Pr. Mallmann, whose article inspired this video,
got results that were only 2% off from the actual density of the Sun.
However, the article doesn't specificy how many tries he's had to go through to get there.
Density is important data because it is directly linked to gravitational attraction.
The denser a body, the stronger its grativational attraction.
Obviously the method we used today isn't used to determine celestial bodies' grativational attraction,
mainly because only the Sun sends light rays we can examine.
But in general, density is measured thanks to the bodies' mass and volume.
How we get this data is a whole other topic which I won't get into today.
If you enjoyed this kind of challenge, you'll be glad to hear that you can aslo measure the diameter of the Sun.
The method is quite similar to but simpler than our first exercise:
grab a ruler, a piece of paper and a coin.
If you'd like to know about that, click on the link in the description and you'll see how it is done.
And on that note, see you next time!