As a school boy, I encountered this question that made an impression on the way I thought about science:
You step out of the house during an eclipse, and see little rings beamed onto the pavement by the trees. Find the density of the sun.
[solution follows]
You step out of the house during an eclipse, and see little rings beamed onto the pavement by the trees. Find the density of the sun.
[solution follows]
The density of the sun! Surely there's not enough information given? I spent two days thinking about it, before I looked at the solution. 
Where are these rings coming from? Gaps in foliage act like pinholes, creating hundreds of pinhole cameras.
We can learn something about sun through this pinhole principle. Let's grab a tape and measure the size of the ring and the distance to the foliage.
We can learn something about sun through this pinhole principle. Let's grab a tape and measure the size of the ring and the distance to the foliage.
We now know the ratio between the distance to the sun and its radius. We don't know the mass of the sun. We are still quite far from the density.
Now for the leap of imagination:
Kepler's third law, which tells us how the time period of revolution of a planet depends on its distance from the sun. (T^2 ~ r^3)
Kepler's third law, which tells us how the time period of revolution of a planet depends on its distance from the sun. (T^2 ~ r^3)
Now if you write the mass in terms of the density ρ, something very convenient happens:
The ratio that we determined using the pinhole idea has now appeared.
And of course, we know the period of revolution of the earth— 1 yr.
All the unknowns are now known, except the density!
The ratio that we determined using the pinhole idea has now appeared.
And of course, we know the period of revolution of the earth— 1 yr.
All the unknowns are now known, except the density!
Soon after, there was an annular solar eclipse visible from Bangalore in 2010. I did the measurements, and found the density to be correct to an order of magnitude.
I admire this problem for its elegance.
Much like Eratosthenes' determination of the earth's radius, it demands very little knowledge, but reveals something that seems beyond reach.
Much like Eratosthenes' determination of the earth's radius, it demands very little knowledge, but reveals something that seems beyond reach.
This was probably the beginning of my realisation that science is not about knowing all the equations and theories. Being able to solve every problem in a textbook might not mean very much.
Every problem is easy in the textbook, where assumptions and contexts are clear. The real word is much messier and decontexualised. Learning to operate in such an environment is the really valuable scientific training.
