“Question of the day #V”
In my series of “question of the day” today one from a conversation with my 9 year old daughter who is preparing for a school presentation about “The Universe”. Other kids in her class talk about their cats and rabbits… The subject is totally her choice and she has been thinking about the subject for months now. Her favourite outing is to go with with me to the Space Expo in Noordwijk, the Netherlands during the upcoming holidays.
She wanted me to tell her how the moon reflects the light of the sun, amongst a host of other stuff intriguing for both a little girl as for any grown up.
So she asked me: “If I compare the moon with a droplet of water and how that reflects the light in all directions then this will be the same for the moon?”. I thought that I got the drift of her question and did not bother her with diffraction of light or what have you and said “Yes”. She was silent for a few seconds and then she asked: “How much of the light of the sun reaches the earth?”
The magnitudes of the universe are totally lost on us and our imagination. Luckily we have the beauty of mathematics in general and “pi” in particular in this case to help us.
I answered: “Well a tiny fraction, but we can calculate how tiny when we get home”. I tried: It should not be to hard to calculate the surface area of the earth seen as a flat circle – 2pi(average radius earth)^2 – and divide that by the surface area of the sphere with a radius of the distance from the sun to the earth – 4pi(average distance sun to earth)^2 – This was lost on her completely…
Anyway, at home she kept on asking for the answer. With some help from WolframAlpha I got to 0,000.000.09% (a tat less then 1 billionth of the light emitted). This figure was (of coarse) lost on her. I then explained to her that if the sun was throwing the amount of people who are living on this planet around itself 6 would reach earth, coincidentally just the size of our family. I should have realised that not only for grown ups but for kids as well a number of 7.000.000.000 is unfathomable.
Just to show how big the sun is compared to our earth: If our earth would be at zero distance to the sun we still would only catch 0,004% of the light emitted.
The magnitudes of the universe are totally lost on us and our imagination. Luckily we have the beauty of mathematics in general and “pi” in particular in this case to help us.
Coincidentally, it is the day of pi today!