This week our question comes from our G+ Community, from Ben Trendkilla who asked ”How big would the space station have to be to be able to see it with the naked eye and make out its shape during the day?”
Before we get ahead of ourselves, yes we know some of you give a #ISSwave to the station when you see sunlight reflected off it at night. But Ben’s hypothetical question requires a little more thought, and a hefty bit of calculation to answer. Specifically, Martin has used the formula for angular diameter. We do need to think about the human variables first however…
00:54 How do we see with our eyes and then how does that get put together into a picture by our brain? Our eyes are busy at work essentially auto-stitching together loads of images to create a panorama of about 160 by 175 degrees.
01:47 In order to assess how “big” something is we need to consider perspective. The mathematical expression Martin is using to calculate the size of the ISS is the following:
02:47 How good is human eyesight? What’s the smallest that we can see? Well scientists have been arguing about an average value for this for years.
More discussion on that here: http://books.google.co.uk/books?id=fEgUjUPCtsEC&pg=PA8&redir_esc=y#v=onepage&q&f=false
However, the maximum resolution of human eyesight is generally thought to be 0.3 arc minutes or 0.005 degrees.
03:57 Time to crunch the numbers then! Inserting the closest altitude that the ISS sits at with the smallest angle we can see tells us that the ISS needs to be at least 367m long for us to see it with the naked eye. That’s 5 times bigger than it is now! But you’re still only going to be able to see one pixel worth — it would be a dot!
To see at least 5 pixels in width of the ISS, it would need to be 25 times its current size! That would just be, quite frankly, ridiculous!
05:46 Using the formula we can also ask how far away would the ISS have to be at its current size for us to see it? It would have to be at an altitude of 11.9km… the same height as most planes fly at so you couldn’t really call it the International SPACE station.
The same formula can be used for working out all sorts of ‘how big’ or ‘how far away’ questions.
The film Elysium has already been proven to have got the size of their space station massively out of whack: http://blog.wolframalpha.com/2013/08/16/elysium/
Use our calculators here to work out some of your questions:
How big would it be: http://www.wolframalpha.com/input/?i=evaluate+2*D*tan%28a%2F2%29+at+D%3D300%2C000+m+and+a%3D5*0.07+degrees
How far away would it be:
How big would it look:
Here Martin uses the square cube law to ask who would win in a fight, a giant monster or a giant robot?: http://www.youtube.com/watch?v=2zsKu12kY1g
James May explains how digital cameras work: http://www.youtube.com/watch?v=Ic0czeUJrGE
If you want one of your questions answered join our G+ Community ‘Head Squeezers’.