Yeah well, despite all the expected nitpicking (it’s supposed to a fun 
educational night):

 

My calculations in Excel make it 20.65 km (not metres!)

 

Sun diameter = 1,400,4000 km

Light year = 9,460,730,472,581 km

Sand grain diameter = 7e-7 km

Size scaling factor = 5e-13

Distance to alpha Centauri = 41,296,088,512,815 km (4.365±0.007 LY)

Re-scaled distance = 20.65 km

 

Although to be a nitpicker myself, the red digits are meaningless due to the 
rounding error on the exact distance to Alpha Centauri. The resulting distance 
is in the range 20.615 to 20.681 km. Even worse, the exact diameter of the sun 
is a bit fudgy, and you could argue about the size of the beach sand grains, 
and you can dispute how they measure the speed of light, but the important 
thing is the shocking realisation of how much empty space there is out there.

 

It is a binary system, but it’s not a trick question. If someone wants to work 
out the variation of distance of the A and B stars taking into the account the 
eccentricity and high inclination of the plane of orbit of A and B and scale 
that back, then I leave it as an exercise for the reader. My guess is that it 
would be less than a couple of metres variation over the 20 km.

 

And don’t mention Proxima Centauri, that dilapidated crappy star should be 
erased like Pluto.

 

We know that the space between us and A Centauri is not empty, as Lost in Space 
showed us it’s full of space hippies, pirates, miners, teenagers, dragons, 
vegetables, beauty quests and prison planets.

 

Greg

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