A few weeks ago, I showed how to calculate the distance one would need to be from earth in order to be able to see the entire planet.
The answer came to about 4,267km or more. Now Dickson Mwangangi has extended the problem a little bit. He asks how far should a one-shilling coin be placed for it to appear the same size as the sun.
Now, currently, there are three valid one-shilling coins in Kenya. They have different colours and sizes. I will use the latest edition that was issued from 2005. It is about 24mm in diameter.
The sun is about 1,400,000km in diameter and about 150 million kilometres away from Earth.
Therefore, the ratio of its distance to it diameter is 150/1.4, that is, about 107 times. If the shilling coin is to appear the same size as the sun, the ratio of its distance away to its diameter should also be about 107 times. Therefore, the coin should be placed about 24x107 millimetres away; that is, 2,568mm, or 2.57 metres.
Another way of thinking about this is that the coin can be placed as far as 2.57m away and it would still block the sun from view. Anything farther than that and the sun begins to “peep” over the edges.
Let me extend this line of thought further. We know that the sun is a star, but, when we look at it, it doesn’t look anything like the other stars. It is a large bright disc, not a sparkling dot.
So how far should one be for it to appear like a dot? In other words: how far away does an object have to be for it to appear like a dot? Of course that depends of the size of the object.
Now, we know that the farther away an object is, the smaller it appears; so the question is, what is the largest ratio of distance to size beyond which the object becomes a point? It turns out that, for most people, this ratio is 3,400.
So, with a diameter of 1.4 million km, the sun needs to be about 4,760 million km away for it to appear like a star, that is, 4.76bn km.
Although 4.76bn km is a very large distance, it is not too far when placed in the scale of the solar system. Neptune, the most distant planet, is about 4.5 billion km from the sun.
Furthermore, there is a man-made object much farther away – beyond Neptune and Pluto. This is “New Horizons” which is current about 6 billion km from the sun and flying deeper into space at about 14km/second (50,000km/h!).
If there were any humans on this probe, the sun would appear to them like an ordinary, but very bright, star. For the avoidance of doubt, let me reiterate: there are no humans in the probe!