#angular resolution

Event Horizon Telescope Provides New Evidence for Existence of Black Holes

An artist’s impression of a supermassive black hole. Astronomers believe that such objects lie at the centers of most galaxies in the Universe. A recent study which was undertaken with the help of the Event Horizon Telescope, has provided new indirect evidence that indeed this is the case. Image Credit: ESO/L. Calçada

It’s one of the ultimate mysteries of astrophysics: Do black holes really…

The Beginnings of Galaxy Clusters: Proto-Clusters Finally Seen!

The deeper we peer through the cosmos, the more we are looking into the distant past.  Light from other galaxies takes millions of years to reach us, and so when that light has finally arrived at Earth, it is millions of years old, a snapshot in time of the distant galaxy.  The furthest we can see is so far back in the history of the universe, that galaxies haven’t even formed yet.  As we look at…

The angular resolution of an optical device is the smallest scale at which details can be made out; anything smaller than that won’t register as a distinct object. The angular resolution depends on the wavelength of the light being used to see with (in the eye’s case, visible light, so from about 400nm-700nm), the size of the aperture (in the eye’s case, the pupil) and also the spacing of the light detectors (in the eye’s case, the rods and cones - light sensitive cells - on the retina). (The wavelength and aperture are relevant because the wave nature of light blurs images at very small scales.) So it varies for different eyes and (slightly) for different colours of light, but in general the smallest angle the human eye can make out is about 4 arcminutes, or 0.07 degrees (source:Wikipedia). Anything smaller than that won’t register as a distinct object.

So the question is: how big would an object on Earth have to be to look 0.07 degrees across from the Moon? Earth is about 384,400km from the Moon, so the diagram looks like this: 

(Not to scale, of course!)

But you can see that tan 0.07 degrees = opposite / adjacent

—> tan 0.07 degrees = x / 384,400km

—-> x = 384,400km * tan 0.07 degrees

—-> x = 469.6km (1dp).

That would make features like large islands, lakes, seas and so on clearly visible (unless they were covered with cloud), but not small islands and certainly nothing artificial! The Great Wall of China is definitely long enough, but it’s far too thin to be made out from the Moon’s surface (so that’s an urban myth).

There’s a way to try estimating it as well without calculating. The Moon is a bit bigger than a quarter of Earth’s diameter, so if you were to stand on the Moon and look at the Earth, it’d appear a bit less than four times wider than the Moon does in our sky. If you can visualise an Earth globe that big, you can get a rough idea of what Earth would look like and how big everything would look!

Earthrise from Apollo 8.

And of course, with binoculars or a telescope you could see much, much more.