What is visual angle?

 

          What is visual angle? Visual angle is the angle that an object subtends in our eyes. In detail, it is the angle between the straight lines drawn from the two ends of an object to our eyes. If this angle is large, we say the object looks larger and if that angle is small, we say that the object is small. This depends on two things, i.e. the original size of the object and its distance from us. If two objects of same size are at different distances, the nearer object looks larger than the other one, because it subtends a larger angle in the eyes of the observer.

            

          There is another interesting possibility that we daily see in our sky. Two objects of different size may look similar in size because of the difference in their distance from us. The best example for this is our sun and the moon. Both look exactly the same size from Earth, not because they are of the same size, but because of the co-incidence of the ratio between their diameters and their distances from us. The sun’s diameter is about 400 times the diameter of the moon and it is exactly 400 times away from us compared to moon. So both of their visible disks subtend an angle of about half a degree in our eyes. Because of this coincidence, we can see total solar eclipse, which is one of the rarest celestial events that can never be seen from the surface of any other planet in our solar system. In their skies, either the image of moon is either too big and completely hides the image of sun behind them, or too small to cover the image of sun completely.

          There is a rough mathematical calculation that one can use to find the approximate visible angle of any planet. If a planet is at a distance of about 57 times their diameter, then that planet would subtend an angle of one degree in the eyes of observer. If its distance is 114 times its diameter, then it subtends half a degree and if its distance is 171 times the diameter, it subtends one third of a degree and so on. (This relationship is not as simple as arithmetic multiplication of this number, but we can easily ignore the error in case of any celestial body we see in our skies. If the objects are very close to the observer, this simple relationship no longer olds good and we need to get the help of complex trigonometric relationships to measure the visual angle, but none of the celestial bodies in our sky are so close to us. In case of planets whose distance is several thousand times their diameter, this error is only a miniscule part of decimal and that can easily be ignored as it makes no difference for our naked eyes.

          With the exception of sun, all other stars are quite far away from us, much further compared to even the farthest planets. Even the closest star to us, Proxima Centauri, is about 9000 times further away from our earth than the farthest planet, Neptune! You can easily understand why the planets appear to be having a visible disc outlined against the black background while the stars appear to be tiny points of light, no matter however powerful your telescope is.