Exercises

The problem of a measure of an inaccessible distance, as of a celestial body, seems difficult, while in reality is relatively simple. You have to resolve some triangles. A very worn method is that of the parallax.  Parallax is the angle under which an observant place on the Moon would see the earthly ray. The observant place in to see the Moon to the horizon; another observer in B sees the Moon to the zenith. The triangle will have for base the earthly ray (6378 km). We have so our base. The angle LAO is supported; the angle in OR comes to know easily calculating the difference of latitude between O and B. When you know the lunar parallax too, the angle ALO, we have all of the elements to resolve the triangle and to find the distance sought. You can find the value of the parallax subtrahend from 180° the sum of the two angles in A and in O: it is always of 0° 57'. To measure the distance Earth-Sun, an earthly base would be too small, even if the two observers were at the poles. It is necessary therefore to take our base in the space, for example the distance Earth-Moon. 

Known the three angles of the triangle, LAO, it is easy  calculating the side AL, distance Earth-Moon.

Different points of view.

       

 

 

1) Image of being in a point A on the equator. Wait that the Moon rise up and marks this instant (that we will call T 0.) After this , mark the time in which the Moon is at the highest position on the horizon (that we will call T 1 ). In the same time, at the instant T 1 , you will be moved in the space from the point A to the point A' for effect of the earthly rotation. 

O bserve the picture. The angle A is of 90 degrees, because you have  observed the Moon in the moment when it was on the horizon. The angle P is the equatorial parallax of the Moon, and you can measure it with the data that you have. In fact p = 90o - b where b is the angle that you have route in the space between T 0 and T 1 for the earthly rotation. Knowing that the Earth has a rotation of 360o in 03s 56m 23h, determine b and also the distance of the Moon. Advise: the distance between the point A and the point C (center of the Earth) is equal to the ray equatorial earthly, that is about 6378km. Then you can find the distance of the Moon building a like triangle smaller and measurable and you know that the horizontal equatorial parallax for the Moon is equal to 57'2''.44. 

Results: b = 360 o x (T 1 - T 0 ) : 23 h 56m 03s; 384.400km.

2) Suppose that you are 20m far, that is the same to say 2000cm, from  your friend. A coin of 500L covers your friend when you put it to 30cm from your eyes. Then the relation between the height of your friend and the coin's is equal to 2000/30. The same relation exists between the diameter of the coin and the height of your friend. Seen that a coin from 500L has a diameter of about 2,6cm, how much will be high your friend?

R: 173,3cm