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# As I measured the distance from the earth to the moon?

The distance from the earth to the moon tried to measure the ancient Greeks.

Only survived the composition of Aristarchus Zamorskogo "On sizes and distances of the Sun and moon" (III century BC), where he for the first time in the history of science have tried to set the distance to these heavenly bodies and their sizes.

To solve this issue Aristarchus came very clever. He proceeded from the assumption that the Moon is shaped like a ball and the light reflected from the Sun light. In this case, in those moments when the Moon is kind of paludica, it forms a right-angled triangle with the earth and the Sun:

If at this time to accurately determine the angle between the directions from the Earth to the moon and the Sun (CAB), from simple geometric relationships to find how many times the leg (the distance from the earth to the moon AB) is less than the hypotenuse (distance from the earth to the Sun AC). By Aristarchus, CAB=87°; therefore, the ratio of the sides 1:19.

Aristarchus was mistaken about 20 times: in fact, the distance to the moon is smaller than the Sun, almost 400 times. The catch is that to accurately determine the moment when the Moon is in the vertex of the right angle, only on the basis of observations impossible. The slightest same inaccuracy entails a huge deviation from the true value.

The greatest astronomer of antiquity Hipparchus of Nicea in the middle of the II century BC confidently determined by the distance to the moon and its dimensions, assuming a unit radius of the globe.

In his calculations Hipparchus came from a proper understanding of the causes of lunar eclipses: the Moon enters the earth's shadow, having a cone shape with the apex located somewhere in the side of the moon.

Diagram illustrating the determination of the radius of the moon according to the method of Aristarchus.
Byzantine copy of the X century.

Look at the picture. It shows the position of the Sun, Earth and moon during a lunar Eclipse. From the similarity of triangles, it follows that the distance from the earth to the Sun AB is as many times greater than the distance from the earth to the moon BC, many times the difference of the radii of the Sun and Earth (AE - BF) is greater than the difference of the radii of the Earth and its shadows on the distance of the moon (BF - CG).

From observations using simple goniometric instruments showed that the radius of the moon is 15', and the radius of the shadow of approximately 40', that is, the radius of the shadow of larger radius of the moon is almost 2.7 times. Taking the distance from the earth to the Sun per unit, it was possible to establish that the radius of the moon is almost 3.5 times smaller than the radius of the Earth.

It was already known that at an angle of 15' monitored object, a distance which exceeds its size in 3 483 times. Therefore, reasoned Hipparchus, at an angle of 15' observed object will be 15 times closer. Hence, the Moon is away from us, 230 time (3 483 : 15) exceeds its radius. And if the radius of the Earth is approximately 3.5 radius of the moon, the distance to the moon is 230 : 3,5 ~ 60 radii of the Earth, or about 30 earth diameters (about 382 thousand kilometers).

In our time, measure the distance from the earth to the moon was made using the method of laser location. The essence of this method consists in the following. On the surface of the moon is set angular reflector. From the Earth with a laser on a mirror reflector is directed laser beam. This helps us accurately measure the time when the signal was emitted. Reflected from the device on the moon light for about one second returns to the telescope. Determining the exact time at which the light beam passes the distance from the Earth to the moon and back, you can set the distance from the radiation source to the reflector.

Using this method, the distance from the earth to the moon is dened up to a few kilometers (maximum measurement accuracy at the present time is 2-3 centimeters!): on average it amounts to 384 403 km. "On average," not because it is the distance taken from different or approximate measurements, but because the lunar orbit is not a circle but an ellipse. At apogee (farthest from Earth point of the orbit) the distance from the center of the Earth to the moon 406 670 km, the perigee (the closest point of the orbit) - 356 400 km.

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