## Calculating distance and size of moon

### Distance of moon (reflection method)

Using reflection method we will calculate the distance of moon.

A laser beam is a source of very intense, monochromatic and unidirectional beam. By sending a laser beam towards the moon instead of sound waves, the echo method becomes useful in finding the distance of moon from earth. If t is the total time taken by laser beam in going towards moon and back, then distance s of moon from earth’s surface is given by:

s = ct/2.

Where c =3 × 10^{8} m/s, is the velocity of light.

** Calculation of size of an astronomical object like moon (Triangulation method)**

Suppose moon be the astronomical object, whose diameter D is to be measured shown in the above figure. In order to do so, moon is observed with the help of a telescope from a place E on the earth and the angle θ made by two diametrically opposite ends P and Q of the moon at point E on the earth is determined. The angle is called the angular diameter of the moon. If d is the distance of the moon from earth then PQ can be taken as the arc of radius d, then

Θ =PQ/d=D/d or D = θd

Thus by determining d and θ, D can be calculated.

**Calculation of distance of moon from earth (Parallax Method)**

The position of moon M in the solar system is observed simultaneously from two place P_{1} and P_{2} o the surface of the earth which is far removed from each other. From positions P_{1} and P_{2}, the parallaxes θ_{1} and θ_{2} respectively of moon M with respect to sum distant star S are determined with the help of an astronomical telescope. Therefore, the total parallax of the moon subtended on P_{1}P_{2} is θ_{1}+θ_{2}=θ. Shown in above figure.

Because θ = P_{1}PP_{2}/PM

Hence PM = P_{1}PP_{2}/θ

As astronomical bodies are at very large distance from earth, hence P_{1}PP_{2} ≈P_{1}P_{2} and PM ≈MO

OM = P_{1}P_{2}/θ

Thus by measuring distance P_{1}P_{2} between two places of observation and total parallax θ, the distance OM of moon from the earth can be calculated.