Calculating distance and size of moon

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 × 108 m/s, is the velocity of light.

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

Calculation of size of an astronomical object like moon
Calculation of size of an astronomical object like moon

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)

Calculation of distance of moon from earth
Calculation of distance of moon from earth

The position of moon M in the solar system is observed simultaneously from two place P1 and P2 o the surface of the earth which is far removed from each other. From positions P1 and P2, the parallaxes θ1 and θ2 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 P1P2 is θ12=θ. Shown in above figure.
Because   θ = P1PP2/PM
Hence   PM = P1PP2
As astronomical bodies are at very large distance from earth, hence P1PP2 ≈P1P2 and PM ≈MO
OM = P1P2
Thus by measuring distance P1P2 between two places of observation and total parallax θ, the distance OM of moon from the earth can be calculated.