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)

Calculating distance and size of 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

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 θ₁+θ₂=θ. Shown in above figure.
Because   θ = P₁PP₂/PM
Hence   PM = P₁PP₂/θ
As astronomical bodies are at very large distance from earth, hence P₁PP₂ ≈P₁P₂ and PM ≈MO
OM = P₁P₂/θ
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.