Measurement of Large Distances Physics Notes
Measurement of Large Distances:
Length: It is defined as the difference between two positions taken by two events that occur instantly.
1. Parallax Method: When an object is seen by closing our right and left eye alternatively, there is a shift in the position of the object w.r.t. the background observed. This is known as parallax.
Imagine an object P placed at a distance x from our eyes. Let the line joining the object to left and right eye makes 0 angle w.r.t. each other. 0 is called parallax angle.
The distance LR is called basis.
θ = \(\frac{\text { Length of Arc }}{\text { Radius }}\)
Parallax Method
θ = \(\frac{b}{x}\) or x = \(\frac{b}{\theta}\)
2. Size of Astronomical Object: Diameter of Moon: Let Moon be the astronomical object whose diameter is to be measured. We observed Moon with the help of a telescope. Let it be observed from a place E on Earth and make an angle 0 with the two ends P and Q of moon and the point E, as shown in fig. 1.5. 0 is called the angular diameter of the Moon.
Let d be the distance of the Moon from the Earth.
Then, angular diameter, θ = \(\frac{\overline{P Q}}{d}\)
= \(\frac{\text { Length of the arc }}{\text { radius }}\)
or = \(\frac{D}{d}\)
or D = θd
3. Reflection or Echo Method: A gun is fired towards the hill and the time taken between instant of firing and hearing of echo be t.
In this time interval, sound first travels towards the hill from the place of firing and then back from the hill to the place of firing.
Let v be the speed of sound, x be the distance of hill from the place of firing the gun,
then, 2x = v × t or x = \(\frac{v t}{2}\)