Question

how to measure the large distance and small distance​

Answer 1

Answer:

Astronomers use an effect called parallax to measure distances to nearby stars. Parallax is the apparent displacement of an object because of a change in the observer's point of view.

To measure the distance D of a far away planet S by the parallax method, We observe it from two different positions (observatories) A and B on the Earth, separated by distance AB=b at the same time as shown in the given figure.

We measure the angle between the two directions along which the planet is viewed at these two points. The ∠ASB in the figure represented by symbol θ is called the parallax angle or parallactic angle.

As the planet is very far away,

bD<<1

and therefore, θ is very small.

Then we approximately take AB as an arc of length b of a circle with center at S and the distance D as the radius AS=BS so that AB=b=Dθ where θ is in radians.

D=

θ

b

..... (1)

Having determined D, we can employ a similar method to determine the size or angular diameter of the planet. If d is the diameter of the planet and α the angular size of the planet (the angle subtended by d at the earth),

We have α=

d

D

..... (2)

The angle α can be measured from the same location on the earth. It is the angle between the two directions when two diametrically opposite points of the planet are viewed through the telescope. Since D is known, the diameter d of the planet can be determined using Equation (2).