Question

Explain parallax method for measuring distance of a nearly star.

Answer 1

Hint: This problem can be solved by drawing a proper diagram by visualisation of position of earth and nearly star. Parallax is a method based on measuring two angles and sides of a triangle formed by the star, earth on one side and other side six month later. Astronomers find the distance of nearby stars in space by using a parallax method.

Formula used: Parallax Formula
$d = 1/p$
Here \[d = \] the distance to the star (in parsecs)
\[P = \]The parallax angle of the star (in arc seconds)

Complete step by step answer:
Parallax is a method based on measuring two angles and sides of a triangle formed by the star, earth on one side and the other side six month later. Astronomers find the distance of nearby stars in the space by using a parallax method.
First let us draw a diagram to understand the problem better.
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Astronomers use an effect to find the distance to a nearby star. Its apparent displacement by comparing the distance of star respect to the earth.

Step-1 See the position of an object (nearby star) once and then again six month later.

Step-2 calculate the change in position by finding the angle of parallax
There is simple relation between star distance and its parallax
Parallax Formula
$d = 1/p$
Here \[d = \] the distance to the star (in parsecs)
\[P = \] The parallax angle of the star (in arc seconds)
Parallax second :- A star when covering a distance of 1 arc second has equal to the 1 parallax sec(parsec).
1 parsec is equal to the \[3.26{\text{ }}light{\text{ }}years\]
Light year:- It is important to find the distance. One light year is equal to the distance travelled by light for one year.
1 degree parallax angle is equal to \[3600{\text{ }}arc{\text{ }}second\]

The sun nearest star distance =\[1.2948{\text{ }}pc\]
The earth nearest star distance =\[1.2948{\text{ }}pc\]
The Pluto nearest star distance =\[1.2948{\text{ }}pc\]
Limitation: If the star has too much distance then parallax angle will become very small to measure and less precise the distance measurement.

Note:
The best way to solve problems of optics is to draw diagrams. This helps in visualizing the problem clearly. You should have a good knowledge of angle and radius. You should have to calculate the angle after six month.