The nearest star to our solar system is 4.29 light-years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?

Asked by Abhisek | 1 year ago |  59

Solution :-

1 light year is the distance travelled by light in a year

1 light year = 3 x 108 x 365 x 24 x 60 x 60

= 9.46 x 1015 m

Therefore, distance travelled by light in 4.29 light years

= 4.29 x 9.46 x 1015 = 4.058 x 1016 m

Parsec is also a unit of distance

1 parsec = 3.08 x 1016 m

Therefore, the distance travelled by light in parsec is given as

4.29 light years =$$\dfrac{4.508 \times 10^{16}}{3.80 \times 10^{16}}$$

= 1.318 parsec = 1.32 parsec.

Using the relation,

θ = $$\dfrac{d}{D}$$

here,

d is the diameter of Earths orbit, d = 3 × 1011 m

D is the distance of the star from the earth,

D = 405868.32 × 1011 m

θ = $$\dfrac{ 3 × 10^{11}}{405868.32 × 10^{11}}$$  =  7.39 × 10-6 rad

But the angle covered in 1 sec = 4.85 × 10–6 rad

7.39 × 10-6 rad = $$\dfrac{ 7.39 \times 10^{-6}}{4.85 \times 10^{-6}}$$ =  1.52″

Answered by Pragya Singh | 1 year ago

Related Questions

It is a well-known fact that during a total solar eclipse-the disk of the moon almost completely

It is a well-known fact that during a total solar eclipse-the disk of the moon almost completely covers the disk of the Sun. From this fact and from the information you can gather from examples 2.3 and 2.4, determine the approximate diameter of the moon.

The farthest objects in our Universe discovered by modern astronomers are so distant that light

The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?

A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects

A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects underwater. In a submarine equipped with a SONAR, the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine? (Speed of sound in water = 1450 m s–1).