Q20 of 39 Page 35

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?

Given,

Distance of the nearest star, d = 4.29 ly


1 lightyear is the distance travelled by light in one year.


∴ 1 ly = Speed of light × 1 yr


⇒ 1 ly = 3 × 108 m s-1 × (365 × 24 × 60 × 60 s)


⇒ 1 ly = 9.46 × 1015 m


So, d = 4.29 × 9.46 × 1015 m


⇒ d = 4.058 × 1016 m


We know, 1 parsec = 3.09 × 1016 m


So,



⇒ d = 1.313 parsec


We know,



where, θ is the parallax angle


l is the diameter of the Earth’s orbit = 3 × 1011 m


d is the distance of the star from Earth


∴


⇒ θ = 7.39 × 10-6 rad


⇒


∴ θ = (7.39 × 10-6 rad)/(π/648000 rad)


⇒ θ = 1.52”


NOTE: It is to be noted that a lightyear is a unit of distance and not time.


Parallax is a difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines of sight.


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The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit � 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres?

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Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.

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Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):

A. the total mass of rain-bearing clouds over India during the Monsoon


B. the mass of an elephant


C. the wind speed during a storm


D. the number of strands of hair on your head


E. the number of air molecules in your classroom.