Question

Light from our first door neighbouring star reaches us in 4.5 year . Calculate its distance from earth in kilometre . Velocity of light is 3*10 to the power 8 m/s . Take 1 year is 365 days .

Answer 1

Given:

Light from our first door neighbouring star reaches us in 4.5 year.

To find:

Distance of the star from earth ?

Calculation:

Distance can be calculated by multiplying the speed of light with the time taken to reach the star.

$\sf\therefore \: d = v \times t$

$\sf\implies \: d =( 3 \times {10}^{8} \: m/s) \times (4.5 \: yr)$

$\sf\implies \: d =( 3 \times {10}^{8} \: m/s) \times (4.5 \times 365 \: days)$

$\sf\implies \: d =( 3 \times {10}^{8} \: m/s) \times (4.5 \times 365 \times 24 hours)$

$\sf\implies \: d =( 3 \times {10}^{8} \: m/s) \times (4.5 \times 365 \times 24 \times 60 \: min)$

$\sf\implies \: d =( 3 \times {10}^{8} \: m/s) \times (4.5 \times 365 \times 24 \times 60 \times 60 \: sec)$

$\sf\implies \: d =( 3 \times {10}^{8} \: m/s) \times (141912000\: sec)$

$\sf\implies \: d =425736000 \times {10}^{8} \: m$

$\sf\implies \: d =425736 \times {10}^{8} \: km$

So, distance of star from earth is :

$\boxed{ \bf \: d =425736 \times {10}^{8} \: km}$

Answer 2

Time taken by light to come to Earth from the neighbouring star = $4.5 \ yrs = 4.5 \times 365 \ days = 1,642.5 \ days = 2,365,200 \ h = 141912000 \ s$

(∵ 1 yr = 365 days = 365 × 24 h = 365 × 24 × 60 min = 365 × 24 × 60 × 60 s)

Speed of light = $3 × 10^8 m/s$

We know,

$s = vt$

⇒ $s = (3 × 10^8 m/s)(141912000 s)$

⇒ $s = 3 × 141912 × 10^{8+3} \ m$

⇒ $s = 425736 \times 10^{11} \ m$

⇒ $s = 4.25736 \times 10^{11+5} \ km = 4.25736 \times 10^{16} \times 10^{-3} \ m$

⇒ $s = 4.25736 \times 10^{13} \ km$.

∴ Distance between the star and Earth is of $4.25736 \times 10^{13} \ km$.