Question

The diameter of the Sun is 1.39 million kilometres and the Earth is 8.3 light minutes far away.

Proxima Centauri is the nearest star - it has a distance of 4.24 light years to our Sun.

(a) How long does it take to travel to Proxima Centauri with

(i) an airplane (920 km/h) or

(ii) with the Voyager 1 space probe (17 km/s).

(b) Let the Sun have the size of a tennis ball (diameter: 6.7 cm): How far away is the Earth and

how far away is Proxima Centauri on this scale?​

Answer 1

light-year is unit of distance. it is the distance travelled by light during one year.

it means 1 light-year = 365 × 24 × 3600 × 3 × 10^8 m

= 946,08000 × 10^8 m

= 9.46 × 10^15 m

= 9.46 × 10¹² km

as, 4.24 light years >> 8.3 light minutes

so, we can neglect distance distance of the proxima centauri from earth. we just use distance of proxima centauri from sun.

so, time taken by aeroplane = 4.24 light year /speed of aeroplane

= 4.24 × 9.46 × 10¹²/920 h

= 0.0435 × 10¹² h

= 4.35 × 10^10 h

and time taken by Voyager 1 space probe = 4.24 × 9.46 × 10¹²/17 sec

= 2.36 × 10¹² sec

converting 8.3 light minutes into kilometres.

8.3 light minutes = 8.3 × 60 × 3 × 10^8 m

= 1494 × 10^8 m

= 1.494 × 10¹¹ m

= 1.494 × 10^8 km

as you know, diameter of sun is 1.39 million kilometres.

so, diameter = 1.39 × 10^6 km it is assumed to be 6.7cm.

so, 1.39 × 10^6 km <=> 6.7 cm

or, 1.494 × 10^8 km <=> 6.7/(1.39 × 10^6) × 1.494 × 10^8 = 7.2 × 10² = 720cm

hence, the earth is 720cm far away on this scale.

now, 4.24 × 9.46 × 10¹² km <=> 6.7cm/(1.39 × 10^6) × 4.24 × 9.46 × 10¹²

= 193.3 × 10^6 cm

hence, proxima centauri is 193.3 × 10^6cm far away on this scale.