Question

Assume the diameter of the Earth (12,700 km) is scaled down to 1 cm and answer the following:
(a) How large is the Sun (diameter: 1.4×106 km) on this scale?
(b) How far away is the nearest star (distance: 4.24 light-years) on this scale?

Answer 1

Assuming that the diameter of the Earth (12,700 km) is scaled down to 1 cm, the diameter of the sun on this scale is 110.23 cm and the distance of the nearest star on this scale is 3.15 * 10^9 cm.

• As given in the question, 12700 Km is equivalent to 1 cm on the given scale.
• So, 1 Km is equivalent to 1/12700 cm. Thus, diameter of the sun (1.4 * 10^6 km) can be calculated as (1.4 * 10^6) / 12700 = 110.23 cm
• Again, 1 Light year = 9.46 * 10 ^ 12 Km. So, on calculation, 4.24 light year is equal to 3.15 * 10^9 cm.

Answer 2

Answer:

The diameter of the sun = 110.236 cm or 1.10 m

The distance from the nearest star = 3.15 * 10^9 cm or 3.15 * 10^7 m

Explanation:

(a) Assume the diameter of the sun in cm = x

So, we have concluded the proportional relation 12700 / 1 = 1.4*10^6 / x

Finally, by calculating, x = The diameter of the sun = 110.236 cm or 1.10 m

And its volume, at this scale = 4/3*pi*radius^3 = 4/3*3.14*(110.236/2)^3 = 701049.6 or 7.01*10^5 cm^3

(b) Assume the distance from the nearest star in cm = x, and we know that 1 light-year = 9.46*10^12 km

So, to get how many kilometres in 4.24 light-years = 4.24 * 9.46*10^12 = 4.01 * 10^13 km

So, we have concluded the proportional relation 12700 / 1 = 4.01*10^13 / x  

Finally, by calculating, x = the distance from the nearest star = 3.15 * 10^9 cm or 3.15 * 10^7 m