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

a. The Sun is 110.24 cm.

b. The distance of the nearest star at 4.24 light years is 3.1586 ×
`10^(9)` cm.

Step-by-step explanation:

Given a scale :

12700 Km : 1 cm

a. How large is the Sun of diameter 1.4 ×
`10^(6)` Km?

Thus using the given scale, we have to compare the diameter of the Sun to that of the Earth.

=
`(1.4*10^(6) )/(12700)`

= 110.2362

The Sun is 110.24 cm.

b. how far away is the nearest star at a distance of 4.24 light-years on this scale?

A light year is a term that is used to express the total distance that light would travel in an empty space in a year.

One light year = 9.461 ×
`10^(12)` Km

So that,

4.24 light years = 4.24 × 9.461 ×
`10^(12)` Km

= 40.11464 ×
`10^(12)` Km

Using the given scale,

`(40.11464*10^(12) )/(12700)`

= 3.1586 ×
`10^(9)`

The distance of the nearest star at 4.24 light years is 3.1586 ×
`10^(9)` cm.