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

We need to convert km to cm, therefore convert earths diameter from km to cm.

• Conversion 12700Km to 1.27e+9 cm
• Now conversion for sun diameter is 1.4e+6 to 1.4e+11.
• Now the difference between there diameter is
• 1.4e+11 -1.27e+9 = 1.3873e+11
• There nearest star at a distance of in cm conversion is 4.0113e+18cm

Answer 2

(a) d = 110.18 cm

(b) The distance of the nearest star, $D=3.15\times 10^9\ cm$

Explanation:

Given that,

Diameter of the Earth, d = 12,700 km

If the diameter of the Earth is scaled down to 1 cm, we get the diameter of the earth as :

$1\ km=\dfrac{1}{12700}\ cm\\\\1km = 7.87\times 10^{-5}\ cm$

(a) The diameter of Sun on this scale will be :

$d=7.87\times 10^{-5}\times 1.4\times 10^6\ km\\\\d=110.18\ cm$

(b) We know that :

$1\ \text{light year}=9.46\times 10^{12}\ km$

So,

$4.24\ \text{light year}=4.24\times 9.46\times 10^{12}\ km\\\\=4.01\times 10^{13}\ km$

Therefore, the distance of the nearest star will be :

$D=\dfrac{1}{12700}\times 4.01\times 10^{13}\\\\D=3.15\times 10^9\ cm$

Learn more,

Conversion from one unit to other

https://brainly.in/question/15971375