QUESTION

# The diameter of the sun is $1.4\times {{10}^{9}}$ m and that of the Earth is about $1.2768 \times {{10}^{7}}$m. Find the approximate ratio of the diameter of the Sun to that of the Earth.

Hint: We need to find approx. ratio of diameter of the Sun to Earth. So divide the diameter of the Sun to Earth. Simplify it and get the ratio of diameter of the Sun to that of the Earth.

We have been given the diameter of the Sun as $1.4\times {{10}^{9}}$ m.
Similarly, the diameter of the Earth is $1.2768\times {{10}^{7}}$ m.
What we need to find here is the approximate ratio of diameter of the Sun to that of the Earth.
The ratio = $\dfrac{Diameter\text{ }of\text{ }the\text{ }Sun}{Diameter\text{ }of\text{ }the\text{ }Earth}$= Diameter of the Sun : Diameter of the Earth.
Ratio = $\dfrac{1.4\times {{10}^{9}}}{1.2768\times {{10}^{7}}}$.
Now let us simplify the above expression.
Ratio = $\dfrac{1.4\times {{10}^{2}}\times {{10}^{7}}}{1.2768\times {{10}^{7}}}$.
Cancel out ${{10}^{7}}$ from the numerator and denominator.
Ratio = $\dfrac{1.4\times {{10}^{2}}}{1.2768}$.
Multiply by 1000 in the numerator and denominator.
Ratio = $\dfrac{140\times 10000}{1.2768\times 10000}$
Ratio = $\dfrac{1400000}{12768}$
Now we need to simplify the ratio by dividing it with 2.
Ratio = $\dfrac{700000}{6384}=\dfrac{350000}{3192}=\dfrac{175000}{1596}=\dfrac{87500}{798}=\dfrac{43750}{399}$
Thus we got the ratio of the diameter of the Sun to the diameter of the Earth as $\dfrac{43750}{399}$.
$\therefore$Diameter of the Sun : Diameter of the Earth = 43750 : 399.
Thus we got the required ratio.

Note: The sun is nearly a perfect sphere. Its equatorial diameter and its polar diameter differ by only 6.2 miles (10 km). The diameter of Earth is measured by an Eratosthenes to measure, i.e. you will need to accurately measure the length of the shadow cast by two sticks that are several hundred miles north and south of each other on the same day.