Chapter 12, Problem 1QFR

To determine

The size of the Sun compared to Earth.

Answer to Problem 1QFR

The radius of the Sun is $100\text{ times}$ that of Earth and a mass $3,00,000\text{ times}$ Earth’s mass.

Explanation of Solution

The Sun is huge star in our solar system. It is about $150\text{million kilometers}\left(1\text{AU}\right)$ from the Earth. Using Kepler’s third law, astronomers measured its distance which is $1\text{AU}$. We can find its radius from its angular size and using Newton’s law, to find the Sun’s distance from the Earth.

From its radius and mass, its surface gravity is about $30\text{times}$ Earth’s. The radius of the Sun is $100\text{ times}$ that of Earth and a mass $3,00,000\text{ times}$ Earth’s mass.

The radius of the Sun is $7\times {10}^5{\text{ km or about 109 R}}_{\text{Earth}}$ and a mass of the Sun is $2\times {10}^{30}{\text{ kg or about 330,000 M}}_{\text{Earth}}$.

Conclusion:

Therefore, the radius of the Sun is $100\text{ times}$ that of Earth and a mass $3,00,000\text{ times}$ Earth’s mass.