Question

The distance of Neptune and Saturn from the sun are nearly ${10}^{13}$ m and ${10}^{12}$ m respectively. Assuming that they move in circular orbits, their periodic times would be in the ratio of

• A. $10$
• B. $100$
• C. $10\sqrt{1}0$
• D. $1000$

Answer 1

The correct option is C $10\sqrt{1}0$

According to Kepler's Third law:

$P^2=a^3$

For Neptune

$P_N^2={\left({10}^{13}\right)}^3={10}^{39}$

For saturn,

$P_S^2=({10}^{12}{)}^3={10}^{36}$

$\therefore \frac{P_N}{P_S}=\sqrt{\frac{P_N^2}{P_S^2}}=\sqrt{\frac{{10}^{39}}{{10}^{36}}}=\sqrt{{10}^3}$

$=10\sqrt{10}$