The distance of the two planets from the Sun are `10^(13)m` and `10^(12) m`, respectively. Find the ratio of time periods and speeds of the two planets.

Explanation

To find the ratio of the time periods and speeds of two planets orbiting the Sun at different distances, we can use Kepler's laws of planetary motion.

### Step 1: Determine the ratio of the time periods

According to Kepler's third law, the square of the time period (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit. This can be expressed mathematically as:

\[
T^2 \propto r^3
...