The period of a planet around sun is 27 times that of earth. The ratio of radius of planet’s orbit to the radius of earth’s orbit is

According to Kepler’s third law of planetary motion, the relation between the orbital period of a planet and the radius of its orbit around the Sun is as follows. The square of a planet’s orbital period is proportional to the cube of the radius of its orbit. In this case, if a planet’s orbital period is 27 times that of Earth, we can infer the ratio of the radius of the planet’s orbit to that of Earth’s orbit.

Since the planet is much farther away than Earth, its period is many times longer than Earth. From Kepler’s third law, we can then immediately see that the ratio of the radii of the orbits is inversely related to the ratio of the periods. More specifically, if the period increases then the radius must also be increased in order for both quantities to increase in an inverse proportion according to Kepler’s law.

With a period of the planet 27 times that of Earth, the calculation shows that the radius of the planet’s orbit is 9 times larger than that of Earth. This means the planet orbits farther from the Sun, and its orbital path is longer and thus slower than that of Earth.