Question

Planet x is 265 earth orbital radii from the sun, what is the period of revolution in earth year?

Answer 1

1. Planet x is 265 earth orbital radii from the sun, what is the period of revolution in earth year?

Solution

According to the third Kepler's law we have:

$$\frac {P _ {\text {planet}} ^ {2}}{a _ {\text {planet}} ^ {3}} = \frac {P _ {\text {earth}} ^ {2}}{a _ {\text {earth}} ^ {3}}$$

Where

$$P _ {\text {planet}}, P _ {\text {earth}}, a _ {\text {planet}}, a _ {\text {earth}}$$

are the orbital period of planet, orbital period of Earth, radius of planet's orbit and radius of orbit of Earth.

We have

$$a _ {\text {planet}} = 265 \text{a.u.}$$ $$P _ {\text {earth}} = 1 \text{year}$$ $$a _ {\text {earth}} = 1 \text{a.u.}$$

where a.u. is the astronomical unit (distance between Sun-Earth)

Hence we have

$$P _ {\text {planet}} = P _ {\text {earth}} \sqrt {\frac {a _ {\text {planet}} ^ {3}}{a _ {\text {earth}} ^ {3}}} = \sqrt {265^3} \text{years} \approx 4313.89 \text{years}$$

**Answer:**

Revolution period is

$$P _ {\text {planet}} \approx 4313.89 \text{years}$$