# If a small planet were located 7 times as far as the Earth's distance from the Sun, what is its...

## Question:

If a small planet were located 7 times as far as the Earth's distance from the Sun, what is its period in earth years?

## Kepler's Laws:

Kepler used his (and his mentor's) observations of the planets and empirically derived three laws about the orbits of planets. The first stated that the orbits are elliptical with the Sun at one of the locii. The second law states that the planet orbits faster near the perihelion and slower at the aphelion. The third law relates the period and distance of the planets from the Sun.

## Answer and Explanation:

Kepler's Third Law states that the relation between the period and distance is given by:

{eq}P^2 = a^3 {/eq}

where {eq}P {/eq} is in years, and {eq}a {/eq} is in AU.

Therefore, since Earth is at 1 AU, the planet is at 7 AU, giving:

{eq}p = a^{3/2} = 7^{3/2} = 18.5 \text{ years} {/eq}

The period of this planet is about 18.5 years.