the mass of the sun is 2 × 10³⁰ kg, and the distance between neptune and the sun is 30 au. what is the…

the mass of the sun is 2 × 10³⁰ kg, and the distance between neptune and the sun is 30 au. what is the orbital period of neptune in earth years?\n30 earth years\n164 earth years\n3.8 × 10¹¹ earth years\n2.3 × 10¹⁷ earth years

the mass of the sun is 2 × 10³⁰ kg, and the distance between neptune and the sun is 30 au. what is the orbital period of neptune in earth years?\n30 earth years\n164 earth years\n3.8 × 10¹¹ earth years\n2.3 × 10¹⁷ earth years

Answer

Explanation:

Step1: Recall Kepler's third - law

$T^{2}=kR^{3}$, where $T$ is the orbital period, $R$ is the semi - major axis of the orbit, and $k$ is a constant. For objects orbiting the Sun, when $R$ is in astronomical units (AU) and $T$ is in Earth years, $k = 1$.

Step2: Apply the formula

Given $R = 30$ AU. Substitute $R$ into the formula $T^{2}=R^{3}$. So $T^{2}=30^{3}=27000$.

Step3: Solve for $T$

$T=\sqrt{27000}\approx164$ Earth years.

Answer:

164 Earth years