Question

the solar mass of the sun is 1. the orbital period of jupiter is 11.9 earth years. what is the distance between jupiter and the sun? ○ 5.2 au ○ 41 au ○ 52 au ○ 410 au

Explanation:

To determine the distance between Jupiter and the Sun, we use Kepler's Third Law, which is given by the formula \( T^2 = a^3 \) (where \( T \) is the orbital period in Earth years and \( a \) is the semi - major axis in astronomical units (AU) for objects orbiting the Sun, assuming the solar mass \( M = 1\)).

Step 1: Take the given orbital period

We know that the orbital period of Jupiter \( T = 11.9\) Earth years.

Step 2: Apply Kepler's Third Law

From \( T^2=a^3\), we can solve for \( a \) by taking the cube - root of \( T^2 \). So \( a=\sqrt[3]{T^{2}}\).

Substitute \( T = 11.9\) into the formula: \( a=\sqrt[3]{(11.9)^{2}}=\sqrt[3]{141.61}\approx5.2\) AU.

Answer:

A. 5.2 AU