The distance from the sun is option 2 5.59 astronomical units.
Step-by-step explanation:
Step 1; To solve the question we need two variables. P which represents the number of years a planet takes to complete a revolution around the Sun. This is given as 13.2 years in the question so P = 13.2 years. The other variable is the distance between the planet and the sun in astronomical units. We need to determine the value of this using the given equation.
Step 2; So we have to calculate the value of 'a' in Kepler's equation. But the exponential power [tex]\frac{3}{2}[/tex] is on the variable we need to find so we multiply both the sides by an exponential power of [tex]\frac{2}{3}[/tex] to be able to calculate 'a'.
P = [tex]a^{\frac{3}{2} }[/tex], [tex]P^{\frac{2}{3} }[/tex] = [tex]a^{\frac{3}{2}*\frac{2}{3} }[/tex], [tex]P^{\frac{2}{3} }[/tex] = a, [tex]13.2^{\frac{2}{3} }[/tex] = a = 5.58533 astronomical units.
Rounding it over to nearest hundredth we get 5.59 astronomical units.
