Question

I really need help with this one please

Answer 1

The distance from the sun is option 2 5.59 astronomical units.

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
`(3)/(2)` is on the variable we need to find so we multiply both the sides by an exponential power of
`(2)/(3)` to be able to calculate 'a'.

P =
`a^{(3)/(2) }`,
`P^{(2)/(3) }` =
`a^{(3)/(2)*(2)/(3) }`,
`P^{(2)/(3) }` = a,
`13.2^{(2)/(3) }` = a = 5.58533 astronomical units.

Rounding it over to nearest hundredth we get 5.59 astronomical units.