Physics worksheet featuring step-by-step examples of Kepler's Third Law applied to planets in our solar system and exoplanets.

Final Answer:
a) 28650
b) 169 years

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Explanation:
We’re using Kepler’s Third Law, which says:
P² = a³,
where:
- P is the orbital period in Earth years,
- a is the average distance from the Sun in astronomical units (AU).

For Neptune:
- Given: a = 30.6 AU
- So, a³ = 30.6 × 30.6 × 30.6
Let’s compute step by step:
30.6 × 30.6 = 936.36
936.36 × 30.6 ≈ 28,650 (rounded — that’s a³)
So P² = 28,650
Then P = √28,650 ≈ 169 years.

That’s why:
a) P² = a³ = 30.6³ ≈ 28,650
b) P = √28,650 ≈ 169 years