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Solution

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Solution Steps

Step 1: Kepler's Third Law

Kepler's Third Law states that the square of the orbital period (P) of a planet is proportional to the cube of the semi-major axis (a) of its orbit. Mathematically, this can be expressed as P² = a³. When 'P' is measured in Earth years, and 'a' is measured in astronomical units (AU), the constant of proportionality is 1.

Step 2: Applying Kepler's Third Law

In this problem, the asteroid has a semi-major axis a = 4 AU. We can plug this value into Kepler's Third Law:

P² = 4³ = 64

Step 3: Solve for the Period (P)

To find the orbital period (P), we take the square root of both sides of the equation:

P = √64 = 8 years

Final Answer: The orbital period is 8 years.

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