Predict: Pluto has an orbital radius of 39.529 AU. Based on Kepler's third law, what is the approximate period of Pluto's orbit? (Hint: Find the cube of the orbital radius first, and then take the square root.)

In our solar system, anything orbiting the Sun obeys a simplified form of Kepler's third law if the period T is measured in years and the semi-major axis a distance is measured in AU.

T^2=a^3

If Pluto has a semi-major axis distance a=39.529 AU then T^2=(39.529)^3 which gives T=248.52 years.

Therefore, period of Pluto is 248 years which is close.

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Lanuel Lanuel · Answer 2 · 2021-12-09T23:45:29+01:00

The approximate period of Pluto's orbit is equal to 249 years.

Given the following data:

Orbital radius or semi-major axis distance = 39.529 AU.

To determine the approximate period of Pluto's orbit, we would apply Kepler's third law of planetary motion:

Kepler's third law of planetary motion states that the square of any planetary body's orbital period (P) is directly proportional to the cube of its orbit's semi-major axis (a).

Mathematically, Kepler's third law of planetary motion is given by the formula:

[tex]P^2=a^3[/tex]

Substituting the given parameters into the formula, we have;

[tex]P^2=(39.529)^3\\\\P^2=61765.72\\\\P=\sqrt{61765.72}[/tex]

P = 248.53 ≈ 249 years.

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