Calculate the Average Distance of a Planet from the Sun

Calculating the Average Distance of a Planet from the Sun

To calculate the average distance of a planet from the sun, we can use Kepler's third law of planetary motion. According to Kepler's third law, the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of the planet's orbit. In this case, we are given that the orbital period of the planet is 6.13 years. Using Kepler's third law, we can set up the following equation:

Orbital Period^2 = Cube of Semi-Major Axis

Substitute the given orbital period into the equation:

(6.13 years)^2 = Cube of Semi-Major Axis

37.5769 = Cube of Semi-Major Axis

Now, to find the semi-major axis, we need to take the cube root of 37.5769:

Cube Root of 37.5769 ≈ 3.353 AU

Therefore, the average distance of the planet from the sun is approximately 16.17 AU (twice the value of the semi-major axis). In conclusion, by applying Kepler's third law of planetary motion, we can calculate the average distance of a planet from the sun based on its orbital period. This law helps us understand the relationship between the orbital period and the distance of a planet from its star.
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