If the planet, Vulcan, takes 4 years to orbit the Sun, then what is the average Vulcan to Sun distance? [Hint: what factor are you solving for: P or R?]Group of answer choices1.5 AU2 AU2.5 AU3 AU8 AU
Question
If the planet, Vulcan, takes 4 years to orbit the Sun, then what is the average Vulcan to Sun distance? [Hint: what factor are you solving for: P or R?]Group of answer choices1.5 AU2 AU2.5 AU3 AU8 AU
Solution
To answer this question, we need to use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period (P) of a planet is directly proportional to the cube of the semi-major axis of its orbit (R), or the average distance from the Sun. This can be written as P^2 = R^3.
In this case, we know that Vulcan takes 4 years to orbit the Sun, so P = 4. We're trying to find R.
Rearranging the formula to solve for R gives us R = cube root of (P^2). Substituting P = 4 into the formula gives us R = cube root of (4^2) = cube root of 16.
The cube root of 16 is approximately 2.52. However, this is not one of the answer choices. The closest answer choice to 2.52 is 2.5 AU. Therefore, the average Vulcan to Sun distance is approximately 2.5 AU.
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