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The planet Neptune is the most distant planet that we have studied so far. The semi-major axis of its orbit is approximately 30 AU, that is, it is 30 times farther from the Sun than the Earth.

a. Using Kepler's third law, calculate how long it takes for Neptune to orbit the Sun once if its semi-major axis is exactly 30 AU.

b. Neptune was discovered officially in the year 1846. Has it completed an entire orbit of the Sun since its discovery? How many times, approximately, has Mars orbited the Sun since Neptune was discovered?

c. What does this suggest the seasons may be like on distant planets like Neptune? For example, how long does winter last?

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