Measuring a Year

Here’s a puzzle:

You find yourself on an unknown uninhabited planet. You look up the sky and notice a giant star that looks like our sun. It rises in one particular direction and sets in the opposite, so you figure that this planet (that you’re on) orbits around this particular star. Now it’s easy to define a day on this planet: it’s the time between two subsequent sunrises. The question is: how would you define a year on this planet? (Assuming, of course, that your survival on this planet is not an issue.)

Someone posted this question on Quora, which got me thinking about the definition of a year. One earth-year is defined as 365 days, or 12 moon cycles, and these measures are not arbitrary. They (approximately) represent the time it takes for the earth to complete one orbit around the sun. With that in mind, the answer to the above puzzle is rather straight-forward for a planet that has an axial tilt.

If you landed on a planet with an axial tilt then the sun’s trajectory in the sky will change over time and you can track it to measure one year. The following approach can be used to measure one complete orbit: Mark the point at the horizon where the sun rises the next morning. Every subsequent morning the sun will rise at a slightly different point. (The amount of shift depends on the degree of axial tilt and how fast the planet is orbiting its sun.) For a while, the sunrise points will shift away from your initial mark in one particular direction (either left or right). And after a certain period, like a pendulum, they will start moving back towards the initial mark. (This U-turn marks a solstice on this planet.) It will keep moving and bypass the initial mark, move in the opposite direction, and then take another U-turn to come back to the initial mark. The morning when sun rises again from the original reference point would mark the completion of one year on this planet. (Note that this description changes slightly if you started observing the sunrises exactly on the day of one of the two solstices on this planet.)

Here’s how the sun’s trajectory looks like from Earth (looking southward from the Northern hemisphere):

SunPathDay

In our solar system, most planets have an axial tilt. Earth’s current axial tilt of 23.4° is responsible for seasons, rain, and consequently, the existence of life on Earth. The most curious among these are Venus and Uranus; they are the only planets that rotate clockwise (while looking at the solar system from the top). Venus has flipped almost completely and is upside down as compared to other planets. While Uranus, with an obliquity of 98°, would look like a tilted rolling ball — as opposed to all other planets that look like tilted spinning tops.

Obliquity of the Nine Planets

Back to the question of measuring one year, if you landed on a planet without an axial tilt, I have no idea how you would measure a year.

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4 responses to “Measuring a Year

  1. Is there a relation between a day’s length and a year’s length?

    • The day’s length depends on how fast a planet rotates around its own axis, while the year’s length depends on how fast the planet orbits around the sun. Intuitively, it may seem like that, but I don’t think there’s a relationship between them.

      The biggest outlier, again, is Venus. As I mentioned in my post, it rotates clockwise (so the sun would rise in the West on Venus) and extremely slowly at that. One year on Venus is actually shorter than one day on Venus. In other words, it takes longer for Venus to complete one rotation than it takes it to finish one orbit around the sun. One day on Venus is approximately twice as long as one year! How crazy is that?!

      Interestingly, there is a direct relationship between planet’s orbital period (i.e., year) and its distance from the sun. See Kepler’s third law: http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

  2. Pingback: Quora

  3. Raja

    Is it possible for planets without axial tilt to have seasons because of an elliptical (or ovoid) orbit with huge difference between transverse diameter and conjugate diameter (e ~ 1)

    Is it possible for a planet to have at least two different lengths of days?

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