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Question
- why is the length of a year not the same for each planet?
the sun changes location throughout a calendar year and therefore changes the length of a year for each planet year to year.
the shape of each planets orbit is different. not all planets revolve around the sun in a circular path, which causes a difference in the length of a year on each planet.
each planets revolution around the sun is different. a planets distance from the sun affects its revolution period and therefore the length of its year.
each planet has its own moon, which affects the gravitational pull of the sun and therefore the length of the planets revolution around the sun.
The length of a year for a planet is determined by its orbital period around the Sun. According to Kepler's third law, the square of the orbital period ($T$) of a planet is proportional to the cube of the semi - major axis ($a$) of its orbit ($T^{2}\propto a^{3}$). Planets are at different distances from the Sun (i.e., different semi - major axes of their elliptical orbits). A planet farther from the Sun has a larger orbital radius (or semi - major axis for an elliptical orbit), and thus a longer orbital period (year).
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The shape of each planet's orbit is different. Not all planets revolve around the sun in a circular path, which causes a difference in the length of a year on each planet.