What is the relationship between the distance of a planet from the Sun and the length of its year?

Yes, there is a relationship between the distance from the sun and the length of the year for the planets. The greater the distance from the sun, the longer the year. The reasons are explained in Newton's Laws of Gravity and Einstein's Theory of Relativity.

A planets year is known as the distance a planet takes to travel around the Sun in a complete orbit. For example, in 365 days time, or one year, the Earth will have traveled around the Sun and be back in the position it is in right now. When compared to Earth, the closer a planet is to the the Sun, the shorter its years are (Mercury, Venus). Planets further away from the Sun have longer years when compared to an Earth year (Mars, Saturn, Jupiter, Uranus, Neptune, Pluto). So we say that a year on Mercury compared to ours only lasts 88 Earth days, whereas a year on Neptune takes about 60000 Earth days (nearly 165 Earth years).

The cube of the distance is proportional to the square of the length of the year or orbital period.

For example, Jupiter is about 5.2 times as far from the Sun as the Earth is. Cube 5.2. Now take the square root of the result. That's how many times longer Jupiter's year is than Earth's year.

Distance (in AU's) cubed equals orbit time (in earth years) squared. For example, Mars is 1.52 AU with an orbit time of 1.88 Earth years. 1.52^3 == 1.88^2 (�= 3.54) Neptune is 30.11 AU and orbit time of 164.79 Earth years. 30.11^3 == 164.79^2 (�=27295.25)

The length of the planet's year is equal to the distance to the power 1.5. So for a planet at 4 times the distance, the rotation period would be 8 times longer (Kepler's 2nd law).

   Question

Is it true that the further a planet is from the Sun, the faster it rotates around itself?

Asked by: Navid Dianaty Answer

There is no connection between a planet's distance from the Sun and its rate of rotation (spin on its own axis or Planetary Rotation Period). While it is true that, generally speaking, the gas giants have higher rotation rates than the earth like planets closer to the Sun, any correlation is only coincidental. Mars, for example, is further from the Sun than Earth but has a slightly slower rate of rotation - its planetary rotation period is 1.03 Earth days. Pluto. the furthest planet from the Sun, has a planetary rotation period of 6.39 Earth days. You can see in the plot below that there is no correlation between the planetary rotation period and the distance from the Sun.

There is, however, a relationship between a planet's distance from the Sun and its period of revolution. Kepler's third law of planetary motion says that the square of the planet's orbital period is proportional to the cube of its semimajor axis. For now, just read that as saying that a planet's 'year' is determined ONLY by its average distance from the Sun. The further away from the Sun it is, the slower the planet's orbital speed and the longer its path. Both of those factors result in taking longer to make one complete orbit and a planet having a longer year.



Answered by: Paul Walorski, B.A., Part-time Physics Instructor

QUESTION #477


Asked by: Navid Dianaty There is no connection between a planet's distance from the Sun and its rate of rotation (spin on its own axis or Planetary Rotation Period). While it is true that, generally speaking, the gas giants have higher rotation rates than the earth like planets closer to the Sun, any correlation is only coincidental. Mars, for example, is further from the Sun than Earth but has a slightly slower rate of rotation - its planetary rotation period is 1.03 Earth days. Pluto. the furthest planet from the Sun, has a planetary rotation period of 6.39 Earth days. You can see in the plot below that there is no correlation between the planetary rotation period and the distance from the Sun.

There is, however, a relationship between a planet's distance from the Sun and its period of revolution. Kepler's third law of planetary motion says that the square of the planet's orbital period is proportional to the cube of its semimajor axis. For now, just read that as saying that a planet's 'year' is determined ONLY by its average distance from the Sun. The further away from the Sun it is, the slower the planet's orbital speed and the longer its path. Both of those factors result in taking longer to make one complete orbit and a planet having a longer year.


Answered by: Paul Walorski, B.A., Part-time Physics Instructor

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