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stayAstrodynamicsAny track constructed under the standard hypothesis must be in the shape of a conical section.The eccentricity of the cone section and the eccentricity of the orbit are important parameters to define the shape of the orbit, and the absolute shape is defined.Eccentricity can be explained by how far the shape deviates from the circle.
For example, the eccentricity of the Earth's orbit is 0.0167, but due to the gravitational attraction between planets, it will slowly become close to 0 after a period of time, and the maximum value is about 0.05.(Refer to [1] for the figure).
In other values, the eccentricity of Mercury (0.2056) is the largest among the planets in the solar system.In the planetary redefinition in 2006, Pluto, a dwarf planet, has a larger eccentricity of about 0.248, and the moon has a noteworthy eccentricity of 0.0554.The eccentricity of other planets can be referred to the planetary table of the solar system.
Impact on climate
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The length of the season corresponds to the area swept by the earth in its orbit between the equinoxes and solstices.
Track eccentricity diagram
Orbital mechanics requires that the seasonal length should be proportional to the swept area of the corresponding seasonal quadrant, so the time (date) at the apocentric point will be longer than that at the pericentric point at the extreme value of orbital eccentricity.Today, in the Northern Hemisphere, in autumn and winter, the Earth moves at the fastest speed near the perihelion, so winter and autumn are shorter than spring and summer.In 2006, summer in the Northern Hemisphere was 4.66 days longer than winter, and spring was 2.9 days longer than autumn.(source) The axial precession slowly changes the position of the Earth's equinoxes and solstices in the orbit. See the regression year for more detailed descriptions and values.In the next 10000 years, the winter in the Northern Hemisphere will gradually become longer and the summer will become shorter. Finally, the created environment will naturally trigger the next ice age.
A simple proof of an elliptical orbit is as follows:
sin−1e。
You can look at the eccentricity like this. The eccentricity e of an ellipse is the angle projection of a circle.For example, the eccentricity of Mercury is (0.2056). A simple calculation of the inverse function of sine can get the projection angle of 11.86 degrees. Then observe any circular object (such as a coffee cup viewed from above) at the slant angle of that value. The ellipse projected into your eyes will have the same eccentricity.
calculation
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The eccentricity of the orbit can be calculated from the orbit state vector to know the magnitude of the eccentricity vector: e is the eccentricity vector.
For elliptical orbits, it can also be calculated from the near arch point and far arch point:
