That half-way point can be defined a second way: it's the point on either side of the orbit between the minima and maxima where the first derivative is zero (doing this requires defining the first derivative at the minima and maxima as infinity. Sue me.) we now have one local minima, one local maxima, and the "half-way" point between the two. cartesian coordinates in a polar coordinate conversation. With the sun no longer at (0,0) (yeah, yeah, yeah. But it doesn't take much - especially with an axial tilt > 0°. It's worth noting that Earth's orbit is only slightly elliptical and only slightly off-center (and I might be wrong about that). Offset the elliptical orbit such that the sun is no longer at the center of the orbit But there's something magic about the equinoxes we experience on Earth, and it doesn't happen when the axial tilt is 0°.ģ. That's because an equinox is, simplistically, the point along the orbit when the distance between the sun and the planet is (maxima - minima)/2 minima. Now, philosophically there are four equinoxes. Remember that the planetary axial tilt is still 0°. We do have two solstices: one winter, one summer, and they happen twice each year. In this circumstance, we have no equinoxes. The minima are equal to one another and the maxima are equal to one another. Elongate the orbit, but leave it centered on the sunĪgain, using polar coordinates, we now have two local minima and two local maxima. The distance from the sun never changes.Ģ. Measuring the orbit in polar coordinates, there are no local minima or maxima. There are no solstices, no equinoxes, and no seasons. Planetary axis is 90° off the orbital plane.$\lambda\simeq \bar, $Īny of the astrophysicists on this site could do a better job than I, but here goes. For the case of the vernal equinox, we can first estimate the time at which this event takes place by approximating the solar longitude as the mean solar longitude: i.e., The vernal equinox (i.e., the point on the sun's apparent orbit at which it passes through the celestial equator from south to north) corresponds to $\lambda = 0^\circ$, the summer solstice (i.e., the point at which the sun is furthest north of the celestial equator) to $\lambda = 90^\circ$, the autumnal equinox (i.e., the point at which the sun passes through the celestial equator from north to south) to $\lambda = 180^\circ$, and the winter solstice (i.e., the point at which the sun is furthest south of the celestial equator) to $\lambda = 270^\circ$.Ĭonsider the year 2000 CE. We can also use Tables 32 and 33 to calculate the dates of the equinoxes and solstices, and, hence, the lengths of the seasons, in a given year. A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere.Īn equinox is the instant of time when the plane of Earth's equator passes through the geometric center of the Sun's disk.įor the actual calculation you would need tables with the equation of time and the anomalies of the Sun, an example of actual calculation is given here
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