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13

This is because the summer and winter solstices (approx. June 21st and December 21st) do not correspond to the aphelion and perihelion (approx. July 5th and January 4th). Therefore, the average distance from the Sun is longer in the period from the Summer Solstice to Winter Solstice than vice versa, so the Earth is moving slower (on average) and it takes ...


8

First, don't think that equinox is when the day and night are the same. It is the moment, when the sun's declination is zero, or when the sun is directly over the equator. Let me explain ... Earth is always rotating around the Sun, so declination of the Sun is always changing (except at the solstices when it stops for a minute and goes in the other way). As @...


7

As you said, the Sun takes a year to cycle the Zodiac, and it takes a year between two spring or autumn equinoxes. Both statements are true, but "year" in them means two different things. It takes a sidereal year to cycle the Zodiac, but it takes a tropic year to cycle between equinoxes. Since the tropic year is about 20 minutes shorter, the equinoctial ...


7

The only idea I have that it might be due to the definition of sunset. The instance of sunrise occurs when the first bit of the Sun becomes visible at the horizon, while the instance of sunset occurs when the last bit of the Sun disappears below the horizon. This means the actual position of the center of the Sun is about 50 arc minutes below the horizon at ...


5

As Mike G said, the Sun's ecliptic longitude is ideal for this application. I see from your profile that you're a coder, with some knowledge of Python. Here's a short Python script that prints solar ecliptic longitudes for each day for any given year. (It actually prints 367 days, I figured an extra day or two may be useful). The code mostly avoids features ...


5

Two further points to make are that: (1) because of the way we define sunrise and sunset as being when the entire Sun is below the horizon not just the centre of the Sun. (2) When the Sun is close to the horizon the Sun’s ray are refracted (bent) by the Earth’s atmosphere so that the Sun appears to be slightly higher in the sky that it would be if the ...


5

The easiest graph to consider is the graph of day-length. If the day-length varies from 8 to 16 hours, there can only be two equinoxes: At the time of equinox, the day length changes at the fastest rate, by a few minutes in temperate regions, compared to the solstices, which change by a few seconds every day. So, the equinox doesn't exist perfectly, the ...


4

Instead of looking at sunset/sunrise times, it's easier to look at noon, which is right in the middle between sunset and sunrise: 11:50am in March and 11:35am in September. The fact that noon doesn't always happen at the same time of the day (when measured with steady clocks) is expressed by the Equation of Time. Two factors play a role here: The plane in ...


4

The Vernal Equinox is defined by the point where the sun's path across the sky, the Ecliptic, crosses the Celestial Equator. It is always going to be on the Celestial Equator. Given the various ways that objects in orbit over Earth are perturbed, any set of keplerian orbital parameters that describe the orbit of any object over the Earth (including the Moon!...


4

The main factors that affect the length of the March equinox year (*1) over time can be divided into three components: Changes in the length of the solar day Changes in the length of the mean tropical year Difference between the mean tropical year and March equinox year Of these, the change in the length of the solar day is most significant in the long ...


4

The diagram below illustrates the reason, which is that the earth moves at different speeds during it revolution around the sun and the distribution of those speeds is not equal because the solstices/equinoxes are not located at symmetrical points on the ellipse vis-a-vis the speed symmetries, which are centered on the aphelion and perihelion. Diagram by ...


4

What you need is the Sun's ecliptic longitude for a given date. As you expect, it increases faster near perihelion (1.02°/day in early January) and slower near aphelion (0.95°/day in early July). It is exactly 0° at the March equinox, 90° at the June solstice, 180° at the September equinox, and 270° at the December solstice. Wikipedia:Position of the Sun ...


3

Or is 0 degrees the direction towards the ascending node 'equinox'? Which is NOT towards the Sun on January first... The answer is yes, more or less. From JPL's HORIZONS, the location of the Sun at Noon Terrestrial Time on 1 Jan 2000 is, ignoring atmospheric effects, a right ascension of 18 hours, 45 minutes, and 9.36 seconds. This is nowhere close to a ...


3

This might happen if you model the ring as opaque but of very little thickness and in the same plane as the vector between the planet and the sun Seen edge on from the equator, the ring would block none of the sun's light, but from a little north or south of the equator, the ring would block more of one hemisphere of the sun. So I would check first if your ...


3

The fact that equinox and solstice dates don’t line up with the quadrants of the circle is due to the ellipticity and eccentricity of Earth’s orbit around the Sun. Let’s go back in history a little. Ancient Greeks thought all celestial movements were circular. This model was followed for approximately 2,000 years until Copernicus finally realized the Earth ...


3

Yes, the constellations that are visible at midnight on Jan 1 are different than those visible at midnight on July 1 (6 months later). The website Stelvision has a star chart that you can customize for date, time, and location. This is due to the Earth's revolution around the Sun and the direction that an observer is facing at midnight. From a given ...


2

The "specified value" would be the latitude of the observer, and would be the average of the maximum and minimum values observed at the solstice. The altitude of the sun above the horizon is measured when it is due South. This is what "meridian elevation" means. So no clock is required. However this method can at best determine the date of the equinox. ...


2

Sunrise or sunset is usually defined as the moment when the upper limb of the Sun appears on the horizon. This is conventionally computed as the time when the center of the Sun is 50' below the horizon, using a 16' angular radius and assuming 34' atmospheric refraction. Let δ be the Sun's declination and φ be the observer's latitude north of the ...


2

The celestial equator's plane intersects the horizon due east and due west, no matter where you are on Earth (except at the poles where the horizon is the celestial equator). Those that have the sunrise at the exact time of the equinox will see the sun rise in the east (90º). For the rest, it will be too late, the sun will have made the crossing, and it ...


2

The shadow cast by the rings onto Saturn is much more pronounced as shown by the Cassini spacecraft (e.g. here). Mind also, that the shadow is comparatively sharper than on Earth as the sun's apparent diameter is smaller at the ring planets' distance. And, of course, the intensity of the shadow depends on the density of the rings - and the obliquity of the ...


2

The equinoxes are where the ecliptic crosses the equator. As the Earth's axis and equatorial plane pivot under precession, the equinox points migrate westward along the ecliptic, 360° in 25800 years or 1.4° per century. This animation shows the vernal equinox drifting 28° in 20 centuries of precession: Images generated by Stellarium The Sun ...


2

The climate modelers' VERNAL is equivalent to this formula, where Y is an integer, ΔY = Y - 2000, and JD0 is epoch J2000 = JD 2451545.0 = 2000-01-01 12:00 TT: $$ \text{JD}_\unicode{x2648}(Y) = \text{JD}_0 + 78.813 + 365.24250~{\Delta Y} $$ We can tune the coefficients to fit JPL DE431 for years -5000 to 9000: $$ \text{JD}_\unicode{x2648}(Y) = \text{JD}_0 ...


2

Calculating the exact time of the vernal equinox is essential for many astronomical calculations. I dispute that claim. What is true is that calculating the exact time of the vernal equinox is essential for some astrological and religious calculations. My question: Is the above quoted algorithm the most accurate way of calculating the vernal equinox for ...


2

By looking at https://en.wikipedia.org/wiki/Solstice, we find the dates for equinox and solstice in 2021 as March 20, June 21, Sep 22, and Dec 21. These correspond to days 79,172,265,355. That gives us differences of 89, 93, 93,and 90 days. Points need to be 90/89 degrees apart in the first quadrant, 90/93 degrees apart in the second quadrant, etc... Care ...


2

The pattern is possible if there is a very large gap between two rings. Based on the spacing of the shadows, the gap would be at least as wide as a ring. If there is only one ring, then it likely is a quirk of the engine.


1

Given the symmetry of the problem... That's the key to the answer. While we like to imagine motion in the system as having some symmetries, it's all a bit wobbly. As @Glorfindel points out the particular asymmetry is connected to the direction that Earth's tilted axis points relative to the shape of Earth's elliptical orbit. If the Earth's orbit were a ...


1

The earth is smoothly and constantly moving around the sun. At the moment of the equinox, a line from the center of the sun to the center of the earth passes through the equator. That only lasts an instant. Before that instant, the line is on one side of the tilted equator, and after that, it's on the other side. The day labeled "the equinox" is ...


1

Terminology is critical. As mentioned in other answers, precession causes the equinoxes (the points where the ecliptic intersects the celestial equator) to move from one constellation to another. For example, the March equinox was in the constellation Aries in the time of the ancient Greeks, is in the constellation Pisces today, and will be in the ...


1

The azimuth of the sunrise (or sunset, or any object) is a function of the Sun's declination and observer's latitude. It can be calculated from the following forumla: $$\cos(\theta_R)=-\frac{\sin(declination)}{\cos(latitude)}$$ where $\theta_R$ is measured from due south to the location where the object rises or sets. For example, at 55 degrees north ...


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