# Working with Keplerian Elements & Deriving Vernal Equinox

• Philosophaie
In summary, the conversation discusses the use of Keplerian Elements from the JPL website, including the parameters of semi-major axis, eccentricity, inclination, mean longitude, longitude of the periapsis, and longitude of the ascending node. The conversation also mentions the derivation of mean anomaly, eccentric anomaly, true anomaly, radius, and the vernal equinox from these elements. The vernal equinox is explained to occur on March 21 every year and is used as a reference angle for the start of the ascending node. The individual is unsure if their calculations are accurate and also mentions using a website to convert from celestial to galactic coordinates.
Philosophaie
I am working with the Keplerian Elements from the JPL web site.

a - Semi-Major Axis
e - Eccentricity
I - Incilination
L - Mean Longitude
long.peri. - Longitude of the Periapsis
long.node.or N - Longitude of the Ascending Node

http://ssd.jpl.nasa.gov/txt/p_elem_t2.txt

From this you can derive

MA - Mean Anomaly
EA - Eccentric Anomaly
v - True Anomaly
Equ - Vernal Equinox

All of this data revolves around the v=0 point or the Periapsis, the point where the elliptical orbit is the closest to the sun. Now from this point the Vernal Equinox can be derived. The Vernal Equinox occurs on about March 21 every year. When looking thru the Sun on 3-21 the constellation that you see is Pisces. At the angle (the Sun to Pisces from the Periapsis) is the basis of the reference angle for the start of the Ascending Node, I think. It comes out to be 270.02 for the Earth. The data seems to be coming out right, Equ+N+w+v=0 @ 12-21, Equ+N+w+v=90 @ 3-21, Equ+N+w+v=180 @ 6-21 and Equ+N+w+v=270 @ 9-21. I just want to know If I am way off or I am right on target.

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## 1. What are Keplerian elements?

Keplerian elements are a set of orbital parameters used to describe the motion of a celestial body around a central body. They include the semi-major axis, eccentricity, inclination, longitude of the ascending node, argument of periapsis, and mean anomaly.

## 2. How are Keplerian elements derived?

Keplerian elements can be derived from observational data, such as the position and velocity of a celestial body at a specific time. They can also be calculated from mathematical models of orbital mechanics.

## 3. What is the vernal equinox?

The vernal equinox is the point in Earth's orbit around the sun where the equatorial plane and the ecliptic plane intersect. It marks the beginning of spring in the Northern Hemisphere and fall in the Southern Hemisphere.

## 4. How is the vernal equinox used in working with Keplerian elements?

The vernal equinox is used as a reference point in calculating the longitude of the ascending node and the argument of periapsis in Keplerian elements. It also helps determine the orientation of a celestial body's orbit in relation to the Earth's equatorial plane.

## 5. Why is working with Keplerian elements important?

Keplerian elements allow scientists to accurately describe and predict the motion of celestial bodies in space. They are essential for space navigation, astronomical observations, and understanding the dynamics of the solar system.

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