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Double lines around a vector like this : $\mid\mid \textbf{v} \mid\mid$ represents the length or magnitude of a vector $\textbf{e}$ - Eccentricity vector $\textbf{r}$ - Position vector $\dot{\textbf{r} … }$ - Velocity vector $\mu$ - Standard gravitational parameter (mass of the earth multiplied by the gravitational constant G) This formula gives the eccentricity vector but to get eccentricity (which is …

$\omega$ are commonly replaced by the eccentricity vector. … vector. …

This is the eccentricity vector equation, $$e=\frac{1}{\mu}[(v^2-{\mu \over r})r-(r \cdot v)v]$$ $$e=|e|$$ Now this equation is written differently from many different sources but they essentially mean … I understand that the eccentricity of a parabola is 1 but this equation is for ellipses as well. So why is the answer always -1? Am I missing something? Thanks in advance. …

It has a parameterization gamma, a normal vector N, and then eccentricity and semilatus rectum equations. … I'm trying to figure out how they managed to get an eccentricity vector with no velocity and no gravitational parameter. …

When deriving the eccentricity vector you first start of with the equation of motion for the two body problem (we are concerned about the motion of the smaller body around a much larger mass) the equations … ^3}$$ Though I am not too sure why the author does this, it does say that now the equation can be integrated though I am not too sure why that is the case, like could this have been done with any old vector …

I am working on a personal project, and I want to write a program to obtain the RAAN given the angle of the eccentricity vector to the X-axis (ECI) along the XY plane, the declination (angle from XY plane …

All you have is the eccentricity vector and the orbital inclination. … For any orbital inclination and chosen eccentricity vector direction (magnitude is irrelevant for these purposes) where the angle between the eccentricity vector and the reference plane is less than the …

The eccentricity vector has a magnitude equivalent to the orbital eccentricity of the ellipse, and points along the line of apsides in the direction from the central body towards the periapsis. … of the eccentricity vector: $$e = \|\vec{e}\|$$ From that, you can get the perifocal unit vector $\hat{p}$ which points in the same direction as the eccentricity vector: $$\hat{p} = \frac{\vec{e}}{e}$ …

The expression on the right is meant to give the eccentricity vector but the vector notation has been lost. … You can see that the eccentricity vector x component is +0.8 and constant, and the y component is 0.0 That confirms that the eccentricity vector always points towards the direction of periapsis and it's …

An out of plane maneuver definitely changes where the eccentricity vector points. It might or might not change the magnitude of that vector. … This changes the $\hat r$ and $\hat z$ components of the eccentricity vector but leaves the $\hat \theta$ component unchanged: $$\Delta \vec e = \frac{-r v_r \Delta v\,\hat r + r\Delta v^2 \hat z}{\mu} …

Other information which I could add to the script to find the velocity vector is eccentricity eccentricity vector semi-major axis periapsis radius declination of the orbiter at apoapsis With this info … The position vector and the eccentricity vector are in the ECI reference frame if that is important. …

for these calculations: Eccentricity Vector has a positive magnitude Eccentricity Vector is not parallel to Position Vector. … $\hat{p}$ points at the orbital periapsis, and is co-directional with the eccentricity vector. This calculation requires a non-zero eccentricity. …

Why does the eccentricity vector always point towards the periapsis of an orbit? Why is the eccentricity vector used to describe near-circular orbits? … Let's start with this answer to Why does the eccentricity vector equation always equal -1?. …

The eccentricity vector meanwhile, points from the central body to the periapsis, and has magnitude equal to the eccentricity. … With these in hand, calculating the eccentricity is basically the focal length / the semi major axis, which then completely nails down the eccentricity vector. …

$$ This vector is a constant of motion. … The eccentricity vector is thus useful for determining both the eccentricity and the argument of periapsis. …