The Eccentricity Vector calculator computes the orbital eccentricity vector based on the velocity vector (V) and the position vector (R).

INSTRUCTIONS: Enter the following:

• (`vecv`) Velocity Vector in meters per second (comma separated values)
• (`vecr`) Position Vector in meters (comma separated values)

Eccentricity Vector (`vece`): The calculator returns the eccentricity vector. 

The Math / Science

This equation produces the three components of the Eccentricity Vecotor, `vece`

Notes

The orbits and trajectories that can be characterized by eccentricity are:

3D Vector Functions

• k V - scalar multiplication
• V / |V| - Computes the Unit Vector
• |V| - Computes the magnitude of a vector
• U + V - Vector addition
• U - V - Vector subtraction
• |U - V| - Distance between vector endpoints.
• |U + V| - Magnitude of vector sum.
• V • U - Computes the dot product of two vectors
• V x U - Computes the cross product of two vectors
• V x U • W - Computes the mixed product of three vectors
• Vector Angle - Computes the angle between two vectors
• Vector Area - Computes the area between two vectors
• Vector Projection - Compute the vector projection of V onto U.
• Vector Rotation - Compute the result vector after rotating around an axis.
• (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
• (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
• (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
• (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates
• Vector Normal to a Plane Defined by Three Points