Elliptic orbit in 5D Space

Plotting the equation X^2 + Y^2 + Z^2 + W^2 + V^2 = 1 in 5D space explains eccentricity in elliptical orbits rather elegantly:

Values of W and V can only range between 0 & 0.98 if X,Y & Z are assumed to be 0.1. The complete chart made roughly with convert +append, -append command:

Plotting the circle equation in the 4th dimension (initial draft)

A quick summary of the calculations required to plot x^2 + y^2 + z^2 + w^2 = 1 on a graph. First, calculate x, y, z and w using a spreadsheet, for random values that satisfy the above equation:

Plot on a graph and verify:

The figures 2 and 3 in the centre may actually explain scattering and orbital jumping. Geometrically, an infinitesimally small point P can fall only near 1 or -1 since those values alone satisfy the equation x^2 = 1, and therefore, if x^2, y^2 and z^2 are zero or close to it, w^2 = 1, and the point defined by the equation could only fall near 1 or -1 in 4D space.