File:CircularToEllipticalOrbits.jpg

English: The bottom scale denotes the fractional change in velocity from circular, which peaks out at Δv/v_c ≤ 2^1/2-1 ≈ 0.41421, beyond which the orbit becomes unbound (and hyperbolic instead of ellipitical).

The left scale denotes the resulting peri-point radius (bottom) and apo-point radius (top) r_x/r_c following the Delta-v from circular on the bottom axis.

The center scale denotes the eccentricity of the final ellipitical orbit, whose simple dependence on the radius ratio gives it up/down symmetry.

The right scale denotes the elliptical to circular orbit period ratio, which bottoms out at T/T_c ≥ 2^-3/2 ≈ 0.35355 if one simply stops and begins a plunge downwards on a collision course with one's attractor.

The top scale denotes the fractional velocity gain at apo-point (left), and loss at peri-point (right), needed to go circular from an ellipical orbit, which bottoms out at Δv/v_x ≥ 2^-1/2-1 ≈ -0.29289, making even extremely elliptical orbits relatively easy to circularize with a peri-point burn.