Front Cover Equations

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Adapted From Fundamentals of Astrodynamics and Applications, Second Edition by David A. Vallado (Vallado Orange Book)

Note! This is not an exact copy of the front cover. I have made changes to symbols where appropriate for legibility and such. For instance, I use (theta) instead of (nu) for true anomaly, as it looks too much like velocity. Go ahead and try it out! . Also, I use the same symbol for elliptic, parabolic, and hyperbolic eccentric anomaly. They are all used the same way, and it is always clear from context which is which.

I also group things differently, and I add in a couple of equations which are in pencil in my book.

These are provided pretty much without comment, as a reference for someone who knows what to do with the equation, but just needs to see it written out.

Common two-body equations[edit]

Specific angular momentum
Specific Mechanical Energy
Orbital period
Eccentricity Vector
Radial Rate
Angular Rate
Semi-major axis


Circle Ellipse Parabola Hyperbola
Eccentric Anomaly

True Anomaly

Mean Anomaly

Other Parameters[edit]

Circle Ellipse Parabola Hyperbola
Flight Path Angle

Polar Form Equation
Apoapsis (negative)
Semi-parameter (positive)
Semi-major axis
Hyperbolic excess velocity
Asymptotic True Anomaly
Mean Motion