# How to calculate velocity vector in perifocal coordinates [closed]

Well the formula for it is here:

Though if r is the radius and f is the true anomaly (which I assume is radians), then what is r dot and f dot respectively?

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– uhoh
Commented Aug 16, 2021 at 0:27

The formula for velocity vector in perifocal actually very simple, no rotation matrices required:

$$\mathbf{v_{perifocal}} = \begin{bmatrix} -\sqrt{\frac{\mu}{p}} \sin f \\ \sqrt{\frac{\mu}{p}} (e + \cos f) \\ 0 \\ \end{bmatrix}$$

the angular/orbital momentum is equal to the radius squared times by $$\dot{f}$$. As shown here (make sure to take the length of the orbital momentum vector):

$$h = r^2 \dot{f}$$

So we can re-arange the equation to find $$\dot{f}$$ :

$$\dot{f} = \frac{h}{r^2}$$

We get r dot by differentiating the polar equation. The formula for $$\dot{r}$$ is this :

$$\dot{r} = \sqrt{\frac{\mu}{p}} (e \sin f)$$

where $$p$$ is the semi-lactus rectum, $$\mu$$ the standard gravitational parameter and $$f$$ is the true anomaly.

If you dont want to use the orbital momentum vector in your calculation you can now simply re-arange the previous equation which will give your the formula for $$\dot{f}$$ f dot:

$$\dot{f} = \frac{\sqrt{\frac{\mu}{p}} (1 + e \cos f)}{r}$$