I know the formula for orbital velocity but that doesn't seem of much help when I'm trying to calculate how fast the primary wobbles, or since the barycenter is outside Pluto in the Pluto-Charon system, how fast it orbits.
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From the NASA Pluto Fact Sheet:
- Mass of Pluto $m_1 = 1.303\times 10^{22}\ \mathrm{kg}$
- Mass of Charon $m_2 = 1.586\times 10^{21}\ \mathrm{kg}$
- Mean distance from Pluto $r = 19596\ \mathrm{km}$
- Orbital period $P = 6.3872\ \mathrm{d}$
The orbit is nearly circular (the fact sheet gives an eccentricity of 0.0, other sources give very small values). So treat as circular motion.
The radius of the orbit of Pluto around the barycentre is given by:
$$r_1 = r \left(\frac{m_2}{m_1+m_2}\right) = 2126\ \mathrm{km}$$
Then use the usual formula for circular motion:
$$v = \omega r$$
where $\omega = \frac{2\pi}{P}$, giving a value of around $24.2\ \mathrm{m\,s}^{-1}$.
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$\begingroup$ So, just under the speed limit. 54.1 mph. ;-) $\endgroup$– userLTKCommented Jul 11, 2020 at 7:11