The mass and separation of binary system with only information about one star [closed]

If we can observe that a star and an unmeasurable planet are in circular orbit around a common center of mass. If we know the speed of the star to be $100\,m/s$, the mass of the star to be $2 \cdot 10^{33}\,g$ and a period of $432,000$ seconds. how can we try to calculate the separation, the mass of the second planet? Can make approximation when appropriate

I'm confused because I'm not sure if there's enough information to solve without making assumptions on the mass or the radius of the second planet. But that's what the question is asking

the only thing I can really calculate here is the orbit radius for the star with the velocity and the period.

Any help would be welcomed.

closed as off-topic by Rob Jeffries, Kyle Kanos, Jon Custer, Qmechanic♦Feb 21 '17 at 14:51

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There are different radii that you need to consider (see attached image). The Center Of Mass (COM) is indicated with the red X. The radius of the orbit of the star is $R_s$ and the radius of the orbit of the planet is $R_p$; the total separation between the two is the "semi-major axis" $a = R_p + R_s$.
• @casualprogrammer -- You don't have to make any assumptions. Keep it as an unknown value. Kepler's third gives an expression for $(R_s+R_p)^3$ in terms of the known star velocity, period, and mass and the unknown planet mass. The center of mass gives an expression for $(R_s+R_p)$ in terms of the known known star period and mass and the unknown planet mass. That's two equations with two unknowns, $a=R_s+R_p$ and $m_p$. You'll get a cubic. You can make the approximation $M+m\approx M$ at this point to simplify the calculation, but you don't need to (cubics are solvable). – David Hammen Feb 20 '17 at 22:55