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Measuring the geometry of multi-planet extrasolar systems can provide insightinto their dynamical history and the processes of planetary formation. Suchmeasurements are challenging for systems detected through indirect techniquessuch as radial velocity and transit, having only been measured for a handful ofsystems to-date. We aimed to place constraints on the orbital geometry of theouter planet in the $\pi$ Mensae system, a G0V star at 18.3 pc host to awide-orbit super-jovian ($M\sin i = 10.02\pm0.15$ $M_{\rm Jup}$) with a5.7-year period and an inner transiting super-earth ($M=4.82\pm0.85$$M_\oplus$) with a 6.3-d period. We combined astrometric measurements from theHipparcos and Gaia satellites with a precisely determined spectroscopic orbitin an attempt to constrain the inclination of the orbital plane of the outerplanet. We measured an inclination of $i_b=49.9_{-4.5}^{+5.3}$ deg for theorbital plane of $\pi$ Mensae b, leading to a direct measurement of its mass of$13.01_{-0.95}^{+1.03}$ $M_{\rm Jup}$. We found a significant mutualinclination between the orbital planes of the two planets; a 95% credibleinterval for $i_{\rm mut}$ of between $34.5^\circ$ and $140.6^\circ$ afteraccounting for the unknown position angle of the orbit of $\pi$ Mensae c,strongly excluding a co-planar scenario for the two planets within this system.All orbits are stable in the present-day configuration, and secularoscillations of planet c's eccentricity are quenched by general relativisticprecession. Planet c may have undergone high eccentricity tidal migrationtriggered by Kozai-Lidov cycles, but dynamical histories involving diskmigration or in situ formation are not ruled out. Nonetheless, this systemprovides the first direct evidence that giant planets with large mutualinclinations have a role to play in the origins and evolution of somesuper-Earth systems.

A significant mutual inclination between the planets within the $\pi$ Mensae system