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New spectroscopic observations of Gamma Geminorum, a bright, 'normal' A1 IV star have resulted in an improved spectroscopic orbit. The orbital period is 12.632 +/- 0.002 yr, the eccentricity is 0.893 +/-0.002, and the orbital parallax is 0.0291 +/-0.0024 arcsec, or a distance of 34 pc. We determine a v sin i of 8 +/-1 km/s for the A star, which confirms that it is a slow rotator. Near-infrared spectroscopic observations at 8806 A, obtained through the brief nodal passage, have resulted in the probable detection of the secondary. The masses are 2.8 and 1.07 solar mass and the Delta V of the components is 6.0 mag. This Delta V supports the value of 5.6 mag obtained by Sato et al. (1993) from observations of the asteroid occultation of Gamma Gem in 1991. The magnitude difference and mass of the secondary are consistent with a G dwarf spectral type. The detection of such a faint secondary does not compromise the use in most contexts of Gamma Gem as a standard star.