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With its near-to-mid-infrared high contrast imaging capabilities, JWST isushering us into a golden age of directly imaging Jupiter-like planets. As thetwo closest cold Jupiters, $\varepsilon$ Ind A b and $\varepsilon$ Eridani bhave sufficiently wide orbits and adequate infrared emissions to be detected byJWST. To detect more Jupiter-like planets for direct imaging, we develop aGOST-based method to analyze radial velocity data and multiple Gaia datareleases simultaneously. Without approximating instantaneous astrometry bycatalog astrometry, this approach enables the use of multiple Gaia datareleases for detection of both short-period and long-period planets. Wedetermine a mass of $2.96_{-0.38}^{+0.41}$ $M_{\rm Jup}$ and a period of$42.92_{-4.09}^{+6.38}$ yr for $\varepsilon$ Ind A b. We also find a mass of$0.76_{-0.11}^{+0.14}$ $M_{\rm Jup}$, a period of $7.36_{-0.05}^{+0.04}$ yr,and an eccentricity of 0.26$_{-0.04}^{+0.04}$ for $\varepsilon$ Eridani b. Theeccentricity differs from that given by some previous solutions probably due tothe sensitivity of orbital eccentricity to noise modeling. Our work refines theconstraints on orbits and masses of the two nearest Jupiters and demonstratethe feasibility of using multiple Gaia data releases to constrain Jupiter-likeplanets.

Revised orbits of the two nearest Jupiters