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One exoplanet, TOI-1052b, is Neptune-mass and transits the star, and an additional planet TOI-1052c is observed in radial velocities but not seen to transit. We confirm the planetary nature of TOI-1052b using precise radial velocity observations from HARPS and determined its parameters in a joint RV and photometry analysis. TOI-1052b has a radius of $2.87^{+0.29}_{-0.24}$\u2009R\u2295, a mass of 16.9\u00a0\u00b1\u00a01.7\u2009M\u2295, and an orbital period of 9.14\u2009d. TOI-1052c does not show any transits in the TESS data, and has a minimum mass of $34.3^{+4.1}_{-3.7}$\u2009M\u2295 and an orbital period of 35.8\u2009d, placing it just interior to the 4:1 mean-motion resonance. Both planets are best fit by relatively high but only marginally significant eccentricities of $0.18^{+0.09}_{-0.07}$ for planet b and $0.24^{+0.09}_{-0.08}$ for planet c. We perform a dynamical analysis and internal structure model of the planets as well as deriving stellar parameters and chemical abundances. The mean density of TOI-1052b is $3.9^{+1.7}_{-1.3}$\u2009g\u2009cm\u22123 consistent with an internal structure similar to Neptune. A nearby star is observed in Gaia DR3 with the same distance and proper motion as TOI-1052, at a sky projected separation of $\\scriptstyle \\sim$1500\u2009au, making this a potential wide binary star system.<\/jats:p>","DOI":"10.1093\/mnras\/stad2183","type":"journal-article","created":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T07:39:08Z","timestamp":1689925148000},"page":"5804-5816","source":"Crossref","is-referenced-by-count":4,"title":["Discovery and characterization of two Neptune-mass planets orbiting HD 212729 with <i>TESS<\/i>"],"prefix":"10.1093","volume":"524","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5080-4117","authenticated-orcid":false,"given":"David J","family":"Armstrong","sequence":"first","affiliation":[{"name":"Department of Physics, University of Warwick , Coventry CV4 7AL , UK"},{"name":"Centre for Exoplanets and Habitability, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL , UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5899-7750","authenticated-orcid":false,"given":"Ares","family":"Osborn","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Warwick , Coventry CV4 7AL , UK"},{"name":"Centre for Exoplanets and Habitability, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL , UK"}]},{"given":"Vardan","family":"Adibekyan","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP , Rua das Estrelas, 4150-762 Porto , Portugal"}]},{"given":"Elisa","family":"Delgado-Mena","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP , Rua das Estrelas, 4150-762 Porto , Portugal"}]},{"given":"Saeed","family":"Hojjatpanah","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Astrophysique de Marseille , Pole de l\u2019Etoile Site de Chateau-Gombert, 38 Rue Frederic Joliot-Curie, Marseille 13338 , France"}]},{"given":"Steve B","family":"Howell","sequence":"additional","affiliation":[{"name":"NASA Ames Research Center , Moffett Field, CA 94035 , USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3477-2466","authenticated-orcid":false,"given":"Sergio","family":"Hoyer","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Astrophysique de Marseille , Pole de l\u2019Etoile Site de Chateau-Gombert, 38 Rue Frederic Joliot-Curie, Marseille 13338 , France"}]},{"given":"Henrik","family":"Knierim","sequence":"additional","affiliation":[{"name":"Institute for Computational Science, Center for Theoretical Astrophysics\u00a0& Cosmology, University of Zurich , Winterthurerstr. 90, 8057 Zurich , Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9047-2965","authenticated-orcid":false,"given":"S\u00e9rgio G","family":"Sousa","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP , Rua das Estrelas, 4150-762 Porto , Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3481-9052","authenticated-orcid":false,"given":"Keivan G","family":"Stassun","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Vanderbilt University , Nashville, TN 37235 , USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8014-6162","authenticated-orcid":false,"given":"Dimitri","family":"Veras","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Warwick , Coventry CV4 7AL , UK"},{"name":"Centre for Exoplanets and Habitability, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL , UK"},{"name":"Centre for Space Domain Awareness, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL , UK"}]},{"given":"David R","family":"Anderson","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Warwick , Coventry CV4 7AL , UK"},{"name":"Centre for Exoplanets and Habitability, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL , UK"}]},{"given":"Daniel","family":"Bayliss","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Warwick , Coventry CV4 7AL , UK"},{"name":"Centre for Exoplanets and Habitability, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL , UK"}]},{"given":"Fran\u00e7ois","family":"Bouchy","sequence":"additional","affiliation":[{"name":"Department of Astronomy of the University of Geneva, Geneva Observatory , Chemin Pegasi 51, 1290 Versoix , Switzerland"}]},{"given":"Christopher J","family":"Burke","sequence":"additional","affiliation":[{"name":"Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology , Cambridge, MA 02139 , USA"}]},{"given":"Jessie L","family":"Christiansen","sequence":"additional","affiliation":[{"name":"Caltech\/IPAC , Mail Code 100-22, 1200 E. 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