Distance measurements for extragalactic objects are a fundamental problem in astronomy^1,2 and cosmology^3,4. In the era of precision cosmology, we urgently need better measurements of cosmological distances to observationally test the increasing H₀ tension of the Hubble constant measured from different tools^5,6,7. Using spectroastrometry⁸, GRAVITY at The Very Large Telescope Interferometer successfully revealed the structure, kinematics and angular sizes of the broad-line region (BLR) of 3C 273 with an unprecedentedly high spatial resolution⁹. Fortunately, reverberation mapping (RM)¹⁰ of active galactic nuclei (AGNs) reliably provides linear sizes of their BLRs¹¹. Here, we report a joint analysis of spectroastrometry and RM observations to measure AGN distances. We apply this analysis to 3C 273 observed by both GRAVITY⁹ and an RM campaign¹², and find an angular distance of \(551.{5}_{-78.7}^{+97.3} \) Mpc and \({H}_{0}=71.{5}_{-10.6}^{+11.9}\ {\rm{km}}\ {{\rm{s}}}^{-1}\ {{\rm{Mpc}}}^{-1} \). The advantages of the analysis are its pure geometrical measurements and that it simultaneously yields the mass of the central black hole. Moreover, we can conveniently repeat measurements of selected AGNs to efficiently reduce the statistical and systematic errors. Future observations of a reasonably sized sample (~30 AGNs) will provide the distances of the AGNs and hence a new way of measuring H₀ with a high precision (≲3%) to test the H₀ tension.

河外天体的距离测量是天文学^1,2和宇宙学^3,4的一个基本问题。在精密宇宙学时代，我们迫切需要更好地测量宇宙学距离，以观察不同工具测量的哈勃常数H _{0张力的增加}^5,6,7。使用光谱天文学⁸，超大望远镜干涉仪的 GRAVITY 以前所未有的高空间分辨率⁹成功揭示了 3C 273 的宽线区域 (BLR) 的结构、运动学和角度尺寸。幸运的是，混响映射 (RM) ^{10活动星系核 (AGN) 可靠地提供了其 BLR 11}的线性大小。在这里，我们报告了光谱天文学和 RM 观测的联合分析，以测量 AGN 距离。我们将此分析应用于 GRAVITY ⁹和 RM 运动¹²观察到的 3C 273 ，并找到\(551.{5}_{-78.7}^{+97.3} \)  Mpc 和\({H} _{0}=71.{5}_{-10.6}^{+11.9}\ {\rm{km}}\ {{\rm{s}}}^{-1}\ {{\rm{Mpc }}}^{-1} \). 分析的优点是它的纯几何测量，并且它同时产生了中心黑洞的质量。此外，我们可以方便地重复测量选定的 AGN，以有效减少统计和系统误差。未来对合理大小的样本（约 30 个 AGN）的观察将提供 AGN 的距离，从而提供一种高精度（≲ 3%）测量H _0以测试H ₀张力的新方法。