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 H _ { 0 } tension of the Hubble constant measured from different tools [ 5 , 6 , 7 ] .
Using spectroastrometry [ 8 ] , 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 resolution [ 9 ] .
Fortunately , reverberation mapping ( RM ) [ 10 ] of active galactic nuclei ( AGNs ) reliably provides linear sizes of their BLRs [ 11 ] .
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 GRAVITY [ 9 ] and an RM campaign [ 12 ] , and find an angular distance of 551.5 _ { -78.7 } ^ { +97.3 } Mpc and H _ { 0 } = 71.5 _ { -10.6 } ^ { +11.9 } { km s ^ { -1 } Mpc ^ { -1 } } .
Advantages of the analysis are 1 ) its pure geometrical measurements and 2 ) it simultaneously yields mass of the central black hole in the BLR .
Moreover , we can conveniently repeat measurements of selected AGNs to efficiently reduce the statistical and systematic errors .
Future observations of a reasonably sized sample ( \sim 30 AGNs ) will provide distances of the AGNs and hence a new way of measuring H _ { 0 } with a high precision \left ( \lesssim 3 \% \right ) to test the H _ { 0 } tension .