If a star’s distance ($d$) estimate is incorrect by a factor of two, how does this error propagate into the calculated tangential velocity ($V_t$)?

The calculated tangential velocity ($V_t$) will also be off by a factor of two

The conversion of proper motion ($ ext{μ}$), an angular measurement, into the physical tangential velocity ($V_t$) is directly dependent on knowing the star's distance ($d$). The relationship implies a direct proportionality between the distance and the resultant physical speed when the angular drift is held constant. Consequently, if the distance estimate ($d$) used in the conversion formula is inaccurate by a specific factor—for instance, doubled or halved—the resulting calculated tangential velocity ($V_t$) will reflect that exact same proportional error. This dependency underscores why accurate distance determination, often achieved via parallax measurements, is the largest source of uncertainty in the final calculation of the total space velocity for many stars.