g0 is indeed an idealized "surface gravity" for Earth. As arbitrary and nonsensical as that is for many applications, you may be better off just directly using the effective exhaust velocity:

$$\Delta v=v_{e} \ln \left(\frac{m_{0}}{m_{f}}\right)$$

$g_0$ is indeed an idealized "surface gravity" for Earth.¹ As arbitrary and nonsensical as that is for many applications, you may be better off just directly using the effective exhaust velocity:

$$\Delta v=v_{e} \ln \left(\frac{m_{0}}{m_{f}}\right)$$

¹From Wikipedia's Standard gravity:

The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by $ɡ_0$ or $ɡ_n$, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665 m/s2</sup=> (about 32.17405 ft/s2). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration.