# Are Delta-V requirements for leaving the surface of a planet proportional to gravity?

I am trying to gain some intuition about Delta-V requirements.

My understanding is if the Delta-V budget was doubled, the difficulty of the mission is more than double because of the exponential nature of having to carry more fuel.

My question is - how are Delta-V requirements influenced by the planet's gravity?

For example, if Earth's gravity were to double, would Delta-V (to an orbit of similar height) double as well? Or is this a non-linear effect?

The acceleration of gravity is $g={GM\over r^2}$, where $M$ is the mass, and $r$ is the radius of the surface. $G$ is Newton's gravitational constant. The escape velocity from Earth is $v_e=\sqrt{2GM\over r}$.
You would also need to know where you're going. $\Delta V$ to where?
Yes, the rocket equation is exponential in $\Delta V$. For a single stage, ${m_i\over m_f}=e^{\Delta V\over v_e}$, where $m_i$ is the initial mass, $m_f$ is the final mass (the difference being the mass of the propellant expended), and $v_e$ is the exhaust velocity of the engine.