Rocket maximum distance [closed]

Question

let's say I have a liquid rocket what would maximize the distance traveled by the rocket thus consume less fuel constant velocity or acceleration or why?

Answer 1

Newton’s first law, roughly “an object in motion stays in motion,” tells you that any rocket can send you any distance in empty space.

The main way we compare rocket performance is $\Delta V$, defined by the rocket equation:

$$\Delta V = v_e \cdot \ln(\frac{m_0}{m_f})$$

• $\Delta V$ is the change in velocity in m/s
  
• $v_e$ is the rocket exhaust velocity in m/s
  
• $m_f$ is the empty mass of the rocket
  
• $m_0$ is the mass of rocket plus all propellants

There is no component of this equation that says anything about the burn time, so we can infer that there is no way to maximize $\Delta V$ by changing our throttle.

In practice, engines are optimized for ~100% power, and don’t pay the performance price to throttle down except for human comfort/survivability, or for atmospheric and near-landing operations. More importantly, the best time to accelerate and start your trip is right now, so engines, full ahead!