# How much propellant is needed for a 1G continuous trip to the moon?

I've seen some calculations of the energy requirements of 1G propulsion, which are obviously huge, but at least theoretically achievable...but what about propellant? Somebody check my math, but it seems like you could minimize propellant with high exhaust velocity, but there are both engineering and physics limits to that, too.

Anybody know of a good paper on this?

• Probably easier just to spin the toroid, unless you want to get there really fast. – Robert Harvey Dec 10 '18 at 23:32

Starting from Earth orbit at 8km/s, accelerating half of the way, decelerating the other half - the uniformly accelerated motion calculator gives us

v = 61.9271 km/s
t = 1.52699 h

for one half of the trip. So we get there in about 3 hours, but we'll need about 122km/s of delta-V.

$$\Delta v=v_e \ln {\frac {m_0}{m_f}}$$

so,

$${m_0} = {m_f}{e^{\Delta v \over v^e }}$$

Let's ignore the lousy chemical engines, ISp of what - 450s? We can't use ion drives because they'd never achieve TWR sufficient to give us 1g. But let's go with a good advanced Nuclear Thermal Rocket. The prototype NERVA were just shy of 1000s but we're way further down the development line, our sci-fi rocket has 2000s, or exhaust velocity of 20km/s.

$$e^{122/20} = e^{6.2} = 493.$$ So, mass of the rocket fully fueled would need to be - nearly 500 times the mass of the rocket with the fuel depleted. Likely much more, because there's no way you could get 1g out of engine that weighs less than 0.2% of the entire craft - so dropped stages, enormous engines, all that jazz. 1000x is a fair estimate.

You might get a little better achieving 1g average with Project Orion, but it's not a smooth continuous 1g... it's a very bumpy ride on top of shockwaves of exploding thermonuclear bombs.

As an exercise, let's use Space Shuttle main engine, one of best chemical rocket engines... a mere 594574054363 times the dry mass...

• Theoretically, Orion uses a big-ass shock absorber to average out the acceleration to something relatively smooth, but I'll believe it when I see it. – Russell Borogove Dec 10 '18 at 23:51
• What, you don't think a 16-stage hydrolox rocket is practical? – Russell Borogove Dec 10 '18 at 23:57
• @RussellBorogove: /..very relatively smooth. More on the 'survivable' side rather than 'smooth'. – SF. Dec 10 '18 at 23:57
• @RussellBorogove: For payload of a 6u cubesat the craft would be about the size of 67P/Churyumov–Gerasimenko – SF. Dec 10 '18 at 23:59