Maybe this is a good place to talk about the Tyranny of the Rocket equation
So it’s all about Delta v. Every maneuver requires a certain amount of delta independent of the size of the space craft. Delta V is your ability to change your velocity to reach the velocities needed for each maneuver.
If you want to get into LEO it requires X of Delta V.
If you want to get to the moon it requires Y amount of Delta V.
If you to get into orbit around the moon it requires Z amount of Delta V
Over the course of a mission all those Delta V’s add up.
So the rocket equation tells us that our available Delta V is proportional to the velocity of the exhaust and the natural log of the initial mass of fuel divided by essentially mass flow rate.
Exhaust velocity (Ve) of a chemical rocket is limited by the fuel's energy density and in real world rocket design’s they get acceptably close. Rocket engines are also designed for the best mass flow rates (M1) that can be achieved. So in reality the driving component is the mass of the fuel (Mo). Of course you need enough fuel so that you don’t run out but why not just carry more? Well this is why:
The natural log of the mass of the fuel increases less and less.
So let’s say you double the amount of fuel then you only get a 26% increase in Delta V. Double that again and you only get a 24% increase in Delta V. And so on and so on. Not to mention that as you increase the amount of fuel you also are increasing the weight of the container and things get even worse. Plus now your rocket engine has to develop even more thrust to overcome the extra mass. And your burn times increase proportionally with the mass of fuel.
Basically this is what keeps us on the ground. For current engine technology we are severely limited by the amount of fuel that we can carry. Currently we burn RP-1 (kerosene), hydrogen and methane. At the end of the day the achievable exhaust velocities of these fuels aren’t much different. And each have other pluses and minuses.
We are at a limit of what can be done with chemical burning rockets. So ideas have been proposed to help along the journey. Refuel in space so that you don’t have to carry that initial mass. Of course it costs you to get that fuel in space. Or make the fuel at the destination. That’s one of the reasons that SpaceX and Blue Origin are developing methane rockets. On Mars, you can conceivably make methane by bringing along some hydrogen and combining it with the CO2 in the atmosphere to get 10x as much methane.
However this doesn’t solve the problem of how long the trip takes. To make the trip faster and use less fuel we need a new rocket engine technology and fortunately we’ve had one for over 50 years.
Nuclear Thermal Rockets (NTR). Current engines technology hits a limit of around 450 ISP (proportional to Ve). I think the king of ISP, but too lazy to fact check, was the Shuttle Main Engines (SME) at 450 ISP. Even Elon’s new methane rockets are less than that. But NTR’s easily achieve 800 ISP and possibly up to 1200 ISP.ANd real engines were tested and built back in the 50's.
How do they do it? Glad you asked. Current engines burn the fuel, and the Ve is limited to the amount of energy in the fuel. NTR’s don’t burn the fuel. Instead they eject at a higher velocity like air out of a balloon. Of course anything with the word “nuclear” scares the **** out of the lay person. But we put nuclear (radioactive) fuel in space all the time. It’s what powers many long range satellites. NTR’s are different in that fission is happening but the material is no more dangerous in case of a RUD (Rapid Unplanned Disassembly). They don’t melt down or blow up like a bomb.
So why aren’t we developing them.First Clinton killed anything nuclear back in the 80. But now thanks to our forward thinking President NASA now has the
budget to do so. NTR is the next step and it’s actual a very “small step for man”.