It takes 1730 m/s delta-v to get from the lunar surface into low lunar orbit. Mars requires more than double that, needing 3800 m/s delta-v thanks to its larger mass. This corresponds to well over double the fuel requirement thanks to the tyranny of the rocket equation.
Assuming a vehicle similar to the Apollo Lunar Module, with a dry mass of about 5,000 kg and an engine specific impulse of around 300:
A delta-v of 1730 m/s requires 9,005 kg wet mass (fuel + dry weight).
A delta-v of 3800 m/s requires 18,209 kg wet mass.
So the fuel mass increases from 4,005 kg to 13,209 kg, more than a factor of three. Note that the above calculation ignores atmospheric effects and only represents a one-way trip. Assuming we use a single-stage vehicle instead of a staged vehicle (the real LM was a two-stage vehicle), to get down to the surface of the Moon and then get back up actually requires a wet mass of about 16,221 kg, of which 11,221 is purely fuel. For Mars, it's roughly 61,318 kg of fuel. Obviously aerobraking would greatly decrease the amount of fuel needed to get down to Mars and back up since we don't need to spend fuel to slow down.
To get to low Mars orbit from the Earth's surface requires a delta-v of roughly 15,110 m/s. If we assume a spacecraft with a dry mass of around 100,000 kg plus a 60,000 kg fueled lander, for a total mass of 160,000 kg, then we need a vehicle with a wet mass of about 27.3
million kg. Again, this is a non-staged vehicle and we are ignoring the weight of the launch vehicle itself. Adding on another 200,000 kg for a (very) low-ball estimate of the launch vehicle mass increases the total wet mass to about 61.4 million kg. For comparison, the Saturn V wet mass was 2.97 million kg, including payload (CSM+LM + fuel and consumables). A staged vehicle would greatly reduce the total fuel required since we don't have to accelerate/decelerate all that dead weight in the empty fuel tanks and support structure.
As a final comparison, SpaceX's two-stage BFR rocket is projected to have a wet mass of around 4.4 million kg and be able to deliver 150,000 kg to Mars.
Things that would reduce the mass of the vehicle:
- An engine and fuel combination with a higher specific impulse. If we increase the Isp to 350, our 61.4 million kg mass falls to 29,5 million kg, just under half. At Isp = 400 it's just 1.7 million kg.
- Staging. The three-stage Apollo Saturn V needed a total vehicle mass of 2.97 million kg to get the CSM + LM to the Moon and back. A single stage design would have had a wet weight of roughly 22.8 million kg, more than seven times as much. That's almost certainly a low number since I didn't increase the launch vehicle mass as well. This is even more than the Nova rocket for the proposed direct ascent method which would have used a 3-stage launch vehicle of about double the mass of the Saturn-V.
- Longer, more efficient orbital transfers. Less fuel would be needed if you can use gravity assists to change your velocity. However this is very unlikely for a manned mission, as it potentially increases the transfer time to several years instead of a few months.
Note that this is all a very rough, back of the envelope calculation, so don't expect too much from it.
Solar System Δv Reference Sheet
Rocket Equation Calculator
Timothy Schablin said:
So let me ask this... You have 2 space probes just sitting in space. One has a mass of 100. The other has a mass of 30. You want to accelerate both to a velocity of 50. Would they both require the same amount of rocket force? Or would the larger one require more?
The force is somewhat irrelevant. Ion engines have extremely little thrust, but very high specific impulse. In space you don't need to work against things like friction, so applying a small amount of thrust over a long period of time provides an identical delta-v as applying a large amount of thrust for a short time. What you really want is a very 'efficient' engine (high specific impulse). As I showed above, increasing the specific impulse from 300 to 400 cut our fuel requirements by about 97%. Ion engines currently have the highest specific impulse of any propulsion technology in use, with Isp's of around 1,000 - 10,000.
