Hohman Transfer Calculator
Hohman Transfer Calculator
My personal soapbox for thoughts on space exploration, politics, and anything else
First of all, one of the things about the inner solar system is that, unless you are under an atmosphere, water sublimes away. That’s why the moon doesn’t have ice covering its surface like the outer solar moons do. So “near Earth” comets don’t stay near Earth for very long – or they would be gas clouds. They usually orbit the sun at very high eccentricity (having their source in the Kupier belt at 30+ AU from the sun). This means that any mining that takes place is not going to be a fixed base operation. A ship will have to go to a comet, do it’s business, then get back to the moon, and wait until another comet passes by. (Unless you feel like waiting 300 years for your equipment to come back into the inner solar system.) That’s okay though, because there are thousands of near earth objects, one is bound to be in the neighborhood any given year or so.
The dv requirements for meeting up with a high eccentricity comet are quite high however.
- The Earth-moon system orbits the sun at 1 AU. (1 AU is about 1.496E11 meters).
- The sun’s mass is 1.99E30 kg.
- Newton’s Gravity constant is 6.67E-11 Nm^2/kg^2
Suppose a comet happens to be passing by Earth’s orbit (1AU) from it’s home of 30 AU. Semimajor axis is 15.5 AU. Eccentricity is 0.935. Earth is going sqrt(G*Msun/Rearth) = 29786 m/sec tangent to the sun in it’s orbit. The comet, on it’s close approach will be going sqrt(G*Msun/Semimaj*(1+eccin)/(1-eccin)) = 41439 m/sec. This means to catch the comet, an increment of 11650 m/sec in your velocity is required with respect to earth. This is only part of the dv requirements though.
Let’s suppose our hypothetical comet miner is nuclear thermal powered itself (so that it can use the fuel it mines, among other things), and its mission is to take off from the moon (1600 m/sec), break Earth orbit (1439 m/sec from the moon), rendezvous with the comet, then use it’s nuclear engines in a power producing mode to power a hydrogen electrolysis factory. (Water is only 11% hydrogen by mass. It’s far more efficient to transport only the hydrogen). The hydrogen is liquefied and stored in fuel tanks onboard the vessel. Then the fuel miner accelerates back towards earth, re-enters the earth-moon system, and lands back at the moon. Also throw in 800 m/sec for maneuvering.
For the outbound leg, about 15500 m/sec dv is required. For the inbound leg, another 15500 m/sec dv is required. This is an extremely fuel expensive mission, even though we’re not leaving the inner solar system. (We could, assuming we get stranded near the comet on a trajectory out past Pluto). This is another reason why the high fuel efficiency of nuclear thermal is preferred over chemical propulsion.
Iteration 1 Vehicle IdeaThis vehicle will be sized according to the inbound leg. Since no one’s yet built a nuclear thermal rocket ship before, I’ll have to pull a few numbers out of my head.
The NERVA program back in the 60’s created and tested a series of nuclear rocket engines. These engines vastly outperformed even modern chemical engines in terms of fuel efficiency. They were intended as part of a program for upper stage and in-space vehicles to expand our presence in the solar system. A Saturn V with a NERVA upper stage could deliver a whopping 500 tons to LEO, and similarly massive amounts of cargo throughout the solar system. Unfortunately, the program was canceled in 73.
The NERVA engine weighs 30 tons. (I use metric tons btw. I’m using at as an abbreviation for 1000 kg). Even though NERVA 2’s Isp was 820 sec, recent material advances could probably push the operating temperature way up (uranium carbides, or other uranium ceramics could operate hotter without melting). This could lead to 1000 sec Isps in theory. I’m going with that, because it makes the final rocket look nicer.
Let’s also throw on a 10 ton computer/communications/hydrogen electrolysis payload.
Let’s say that since these fuel tanks will primarily operate under low acceleration – the weightlessness of space, or landing/launching from the moon, that they won’t need to be as structurally robust as our launch vehicles. A fuel tank propellant mass fraction of 0.95 will be used.
The Mass ratio required for the return leg is 0.2058. The payload fraction is 0.1640.
Let’s assume, for initial estimation’s sake, that we’re going to mine 500 tons of hydrogen off the comet as payload, and the rest as fuel. The rocket needs to mine a great enough weight in hydrogen off a comet to make up for it’s reactor and vehicle mass on a trip returning to a comet. Since it will use the very fuel it mines to get back to the moon, unload a fraction of it’s payload, and use the rest to get back to another comet, the percentage of payload that it can unload on the moon is proportional to the hydrogen payload to rocket systems mass ratio.
That 500 tons of hydrogen will also require 2615 tons of hydrogen to push it to the moon. It will also require 137 tons of tanks and structure.
The rocket, upon arriving and landing back on the moon can afford to unload 306 tons of hydrogen to a lunar base. It will need 194 tons of it’s payload to take back off and go chase another comet. 61% of the payload can be unloaded to the moon for other uses.
Looking at this vehicle more closely:
This rocket is a massive construction. It would make sense to invest in it only if you intend to run multiple missions from the moon to refuel interplanetary rockets. The nuclear reactor and the rest of the complex equipment would have to be launched direct from Earth. Hopefully there will be a way to construct the tanks and other structure (the “dumb” inert mass) using native lunar materials. This would require some sort of metal processing plant and construction yard present on the moon. A serious space effort would be needed to justify the moon comet runs.
On the positive note – if your space program is large enough to accommodate a moon-comet run, then it will become far easier to fuel your spacecraft. Hydrogen fuel from the moon can be used to power Earth-moon system tugs, and re-usable cargo vessels to Mars and elsewhere in the system. The moon can get not only hydrogen from comets, but also nitrogen and carbon, materials that should also be present in the ‘dirty snowballs’.
The file I used to play with the variables: Comettrip.xls