# Speed of the trans-lunar railway:

sonhouse
Posers and Puzzles 05 Jun '12 21:17
1. sonhouse
Fast and Curious
05 Jun '12 21:17
So a rail service has started on the moon in lunar equatorial region and the train is solar powered, 10 meters wide and 1000 meters long. At the time, solar cells have reached 75% efficiency and last practically forever. The train wants to keep itself at local lunar noon so it the sun is always straight up for maximum solar power and stops and picks up passengers along the way, and just keeps going round and round the lunar equator like that, no fuel needed.

They take excess power and feed it to the rails which power villages along the way.

So how much power does the train generate and how fast does it have to go to stay at local lunar noon?
2. talzamir
Art, not a Toil
25 Jun '12 10:49
Originally posted by sonhouse
So a rail service has started on the moon in lunar equatorial region and the train is solar powered, 10 meters wide and 1000 meters long. At the time, solar cells have reached 75% efficiency and last practically forever. The train wants to keep itself at local lunar noon so it the sun is always straight up for maximum solar power and stops and picks up pass ...[text shortened]... much power does the train generate and how fast does it have to go to stay at local lunar noon?
Well.. hopefully I didn't go totally wrong somewhere.

The radiation from the sun at 1 AU distance is about 1,400 W / m^2. As there are 10,000 square meters on the train to radiate on, that's a power of 14,000,000 W. Given the 75% efficiency and these being ballpark figures, 10 GW seems a sufficiently accurate figure to represent the power generated.

The radius of the moon is about 1,738 km, so the circumference is 10,920 km. The moon keeps the same face towards the earth at all times so it takes almost a month for the moon to rotate - 27.32 days. So the train needs to travel at a pace of about 400 km / day, or 16.6 km/h, or about 10 mph.
3. sonhouse
Fast and Curious
25 Jun '12 19:24
Originally posted by talzamir
Well.. hopefully I didn't go totally wrong somewhere.

The radiation from the sun at 1 AU distance is about 1,400 W / m^2. As there are 10,000 square meters on the train to radiate on, that's a power of 14,000,000 W. Given the 75% efficiency and these being ballpark figures, 10 GW seems a sufficiently accurate figure to represent the power generated.

T ...[text shortened]... . So the train needs to travel at a pace of about 400 km / day, or 16.6 km/h, or about 10 mph.
Spot on except you said 10Gw for the power, it should be 10 Mw.

It's interesting to compare the speed at which you have to travel on Earth V the moon to stay at local noon, on Earth, 1000 MPH, 1600 klicks, about Mach 1.3 but on the moon, 10 mph, 16 klicks.

Next question: Using that railway, it is done to a flatness figure of 1 inch max out of roundness so it is extremely smooth, under those conditions and using driven wheels, can you drive into orbit around the moon? I think orbital velocity is around 3000 MPH or around 4800 klicks.
4. talzamir
Art, not a Toil
26 Jun '12 09:11
Oopsie. 10 MW of course.

The moon's mass is about 7.36 x 10^22 kg and the gravitational constant is 6.673 x 10^(-11) m^3 kg^(-1) s^(-2), and moon's radius as said before 1.7374 x 10^6 m. Liftoff happens when the centrifugal force exceeds gravity.

m v^2 / r > m M G / r^2
v^2 > M G / r
v > (M G / r)^(1/2)

Which is about 1,680 m/s, or Mach 5, not that mach makes much sense in the lunar vacuum. Multiply that by sqrt 2 for 2,375 m/s or Mach 7 and you get enough speed to slingshot stuff out of the moon's gravity well. Sounds doable, and a whole lot cheaper than rockets and space shuttles. Of course, building the rail in the first place and keeping it clear and safe of space debris presents some challenges.
5. sonhouse
Fast and Curious
26 Jun '12 11:08
Originally posted by talzamir
Oopsie. 10 MW of course.

The moon's mass is about 7.36 x 10^22 kg and the gravitational constant is 6.673 x 10^(-11) m^3 kg^(-1) s^(-2), and moon's radius as said before 1.7374 x 10^6 m. Liftoff happens when the centrifugal force exceeds gravity.

m v^2 / r > m M G / r^2
v^2 > M G / r
v > (M G / r)^(1/2)

Which is about 1,680 m/s, or Mach 5, not th ...[text shortened]... il in the first place and keeping it clear and safe of space debris presents some challenges.
Can be a magnetic sling also, like a linear electric motor. If you confine the acceleration to 1 g, it looks like you need 289 odd Km long runway. 10g, 28.7 Km, 100g, 2.8 Km. I divided 2375 m/s by 9.8 which gives a time of 243 seconds or so to get to that velocity at one g, then the old S=(AT^2)/2 (9.8*243^2)/2= 289340 meters or 289 km or about 180 miles. Sound about right?
6. talzamir
Art, not a Toil
26 Jun '12 16:42
With the track record of humanity in using inventions that could be beneficial to everyone, I expect that the slingshots would end up used as a sort of field artillery. But yes, the peaceful applications sound fascinating and plausible. Obviously getting to the moon in the first place to build the thingy won't be easy or cheap, but then, according to a site I googled, "a low-orbit network of fueling stations and a lunar base cost about \$20 billion in 10 years which is about one third of what the state owned Saudi Aramco said it will spend on oil and gas projects over the next five years."

So.. all this seems both fascinating and basically feasible. And making it a one-way trip is a lot cheaper still as a huge problem was getting mined stuff from the moon to earth as anything brought needs to be deccelarated so it won't burn in the atmosphere.

Interesting times for sure.
7. sonhouse
Fast and Curious
26 Jun '12 18:442 edits
Originally posted by talzamir
With the track record of humanity in using inventions that could be beneficial to everyone, I expect that the slingshots would end up used as a sort of field artillery. But yes, the peaceful applications sound fascinating and plausible. Obviously getting to the moon in the first place to build the thingy won't be easy or cheap, but then, according to a site needs to be deccelarated so it won't burn in the atmosphere.

Interesting times for sure.
Things are looking up in that regard. The latest is the finding of 22% water inside at least one crater on the south pole of the moon where they are in constant shadow of the sun so the temperature inside the crater could be 100 degrees Kelvin or so, so no water ever escapes. The idea there is to use the water for drinking, industrial processes and using solar energy, to split the H2 and O2, giving the best chemical rocket fuel or for use in fuel cells for power. Once you have a city on the moon with industrial capacity you don't need to haul crap up from the Earth so often which saves tons of money and makes it much more viable.

That crater they just analysed is over 12 Km wide so there is a LOT of water there and probably in other craters in the same area. All extremely frozen! You could even use the stuff for air conditioning, just dump it on the roof and you get cooling and liquid water in one swell foop! This is for buildings underground I would imagine, less radiation from cosmic rays and solar wind.
8. talzamir
Art, not a Toil
28 Jun '12 10:462 edits
Underground housing on the moon would make sense anyhow, as it would probably be to be bombarded with space shrapnel in near-vacuum 24/7 no matter how much kevlar one has on the roof.

The odds sound good that we'll get to see people living on the moon for prolonged periods of time - and with exit from the moon fairly easy and energy issues straight-forward enough for the next five billion years as solar energy is plentiful and unobstructed, and now a water source too.. as well as oxygen and burning fuel, with a bit of electricity thrown in to cut the water molecules to pieces.. there's hope. We shall hopefully see how this goes. =)
9. sonhouse
Fast and Curious
29 Jun '12 01:311 edit
Originally posted by talzamir
Underground housing on the moon would make sense anyhow, as it would probably be to be bombarded with space shrapnel in near-vacuum 24/7 no matter how much kevlar one has on the roof.

The odds sound good that we'll get to see people living on the moon for prolonged periods of time - and with exit from the moon fairly easy and energy issues straight-forwa ...[text shortened]... to cut the water molecules to pieces.. there's hope. We shall hopefully see how this goes. =)
It's not space shrapnel we need to worry about, it's radiation from solar flares and ions from those flares. It can be deadly if you are caught out in a solar storm aimed at Earth and moon. The moon does not have a magnetic field to deflect solar storms like the Earth does so the nasty stuff slams right down on the surface, so you better have about 10 meters of dirt between you and the outside.

BTW, the crater with the ice in it is named Shackleton:

http://www.nasa.gov/mission_pages/LRO/news/crater-ice.html

There is also a nice video showing how the sun never penetrates inside the crater, only hitting the tops of the outside peaks.