Well, yeah, that's what I'm thinking, anyway.
Why, because the solar wind particles would knock the water molecules beyond escape velocity like billiard balls?
Yep. That and/or break them apart. The hydrogen would probably escape pretty easily at that point, and the oxygen would probably bond with the rocks.
QUOTE
I got as far as looking up lunar gravity (@1.6 m/s^2). Then I can't figure out how to set up the equation for deceleration. Does dividing 640 m/s by 1.6 give the number of seconds or meters before the velocity is 0? Or does the acceleration formula have to be differentiated by multiplying the 1.6 by the 2 from the exponent? It's been a long time since I've done math, as you can see. The logic of the equations made sense to me at the time, but now I just remember that acceleration is rate of change in velocity.
You're on the right track here, I think, if you're trying to figure out the average height the particles will reach. (Well, assuming they're travelling straight up, which they won't be, but it gives us at least a sense of the big picture.)
V_final = V_initial + A * t
V_final = 0 m/s (i.e., it pauses at the top of its journey)
V_initial = 640 m/s (if I didn't screw it up)
A = -1.6 m/s^2 (negative because it's in the
opposite direction of the initial velocity)
t = time
0 m/s = (640 m/s) + (-1.6 m/s^2) * t
-640 m/s = (-1.6 m/s^2) * t
t = (-640 m/s) / (-1.6 m/s^2)
t = 400 s
You were asking if the units were seconds or meters. Besides the obvious point that time is measured in seconds, you could try fiddling with the units to see how it comes out. (m/s) / (m/s^2) = (m/s) * (s^2/m) = (m * s^2) / (m * s) = s. Dimensional analysis is a good skill to have; if it came out to something other than seconds, you'd know to go back and check your work.
So, now, a time of 400 s, you can try to calculate the height:
X_final = X_initial + V_initial * t + (1/2) * A * t^2
X_final = final height
X_initial = 0 m (ground level)
V_initial = 640 m/s
A = -1.6 m/s^2
t = 400 s
X_final = (0 m) + ((640 m/s) * 400 s) + ((1/2) * (-1.6 m/s^2) * (400 s)^2)
X_final = (256000 m) + (-128000 m)
X_final = 128000 m = 128 km
The moon's radius is about 1700 km, so 128 km is large enough that we *could* consider reworking the problem without assuming acceleration is constant, if we're really worried about accuracy. Anyway, since gravity is decreasing with height, we know that the real answer has to be greater than 128 km.
QUOTE (->
| QUOTE |
| I got as far as looking up lunar gravity (@1.6 m/s^2). Then I can't figure out how to set up the equation for deceleration. Does dividing 640 m/s by 1.6 give the number of seconds or meters before the velocity is 0? Or does the acceleration formula have to be differentiated by multiplying the 1.6 by the 2 from the exponent? It's been a long time since I've done math, as you can see. The logic of the equations made sense to me at the time, but now I just remember that acceleration is rate of change in velocity. |
You're on the right track here, I think, if you're trying to figure out the average height the particles will reach. (Well, assuming they're travelling straight up, which they won't be, but it gives us at least a sense of the big picture.)
V_final = V_initial + A * t
V_final = 0 m/s (i.e., it pauses at the top of its journey)
V_initial = 640 m/s (if I didn't screw it up)
A = -1.6 m/s^2 (negative because it's in the
opposite direction of the initial velocity)
t = time
0 m/s = (640 m/s) + (-1.6 m/s^2) * t
-640 m/s = (-1.6 m/s^2) * t
t = (-640 m/s) / (-1.6 m/s^2)
t = 400 s
You were asking if the units were seconds or meters. Besides the obvious point that time is measured in seconds, you could try fiddling with the units to see how it comes out. (m/s) / (m/s^2) = (m/s) * (s^2/m) = (m * s^2) / (m * s) = s. Dimensional analysis is a good skill to have; if it came out to something other than seconds, you'd know to go back and check your work.
So, now, a time of 400 s, you can try to calculate the height:
X_final = X_initial + V_initial * t + (1/2) * A * t^2
X_final = final height
X_initial = 0 m (ground level)
V_initial = 640 m/s
A = -1.6 m/s^2
t = 400 s
X_final = (0 m) + ((640 m/s) * 400 s) + ((1/2) * (-1.6 m/s^2) * (400 s)^2)
X_final = (256000 m) + (-128000 m)
X_final = 128000 m = 128 km
The moon's radius is about 1700 km, so 128 km is large enough that we *could* consider reworking the problem without assuming acceleration is constant, if we're really worried about accuracy. Anyway, since gravity is decreasing with height, we know that the real answer has to be greater than 128 km.
Either way, I'm imagining water molecules on the moon bouncing around at a height of several hundred meters. I wonder how much lower this altitude would be on the dark/cold side.
Looks like a lot more than several hundred meters, now that I've worked it out. Wikipedia says that the moon's surface temperature varies from about 100 K to 390 K at the equator, so... just trying to figure it out in my head here... a factor of four in temperature means a factor of four in energy, which means a factor of two in velocity, which means a factor of four in height. I guess it comes out proportionate to temperature. I used 293 K in my initial figures, so, (100/293)*128 km = 44 km at the low end, and (390/293)*128 = 170 km at the high end.
adoucette
12th November 2009 - 09:16 PM
I think a related question is:
About what would be the minimal number of people that would be needed at a self sustaining colony?
Assumption:
There is a supply ship each year which can bring a limited amount of equipment to the colony, say 4,000 lbs worth.
First Question? What would you ship from earth?
Also there is no, or very limited ability to return to earth, and in any case, one can't return quickly, so emergencies and medical care has to be handled on site.
We presume that only adults will start out, but there will be couples and thus babies etc over time (but don't count kids in number).
We presume that there is sufficient O2 and water for basic needs on mars and doesn't need to be imported, but they do need to be recycled.
Everything else, energy production, food production, livestock, food preservation, butcher, baker, cooking, manufacturing, electrical work, heating, cooling, plumbing, clothing, cobbler, space suits, equipment repair, fabrication, Oxygen, Water recycling, waste recycling, local entertainment, recreational activities, new structures, medical care, teaching, day care, sanitation, legal advice, law enforcement, spiritual needs, mortuary services etc etc has to be handled by the colony members.
So, 10 people, 100 people or 1,000 and why?
Arthur
light in the tunnel
13th November 2009 - 03:50 AM
QUOTE (FlyingSpaghettiMonster+Nov 12 2009, 05:48 AM)
That makes sense that you can cancel out the units in the algebra and end up with seconds as the unit of the answer. I think I knew that but I forgot.
I also didn't think about gravity getting weaker as altitude increases. Now that you've basically established that any surface water on the moon would sublimate and bounce around many km high, my question becomes how any water/ice would ever tend to collect anywhere on the moon without an atmosphere to force it downward? Plus if there's not enough water to generate enough humidity for condensation to occur, how would water end up on or in the ground even if their was an atmosphere?
Same question with regards to Mars. If the atmosphere is too thin or dry, how would water ever do anything other than evaporate? If there was any water present, wouldn't it be in the form of clouds or at least very slight humidity?
RobDegraves
13th November 2009 - 04:27 AM
QUOTE
my question becomes how any water/ice would ever tend to collect anywhere on the moon without an atmosphere to force it downward?
There is a lot of water in the universe.
Hydrogen has been detected in interstellar clouds, produced as a by product of star formation and is found all over our solar system.
Comets are largely balls of dirty ice.
Even if the Moon didn't produce water, there would have been millions of tons of it hitting the Moon over the billions of years in the way of comets, debris, etc.
Mars is largely believe to have had an atmosphere at some point in it's past. If it did, it would have likely had water.
Any of the water on the surface would be long gone, however some of the water underneath the ground may still remain.
PhysOrg scientific forums are totally dedicated to science, physics, and technology. Besides topical forums such as nanotechnology, quantum physics, silicon and III-V technology, applied physics, materials, space and others, you can also join our news and publications discussions. We also provide an off-topic forum category. If you need specific help on a scientific problem or have a question related to physics or technology, visit the PhysOrg Forums. Here you’ll find experts from various fields online every day.
To quit out of "lo-fi" mode and return to the regular forums, please click
here.