I’m thinking that the moon’s orbit has quite a lot to do with its mass, and so if its mass increased substantially (eg if we built skyscrapers and highways and so on), its orbit would be altered.
I guess I’m asking: how much development could we get away with before we threw everything off kilter?
I’m assuming (but please correct me if I’m wrong) that the size difference between the earth and the moon means that the earth losing X amount of mass would have much less effect on its orbit than the moon gaining that same X amount.
Just idly wondering … not planning anything … don’t worry !
I just recently asked a similar question in this thread. Similar, at least, in regards to how much activity it would take to change the moon’s orbit. Great idly wondering minds think alike!
The moon has a mass of approximately 7.35 x 10[sup]22[/sup] kg. The average skyscraper probably weighs about 100,000 lbs at the Earth’s surface, which would give it a mass of 45000 kg.
That means that you would need about 10[sup]18[/sup] skyscrapers to hit 1% of the moon’s mass. I think we could build as many as we need safely.
Why on earth would we import mass from earth (I assume) to build skyscrapers when the moon is (literally) chock full of perfectly good rock and other building materials? If anything, we’d probably end up moving resources from the moon to the earth.
Firstly, I doubt the mass would increase ‘substantially’. If you built a large appartment for every person on earth, made entirely of rock shipped from earth, it’d mass much less than mount everest (according to my back of the envelope calculations) which is ~10^15 kg according to google. The moon is ~10^23 kg. So it would increase 0.000001%.
And that ignores the likehood of quarrying the moon rather than rocket-lifting everest into orbit.
Also, iirc, the force on the moon due to the earth isn’t dependent on its mass. However, I think landing on the moon would exert some small force, changing the orbit very, very slightly.
I’m not worried, though occasionally small changes can be enough to destablise things. But moon orbiting planet is quite stable iirc.
No. The moon weighs 7.36 × 10^22 kilograms, and the Earth weighs 5.9742 × 10^24 (5,974,200,000,000,000,000,000,000) kilograms, for God’s sake. The Sear Tower weighs 7438020384 kg, or 1x10^-11% (1/9895105982544th) of the weight of the moon. Seeing as it costs about $60,000/lb (~$130,000/kg) to lauch cargo into space on the space shuttle, humans are never going to change the orbit of nuthin.’
About 18,000 to 25,000 tons of meteorite dust fall onto the Earth every year, and it doesn’t change its orbit to any degree which could be measured with any human instrument.
The radius of an orbit is a function of only two things: the sum of the masses of the earth and the orbiting body and the speed of the orbiting body. Really, the moon and the earth are both orbiting a common center of mass, but since the earth outweighs the moon by such a huge margin, this center is practically the same as the earth’s center.
So, build away.
Besides, where are you gonna get your building materials? It’s too expensive to lift it from Earth, so you’re gonna get most of your materials right there on the Moon, anyway. So in effect, all you’re doing is pushing it around a bit.
And since the moon doesn’t have Van Allen belts to protect inhabitants from solar radiation, the most practical way to build moon bases is underground. And the moon already has huge networks of lava tunnels that with some shoring up and crack patching will make wonderfully insulated airtight spaces for earth creatures like us.
Ok, I’m probably not thinking this through completely, but if all of the mass that was transplanted to the moon came from the earth it shouldn’t effect the quantity of force between them at all. The moon would gain as much mass as the earth lost, so the product of their mass is still the same no matter what. Meaning that if the earth had the mass of the sun and the sun had the mass of the earth, the orbit of the earth around the sun would be the same as far as the sun and earth are concerned (the other planets might object, though ;)) The distinction of whether the earth orbits the sun or the sun orbits the earth is a relative one.
So if the product of their mass stays constant, the determining factor is their velocity, since that determines their distance. Just landing on and taking off from the moon and back probably doesn’t effect it’s velocity by any significant amount on average, so I doubt there’d be much change. On the other hand, if you took a little mass from the earth, accelerated it to a very high velocity and slammed it into the moon, that would disturb it’s orbit (and the orbit of the earth as well) just like an asteroid strike would. But that probably falls into the “Doctor, it hurts when I do this” category.
Hm, good point. Never thought of using the materials already on the moon. But isn’t it just a big piece of rock? If we wanted to build an Earth-style city, with roads and wires and plumbing, we’re going to need some more material than green cheese, no?
(And cost is no object ! My goodness ! We’re in fantasyland already, I’m not going to worry about maxing out my credit card …)
Bughunter:
That’s really the kind of answer I was looking for … there’s no change in the sum of the masses of the earth and the orbiting body, so does this mean we can ship Mount Everest and the Sears Tower to the moon with no effect on its orbit?
Will our construction affect its speed at all?
I don’t know why I’m so curious … I was reading The Elegant Universe describing the graceful dance of the cosmos (in less purple prose) and it seemed to me that, since there are so many forces acting on every object in space, small changes in one value (ie mass) may affect other values (ie orbit).
Bleh. You’re right, of course. I knew I hadn’t thought that out completely. The example I chose just happened to be the case where x = a - b and I jumped to conclusions to soon.
You do an admirable job of proving what other people are saying about the masses, though. If A and B are the mass of the earth and moon, the orbits won’t be effected significantly as long as X is zero or very close to zero by comparison. Which saves me a little face since what I asserted would still be basically correct for any small amount of mass such as colonists and building material. It would be completely wrong, however, if we wanted to move half of the mass of the earth to the moon. But for relatively small masses, like the ones in this problem, the velocity of impact has a much more important effect on the orbit than the mass.
If I’m not mistaken (again), the kinetic energy of a moving object is directly proportional to its mass, and to the square of it’s velocity (KE=1/2mV^2 right?). Hitting the moon with a mass the size of a Volvo traveling at close to the speed of light would have much more effect than gradually transfering the mass of Mt. Everest a few tons at a time.
I once had a lovely conversation (of sorts) with a bloke who was absolutely convinced that we’d thrown the entire solar system off-kilter by bringing back a few pounds of moon rocks.
(What’s most amusing is that I could not successfully explain to him that, counting the descent and ascent modules from the Apollo landings, we’d actually sent more mass to the moon than we’d carried back from it!)
Anyway, 'possum stalker hit the most important nail on the head: a lot of mass is already being tossed hither and yon in the form of meteoritic dust and other detritus, far in excess of any amount of mass we’ll ever move!
Shifting enough mass from the Earth to the Moon absolutely WOULD have a significant effect. The two bodies would in theory continue to orbit one another, just around a point closer to the Moon than it is now… but the Earth would be significantly affected at least in terms of tides.
Indeed, any shipment of mass from one to the other has some effect, however incredibly small. The Moon’s orbit is not stable anyway - it’s moving further away from us right now, and it wobbles relative to Earth - and is affected all the time by the addition of mass. But the differences made are just unbelievably tiny.
So the answer to your second question is yes, because we could never possibly ship enough mass to make a difference. You could ship all the mass of every single thing that human beings have ever created, and it still wouldn’t make any significant difference. The masses we’re talking about are not anywhere near the same order of magnitude. You could put a billion people on the Moon with cars, skyscrapers, Game Boys and all the stuff people bring with them and it wouldn’t make enough of a difference to notice.
Nah. It was a complete guess to do the order of magnitude calculation. I should’ve made that explicit.
Since we have the mass of the Sears Tower, we can figure out how many of those we’d need to hit 1% of the moon’s mass. It’s about 9.9 x 10[sup]10[/sup].
Not quite the 10[sup]18[/sup] that I came up with earlier, but I don’t think we have to worry too much about knocking the moon out of orbit.
Where do you think we get roads and wires and plumbing? Ultimately, it’s all stuff we’ve dug up out of the ground, and, again, it’d be much easier to make them on the moon than ship it all up from the earth. Yes, to start a colony, you’d need to bring up some tools and whatnot (well, at least, that would make it a whole heckuvalot easier), but it seems to me that if you’re planning a long-term, self-sustaining colony, they’d have to make most of their stuff out of the moon itself.
