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Neil deGrasse Tyson On How To Stop a Meteor Hitting the Earth
An anonymous reader writes "Astrophysicist Neil deGrasse Tyson talks stopping extinction-level meteor hits: '...Here in America, we're really good at blowing stuff up and less good at knowing where the pieces land, you know...So, people who have studied the problem generally – and I'm in this camp – see a deflection scenario is more sound and more controllable. So if this is the asteroid and it's sort of headed toward us, one way is you send up a space ship and they'll both feel each other. And the space ship hovers. And they'll both feel each other's gravity. And they want to sort of drift toward one another. But you don't let that happen. You set off little retro rockets that prevent it. And the act of doing so slowly tugs the asteroid into a new orbit.'"
I'm going to assume Astrophysicist Neil deGrasse Tyson is a much better source than you.
The blast from the little retro rockets hitting the much larger asteroid, will cancel the whole thing out - every action having an equal and opposite reaction and all that pesky old Newtonian conservation of momentum stuff...
Just use a tractor beam instead.
Some drink at the fountain of knowledge. Others just gargle.
I agree, he's great for explaining stupid shit to proles, but as far as a professional scientist goes he has very little credibility in my book.
Great. You'd be comfortable with this future:
Scientists: By the way, there is a huge hunk of rock that is going to hit the earth tomorrow and wipe us all out.
Public: Wait - what? Why didn't you warn us?
Scientists: We discussed it at length at our obscure meetings. Why should we have to take time out of our important work to explain complicated shit in your terms? Stupid proles.
If Slashdot were chemistry it would look like this:Cadaverine
They don't need to be thrusting directly at the asteroid. Think 3 or more at angles, so they cancel each others' sideways thrust and the overall thrust misses the asteroid, whilst providing net 'away' thrust. Yes, this reduces efficiency.
I agree, he's great for explaining stupid shit to proles, but as far as a professional scientist goes he has very little credibility in my book.
It's scientists like him that are personable and able to "explain stupid shit to proles" that help keep people interested in science and help make sure the scientists in your "credibility book" get enough funding from the proles to do their work.
I would normally agree but the whole thing sounds preposterous. The gravitational pull of a spaceship is negligible. If you're going to send a spaceship up there and let it "hover" why not just have it actually contact the meteor and use its thrusters to push it out of the way?
Why do you say that? He's an established scientist and has a Bachelors in Physics and a Graduate/PH-D in Astrophysics. He's held positions at several universities and is the director of the Hayden Planetarium. Sure he goes on television more than your average physicist, but so did Carl Sagan. He's charismatic, and it works well for him. Nothing wrong with that.
Dr. Phil is a pool of waste that puts people on television and exposes their issues to millions of viewers, for the ratings and a fat pay check. He doesn't add anything to his profession, and his discussions on television don't enlighten anyone.
There's a huge difference.
If you are going to use this method, then the more mass in your ship the better. Unfortunately, that means a more expensive launch. If you plan ahead, you figure out a way to accumulate debris and smaller rocks at some stable orbital point so when you need mass you can launch a light ship, go to the rockyard, and gather up more mass at reduced cost.
If Slashdot were chemistry it would look like this:Cadaverine
The asteroidmay not be solid rock. It could be a rubble-pile type, and there might not be anything solid-enough to apply force to in a consistent way. It might be two closely orbiting bodies of rock, in which case you can't push on one in any type of consistent direction.
The benefit of the gravity-tug approach is that if you have a body of some concentrated mass moving at you, then if you have a spaceship sit away from it and maintain a constant position relative to a point other then the asteroid, then you can act on it's entire mass consistently.
Find it early enough, and you can do this with high-efficiency ion thrusters, rather then needing inefficient chemical rockets.
Re: reactive force from retrorockets - you fire them off-angle to the asteroid so exhaust doesn't hit them. You can easily mount orthogonal engines which would carefully cancel the attraction of the asteroid without directing any exhaust at it.
The "pull" between a spaceship and an asteroid would be equal to the apparent weight of the spaceship on its surface, decreased by the square of the distance between the two objects. This would reduce the traction to a very limited amount.
You'd get better results with a cable from the ship attached to the surface, but the problem would be the rotation of both objects.
To do a decent job, the spaceship would need to collect a large quantity of mass before attempting to drag the asteroid.
I think the point is that you don't know how fragile the asteroid is (it could just be a big pile of rubble held together by its own gravity), so anything you do to it through physically touching it, like attaching a cable, landing on it, etc, may break it up into smaller pieces with the result that instead of one large asteroid, you now have a dozen or maybe hundreds of smaller asteroids that you have to deflect. And the set of smaller asteroids will have the same effect on earth as the one large asteroid.
Where's "-1, appeal to authority" when you need it? Either "flyingfsck (986395)" makes a good point or he doesn't. There's no point in even having a comments section if nobody's going to actually discuss the subject, and flyingfsck (986395) is certainly makigna better contribution to that than you are.
I usually welcome hearing Tyson's latest addition to lay science understanding.
I sort of like character-celebrity-scientists. Mister Wizard, Bill Nye, and local college instructor / news-show scientist "Chemical Kim" are just a few of the scientists I applaud for their work in bringing science to the masses as a fun and interesting subject.
I don't like the stand-in experts like Michiu Kaku or Tyson, who take a different tack of bringing science to just a large audience, not really packaged for the masses at all, often with their own opinions added, and typically very pompously presented.
Tyson manages to keep my respect by being relatively sane and mainstream, basing his conclusions and projections on "establishment" science.
I can't say the same for Kaku, who I haven't heard from in awhile because I purposefully stop visiting web sites and stop listening to radio shows that give him a podium (no, this is not a viable way to get me to stop visiting /.)
But Tyson also manages to capture my interest by doing the same thing Bill Nye does: making comments about human affairs and human nature. They both humanize science.
But Tyson's pomposity sort of makes it hard for me to "like" him. And I just read something about him recently, so now it's like a second serving of buttered scallops when I clearly had trouble finishing the first serving.
"Stratigraphically the origin of agriculture and thermonuclear destruction will appear essentially simultaneous" -- Lee
Imagine 3-orthogonally mounted rocket engines. The sum force of the asteroid has to ultimately be a vector combination of force in those 3 directions. You apply thrust off angle such that you counter the asteroid's attraction without thrusting at it.
Because we are currently unable to judge the stability of the object, or it's internal mass distribution just by looking at it from long range.
Pushing it at any point might just lead to breaking off a small piece, or the spaceship slowly sinking into and through it.
If we miss the mass center, the push will mostly be transformed into rotation.
All these problems are a non issue with gravitiational pull.
Even if it wasn't the case, it seems to be it would be a hellva lot more efficient to use the rockets to just push the damn asteroid, rather than rely on gravity. A couple of tonnes of probe isn't going to exert much influence on a couple of hundred (thosand?) tonnes of space rock.
You don't need much deflection if you have enough time.
No, because you use ion engines on the tug which are tremendously more efficient per launch weight than chemical thrusters.
This isn't a strategy for an "OMG - it's going to wipe us out next week!" asteroid - it's for ones where the orbit shows a near hit of Earth fairly far into the future. Small gravitational tugs over a long period of time are all that's required.
Now, ideally those asteroids can be brought into a useful orbit where they can be mined for more mass to deflect more and more asteroids. In the mid-term perhaps only the ion engines need to be sent up from Earth.
Tyson isn't inventing this - it's a well-accepted strategy in the community that he's trying to explain to a larger audience.
My God, it's Full of Source!
OUTSIDE_IP=$(dig +short my.ip @outsideip.net)
But, he just stomped on the idea for the Open Crowd Source Asteroids Initiative.
A giant bank of lasers spread over the Earth activated by an online MMG of people playing a "free" version of " Asteroids" fed by satellite for positioning and trajectory.
Some people just have no imagination...
*Repent!Quit Your Job!Slack Off!The World Ends Tomorrow and You May Die!
So don't push against the asteroid. Spacecraft seem to be able to propel themselves in space just fine without something to push against. Aim the thrusters tangentially to the asteroid so the thrust force doesn't push against the asteroid.
Not Mike Tyson, it's Neil De Grasse Tyson, Miss Latella.
*Repent!Quit Your Job!Slack Off!The World Ends Tomorrow and You May Die!
Only if you let it. The Gravity Tractor idea usually uses two ion engines aimed so the exhaust goes either side of the body being towed. The tractor stays in place and there's no unwanted momentum transfer.
I would normally agree but the whole thing sounds preposterous. The gravitational pull of a spaceship is negligible. If you're going to send a spaceship up there and let it "hover" why not just have it actually contact the meteor and use its thrusters to push it out of the way?
The way the universe works doesn't really depend, in any way, upon you finding physics "acceptable".
And a great many people, who clearly are vastly more knowledgeable than you, have done the math and know what they're talking about
"Knowing where the pieces land" seems like a red herring.
If we detect an asteroid a long way out on a collision course with Earth, then altering its velocity by just a bit will push it off of course and it'll miss us. If you set off an explosion near an asteroid, it will indeed likely fragment, but the only way we're still getting hit is if a large chunk somehow gets *no* delta-v from the explosion, and if that chunk is big enough to survive reentry.
OTOH, if we detect a big asteroid close to us, there may not be time for these things, and we need a large impulse quickly.
Either way, "nuke it" seems like the most sensible thing. Yes, this is a drastic thing, but if it's a true doomsday asteroid then it's called for.
Wouldn't it just be better to smack into one side of the asteroid at full speed rather than use a bunch of energy to get to the asteroid, a bunch more to slow down and rendezvous, then use little puffs of energy to try and modify its orbit?
Seems to me that all that reaction mass would be much better served by hitting the rock traveling at 4X,000 MPH.
I am very small, utmostly microscopic.
Yep. Surely it's far better to fire a cable at it and give it a good pull at 100% engine thrust than wait for a microscopic amount of gravity to have an effect.
No sig today...
It may not be much, but those little tiny bits of acceleration add up.
Actually according to Doug Adams definitive history:
On a planet called Golgafrincham there was an an nouncement that the planet would soon be destroyed in a great catastrophe They planned an evacuation using a group of arcs:.
The passengers of the “A” ark were to be all the brilliant leaders, scientists, great musicians, data analysts, engineers and architects. The passengers of the “B” ark were to be all the “middle men” , marketing executives, telephone sanitizers , sales assistants and telemarketers etc. The passengers of the “C” ark were to be the real workers, construction, manufacturing and other craftsman.
As I remember it, everyone fought for a place on the B Arc which blasted off into space programmed to land on the third planet of an obscure star at the edge of the galaxy. Shortly after its departure, they discovered it was all a mistake and the planet was not going to be destroyed.
Golgafrincham entered into a period of exceptional peace and prosperity.
The planet that was the destination of the B Arc had a different kind of history.
When you are dancing with wolves, never limp
No, it won't. The surface/mass ratio will be different (smaller pieces can burn up more readily), and if they're spread out enough, instead of all that mass hitting at once, we just get a few nights of falling stars of little consequence.
We seem to survive the Leonids OK, and we've been surviving them for a long time.
We don't have to follow the "fight fire with fire" methodology. If the weakest force in the universe is pulling an asteroid towards the earth, we needn't use the weakest force in the universe to steer it away. The electromagnetic force is 10^36 times more powerful. Superconducting magnets require only the energy to get them started and keep them cool. Most asteroids are more than one part in a undecillion feromagnetic. So make use of it. And if threat happens to be composed of a diamagnetic material (e.g. comet water), use that to repel it away. Using gravity is just daft unless you have no alternative.
Well, we can work that out.
As was pointed out earlier, the spaceship needs to be far enough out that its exhaust gases (from the retrorockets used for station-keeping) don't mostly strike the asteroid and cancel the force of gravity. (Perhaps we can use multiple retrorockets at angles pointed away from each other to ensure all the gases miss the asteroid, but this is inefficient -- you can do the trig.) If the asteroid is 500m across, let's say that we'll need to be at least 500m away. But in computing the force we need to compute the distance to the center of mass of the asteroid, giving a total distance of 1km.
Let's say we have a 10-ton spacecraft (very expensive to launch) up there.
Then the acceleration on the asteroid is
(10^4 kg) 7 * 10^-11 / (1000)^2 m/s^2 = 7*10^-7 / 1*10^6 = about 7*10^-13 m/s^2.
A year is 3*10^7 sec, so after a year we'd have a delta-v of about twenty microns per second.
Google Calculator will do this for you too: google "gravitational constant * 10 tonnes / (1 km^2) * 1 year".
Don't know about six, but I can name 7 of 9.
rewriting history since 2109
Actually, they died by a mysterious virus spread through their filthy phones unless I'm mistaken.
Golgafrincham entered into a period of exceptional peace and prosperity.
Um, no. They all died from a virulent disease contracted from a dirty telephone.
No sig today...
Remember, best block, no be there.
If Sam Kinison were alive today, he'd apply his philosophy on world hunger and say:
You want to help end extinction-level meteors? Stop sending up shit to blow them up. Don't send them another one, send up huge orbit-altering rockets. Send the UN a guy that says, "You know, we've been coming up with a plan to blow up meteors for about 35 years now and we were blowing stuff up, and we realized there wouldn't BE extinction-level meteors if you people would live where the METEORS AREN'T! YOU LIVE INSIDE AN ASTEROID BELT!! UNDERSTAND THAT? YOU LIVE IN A FUCKING ASTEROID BELT!! Stop wasting rockets by launching them at each other. You too, North Korea... don't give me that look. We're going to do this together in one shot.
The most-effective solution is don't be where the meteor is going to be. This worked well for me the other week. Giant meteor fell in Siberia and I wasn't there.
The whole idea is conceptually idiotic. You spend a strong force of reaction mass ejection to maintain a weak force of gravity at a constant distance from the target mass producing a microscopic tug on the object. This guy must have received his degree in a box of crackerjack.
Place the reaction mass generator (be it ion jet, or rocket) directly on the mass and divert it.
Amazing that they didn't think of that!!! You must be a genius...
Or... maybe they did consider that, then realised that many, many small asteroids are apparently heaps of weakly bound rubble, just as bad as a solid object when hitting the surface of earth, but impossible to attach a rocket to.
The "gravity tug" concept works the same regardless of the structural integrity of the asteroid, *that* is why this is the proposed mechanism, not because Tyson is stupid...
Bet you feel a lot less like a genius now, smarty-pants?
Do you work for a for-profit, or even well-known non-profit? Then you too work for advertisers...
Browsing at +1 - no ACs, I ignore their posts. So refreshing!
The whole idea is conceptually idiotic. You spend a strong force of reaction mass ejection to maintain a weak force of gravity at a constant distance from the target mass producing a microscopic tug on the object.
I pity the cranially impoverished people who modded this up as "Insightful". Go back to high school, would you? The two forces you're referring to are exactly equal in size, as per Newton's third law. The probe gets positioned at a distance at which the thrust of the engine is equalized by the asteroid's gravity, and the probe consequently pulls the asteroid with identical force (modulo its sign) while keeping a stationary position above its surface.
What you get here is exactly what you'd get by putting the probe onto the asteroid and pushing it, but you're avoiding the potentially dangerous contact with the asteroid. Moreover, the probe is likely to be powered using solar arrays, and asteroids sort of tend to rotate, which would severely complicate your attempts at creating a sustained thrust, not to mention the fact that your thrust vector would also rotate. Separating the probe from the asteroid and acting gravitationally upon it gives you constant insolation of the panels and the ability to exert constant thrust in a single direction.
Ezekiel 23:20
Taking a 30,000 kg ship at 20 km from the asteroid and the gravitational constant to be 6.7x!0^-11 m^3 kg^-1 s^-2, you would have a gravitational acceleration of about 5x10^-14 m/s^2. To move it 6,400,000 m (one earth radius) would require 1.6x10^10 seconds (about fifty years).
Also, for two asteroids orbiting each other, if these are "small" asteroids, what gravity would obtain between them? Two asteroids of radius 20 kilometers each with 50 kilometers between their centers (and having earth's density for a mass of 5x10^13 kg each) would have a mutual gravitational acceleration of 1.3x10^-5 m/s^2. Would it be that hard to separate them?
.... I'm confident that we have little to worry about. Asteroids will tend to avoid our planet out of sheer embarrassment.
I don't care if it's 90,000 hectares. That lake was not my doing.
That gets you around the exhaust problem but worsens the problem of gravitational force limiting. The closer your tractor ship to the asteroid, the more propellant you must use pushing in useless directions. The farther you put it, the more efficient the use of fuel but the amount of time you must pull to get the same delta P increases as the square of the distance to avoid the tractor escaping.
The optima don't align at all. If you want to minimize the amount of time you must spend towing, you put the "tractor" very close, about 1.25 radii from the asteroid. (Actually maybe a little farther to ensure you don't hit the asteroid with any of the propellant.) That that reduces your efficiency to about 60% of what it would be in the limit and your force to about 38% of the weight of the tractor on the asteroid's (assumed spherical) surface. For non-spherical towed objects, it gets worse. But assuming efficiency isn't a consideration, you're still limited to less than the gravitational force between the asteroid and your tractor.
It must have a lot of mass when it gets there because if it doesn't it won't have enough gravity to pull anything anywhere. The smallest objects we'd probably need to move are 100-meter asteroids that mass something like 3E9 kg. So the force you can apply this way is limited to less than .074 Nt/ton of tractor. Over a year of such pulling, you get a delta-v of about .0008 meters per second. How much do you have to change the velocity to miss the Earth? About by the diameter of the Earth. It turns out to do that in a year takes about a 2 ton tractor. A rock twice that big has 8 times the mass and would take 4 times the tractor to move it in the same time.
This has to be compared in practicality to other methods. While it solves the problem of not having to physically land on the object, you still must match velocities exactly and must send a bunch of dead weight to pull your object with.
If it's a rubble type, then a nuke would work to displace enough mass to move it. Seems like this is a one-size-fits-all solution. One solution for the iron-type and one for the rubble piles. The optimal solution for each may not match. Then the question becomes at what range we can distinguish. That, and the one I heard about casting a net over the whole thing and towing it with a long cable.
Learn to love Alaska
Taking a 30,000 kg ship at 20 km from the asteroid and the gravitational constant to be 6.7x!0^-11 m^3 kg^-1 s^-2, you would have a gravitational acceleration of about 5x10^-14 m/s^2. To move it 6,400,000 m (one earth radius) would require 1.6x10^10 seconds (about fifty years).
Also, for two asteroids orbiting each other, if these are "small" asteroids, what gravity would obtain between them? Two asteroids of radius 20 kilometers each with 50 kilometers between their centers (and having earth's density for a mass of 5x10^13 kg each) would have a mutual gravitational acceleration of 1.3x10^-5 m/s^2. Would it be that hard to separate them?
But you aren't talking about moving it X distance, you're talking about deflecting it X angle...
Even 1 degree is a decent change at a few AU
a handful of selfish greedy people are no match for millions of selfish, greedy people -u4ya
And what's the fix for your gravity pulling it away from a collision, but your exhaust pushing it into a collision course?
The solution is to have the exhaust *not* pushing it into a collision course. Isn't that obvious?
What he meant was: you place the tug on one side to bend the trajectory of the asteroid that way, but in order to keep the tug away from the asteroid, it has to fire its engines towards it. The exhaust will hit the asteroid and exert a force in exactly the opposite direction from what you are trying to achieve with the gravitational pull. If the entire exhaust hits the asteroid, the net trajectory change will be precisely zero. The only solution for that is to fire thrusters diagonally from a far enough distance so that the exhausts will miss the asteroid. But this will obviously reduce the amount of tugging you're going to achieve.
I think you may need to consider feasibility when coming up with your plans. It's a lot easier to just fly somewhere and hover than to land, or to make and deploy a gigantic asteroid net.
And its a lot easier to fly somewhere close and send in a rocket powered Bunker Buster bomb.
Most of the rocky bodies we've investigated and photographed are loose creations of material which would most likely burn up in the atmosphere if you simply spread them out a bit. Even a solid rock of extinction size would do less damage if you break it up into more than one piece, and in doing so deflect significant chunks of it such that they would not even hit the earth. 2/3rds of the remaining pieces would land in the oceans as widely dispersed smaller chunks.
In other words, the entire premise of trying to finesse a miss by micromanaging the orbit doesn't put you in any better position than going nuclear. Because you have to have a great deal of time to change the orbit, the ability to predict future orbits, and technology of sufficient size and durability to actually be able to work, and if it fails you still have to have a plan "B". And waiting for a gravity solution to work would mean Plan B, would be a point blank nuclear strike.
The blowing things up bit, while sounding crass and inelegant, is actually the more sensible approach. Do it early, (preferably years in advance) evaluate your results, have another delivery vehicle pre-deployed for a later intercept, rinse, repeat until everything is smaller than a house, then simply take your chances.
Playing with orbit adjustments is an exercise in hubris.
Sig Battery depleted. Reverting to safe mode.
Where do you get your ideas that blowing up a giant rock is a good idea. I'm talking giant, because the smaller ones, while being a problem for whoever's head they land on, don't pose an Extinction Level Event.
Maybe because the full rock DOES pose an extinction event?
And you might also want to look up the definition of "burn up in the atmosphere". And also you might want to supply some actual backup about your claim that they will have the same basic trajectory after a nuclear warhead scatters the big rock into much smaller pieces. Placed close to center, at least half the rock would get a significant retro acceleration. Another significant portion gets a forward acceleration. When you do this early enough there is no reason to suppose that all the parts have the same basic trajectory.
Even if a significant portion did stay on their collision course, they would be spread out, and the shitload of smaller ones represents a far less deadly potential than one giant big one. Because small ones burn up in the atmosphere.
Sig Battery depleted. Reverting to safe mode.
All you have to do is generate a near miss once and the rock's orbit will be radically altered forever after, by the slingshot effect of Earth's own gravity as it passes by. Remember 2012 DA14? It will never pass so close to us again. When it went by that close, it got slung into a new orbit.
But Tyson's pomposity sort of makes it hard for me to "like" him..
They're fine as long as they don't get uppity, eh?
Appeal to authority is, in many, many cases, a perfectly valid argument. Appeal to authority is the entire reason our society can even function at all. We offload complicated decisions to people who are better at them than us.
And in this case, it is once again correct. Neil deGrasse Tyson does indeed know what he is talking about. The gravity tractor idea has been around for a long time, and in theory works just fine.
I mention that the timing may get messed, but I'm stuck in 2D trig? Doesn't the 4-dimensiomality make it easier to solve?
I would normally agree but the whole thing sounds preposterous. The gravitational pull of a spaceship is negligible.
The force of gravity between the asteroid and the ship is small, not necessarily negligible. Let's take some basic physics. The gravitational force between two objects is g (about 9.8 m/s/s) times the mass of the first object times the mass of the second object divided by the square of the distance between them.
F = g*m1*m2/d^2
The acceleration of an object imparted by a given force is the force divided by the mass of the object being accelerated.
F = m*a or a = F/m
So combining those two equations, the acceleration of the meteor being moved due to the gravity of the spaceship is g times the mass of the spaceship divided by the square of the distance between the meteor and the spaceship. The mass of the meteor cancels out.
a = g*m_{ship}/d^2
Now this is likely to be small, true. But just like interest in the financial world, the secret is time.If you can impart even a small acceleration over a long enough time frame, the thing you're accelerating ends up going at a pretty good velocity.
The approach you'd need to use to react to a meteor depends on the size and how long in advance of its impact you can detect it. If you detect it a year or two ahead of time? At _best_ you might have time to prepare an Armageddon-style mission; more likely you'd want to find some way to record information about humanity's progress so the survivors can recover or aliens can learn about the extinct human race. Ten years would be better for that type of "plant a bomb on it" mission or to prepare to launch a nuclear missile at it. Fifty to a hundred years? A low, slow method like gravitational towing may be good enough to ensure that Earth and the meteor don't pass through the same point in Earth's orbit at the same time.
You're right, of course - if a large portion of the mass comes into contact with the atmosphere.
Newton's First Law (aka law of inertia) says that things will keep going in a straight line, unless acted upon by an outside force. We apply such an outside force when we break the asteroid apart; the pieces start dispersing on new courses.
Doing this at a far enough distance from Earth (not unlike nudging the asteroid's course slightly when it's quite far away) means that the parts will be dispersed enough to not all hit the planet, if we do it right.
Back-of-the-envelope math says that if it's broken into a cloud of particles expanding at 20cm/s 20 years before it's supposed to hit us, it will be 100 times the diameter of the earth when we encounter it... I would guess that means we're not going to encounter all the particles.
Actually maybe a little farther to ensure you don't hit the asteroid with any of the propellant.
In a vacuum, the gas from the propellant won't dissipate quite as much...
An additional force to think about - if you're using gas propellant, or perhaps an electrostatically accelerated ion engine, you're going to build up quite a charge throwing those ions around, aren't you? You'd have to consider that in your calcs. Might change the shape of the attraction curve between the two bodies.
Do not mock my vision of impractical footwear
The value that you've given for g is the acceleration due to gravity ON EARTH. G in your first equation should be capitalised, and it's the Universal Gravitational constant. G ~= 6.67 x 10^-11 N(m / kg)^2
This doesn't make your logic less correct, but your numbers are going to be several orders of magnitude off.
http://en.wikipedia.org/wiki/Gravitational_constant
http://en.wikipedia.org/wiki/Gravity_of_Earth