# What would happen if earth's mass suddenly halved?



## Fallowfox (Jan 30, 2013)

On another forum I'm having a discussion with someone about what would happen to you if you jumped through a pole-to-pole tunnel in the earth. 
I said that if you jumped in, ignoring resistance and boiling hot rocks it would take about 40 minutes for you to reach the other side. 

This user however was a little more extreme...they said that boring a tunnel through the earth would disrupt the core's magnetism and therefore send the earth hurtling _out of the galaxy_. 

After making it clear to them that the earth orbits the sun by virtue of _gravity_, not by its magnetism, they raised a different question. *What if the tunnel was sufficiently wide enough so that half of the earth's mass were removed? *...wouldn't_ that _mean earth would be flung out of the solar system? [by now we're ignoring claims of intergalactic travel]

I suspect the earth would maintain its current orbit, because whilst the centripetal force of the earth towards the sun would be halved so would the earth's tangential momentum, so the balance between the centre-seeking force and the tangential force would remain. 

*Can anybody prove this right or wrong? *


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## Aetius (Jan 30, 2013)

Lower Mass? 

I for one would use my newfound gravity powers to conquer Mexico.


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## Retro (Jan 30, 2013)

It wouldn't end well.


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## Inciatus (Jan 30, 2013)

Half the mass of the earth? That is like losing every American in the world! :V

Now how suddenly? Are we taking the mass and poof it is now energy or are we taking the stuff and throwing it off our planet in all directions?


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## Kalmor (Jan 30, 2013)

http://www.youtube.com/watch?v=jN-FfJKgis8&feature=share&list=PLED25F943F8D6081C

MinutePhysics answers many of your questions.


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## Fallowfox (Jan 30, 2013)

Inciatus said:


> Half the mass of the earth? That is like losing every American in the world! :V
> 
> Now how suddenly? Are we taking the mass and poof it is now energy or are we taking the stuff and throwing it off our planet in all directions?



We're considering a contrived scenario in which *poof* half the mass of earth is gone. 

The people I was discussing this with specifically used the example of an alien lazer zapping a tunnel through the earth of significant girth that the vapourised rock [which presumeable escapes] would be significant in comparrison to earth's mass. 

So, an antractica sized pole to pole tunnel or something.



Raptros said:


> http://www.youtube.com/watch?v=jN-FfJKgis8&feature=share&list=PLED25F943F8D6081C
> 
> MinutePhysics answers many of your questions.



Thanks, although I had already watched this and posted it to the user in question.


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## CaptainCool (Jan 30, 2013)

Well, since gravity on it's own isn't based on mass but rather on energy and velocity it probably would maintain it's orbit.
I am not a physicist though so don't quote me on that. (Except for the mass and velocity part. I learned that from MinutePhysics as well :V)


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## BRN (Jan 30, 2013)

Hi! Physics represent.

Technically the force of attraction between two objects is:

[Newton's universal gravitational constant] * [Product of masses] / [Distance between masses, squared].

Now, since the universal gravitational constant and the distance between the masses will remain the same, it's mathematically sensible for this equation to replace [Newton's universal gravitational constant] / [Distance...] with algebraic symbol, *k*.


In this case, K is 2.982119*10^-33 according to Google's calculator and Wikipedia's values for G and 1 au, but we don't really need to know that.

However, the product of the masses is 1.18792831*10^55 kg. 

After a tunnel is dug through the centre of the planet, *this mass doesn't change, genius, because where do you put the mass you excavated from the tunnel?

*Physics out. <3


ED: However, it seems that joke has already been made. :c

The problem with vaporising the matter is that E=MC^2. The released energy from a 100% efficient vaporisation procedure would, uh, melt the stray atoms in the near-vacuum in every bit of space from here to Venus.

A technogically possible procedure would be to drop successions of nukes onto the same part of the crust (presumably the Marianas trench?) but, forgive me if I'm wrong, but by the time you start dropping nukes into the deep mantle you've already killed everyone who wanted to know the answer by setting off supervolcanos.

ED2: If it were possible to simply remove the earth, ship it into space and not catastrophically kill everything... well. I'll make a serious post in a bit.


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## Fallowfox (Jan 30, 2013)

SIX said:


> Hi! Physics represent.
> 
> Technically the force of attraction between two objects is:
> 
> ...



In either case it would be almost entirely impossible to bore a hole through the earth the size of a third world country so we're considering the fantasy scenario in which the mass is poofed away, presumeable by the magic tunnel fairy, I look forward to your ed2.


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## Dreaming (Jan 30, 2013)

Taking a complete uneducated guess here... I'd guess that the atmosphere would collapse and we'd lose all gravity, I'm like 80% certain that the atmosphere and gravity are connected and maintained by the earth's mass somehow. I doubt the earth would fall out of orbit since that's more to do with the Sun's gravitaional pull (I could be wrong?)

But that's an guess based on what I've seen on TV... years ago. I wish I could give a more advanced accurate answer but all that physics and big number stuff makes me cry in a corner >.>'


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## BRN (Jan 30, 2013)

Okay.

Since the earth still keeps a spherical shape and, assuming the bored tunnel is symmetrical *and* exactly equal to half of the earth's mass, you fortunately still get to model the earth as a particle orbiting a particle of matter.

This makes things simpler!

Let's simplify things further by pretending that the earth follows a circular orbit.

Lastly, let's further simply things again by just ignoring the relatively tiny gravitational pulls and pushes of the other planets of the solar system.

If all these things are the case, then only two forces are in play, here: gravity of the sun and centripetal force.

These can be said to be the "pulling in" force, and the "pulling out" force.


*Pulling in:*
GMm / R^2

*Pulling out:*
mv^2/R


At the moment, GMm/r^2 = mv^2/r -- we know this is true because we're not falling into the sun. The pulling out and pulling in forces are equal.

You can simplify this equation to GM/r^2 = v^2/r because in both equations, you've got the mass of the earth (m) being expressed on the top part of the fraction, and can just simply remove it.

Oh wait-!

*isn't this funny?*

If the mass of the earth doesn't matter to this equation, the shape of earth's orbit is determined only by the mass of the sun, the speed of the earth, and the distance from the sun!

*conclusion:* You'd have to half the mass of the sun to change shit. Changing the mass of the earth... changes nothing!



---

ED: If your friend wants to look these figures up and do the math himself...

G = Newton's Universal Gravitational Constant
M = Solar mass
m = Earth mass
R = One astronomical unit of distance (1 AU), or 149,597,871,000 metres
v = Speed of the Earth, or (R^2 * pi) / (365.25 * 24 * 3600)


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## Fallowfox (Jan 30, 2013)

SIX said:


> Okay.
> 
> Since the earth still keeps a spherical shape and, assuming the bored tunnel is symmetrical *and* exactly equal to half of the earth's mass, you fortunately still get to model the earth as a particle orbiting a particle of matter.
> 
> ...



I think it's safe to say as long as the earth's mass is non-zero that its orbit would be unaffected, assuming it is modelled as a particle?


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## BRN (Jan 30, 2013)

Fallowfox said:


> I think it's safe to say as long as the earth's mass is non-zero that its orbit would be unaffected, assuming it is modelled as a particle?



If you don't want to model the earth as a particle, for the sake of accuracy, then that's when you'd have to take the rotation of the earth into account.

However, so long as the bored tunnel was symmetrically bored - i.e, not leaving more mass on one side of the earth's axis of rotation, which is consistent with the idea of a vaporising laser - then the mass of the earth would still be immaterial to its orbit because it would also be immaterial to its rotational velocity.


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## Fallowfox (Jan 30, 2013)

SIX said:


> If you don't want to model the earth as a particle, for the sake of accuracy, then that's when you'd have to take the rotation of the earth into account.
> 
> However, so long as the bored tunnel was symmetrically bored - i.e, not leaving more mass on one side of the earth's axis of rotation, which is consistent with the idea of a vaporising laser - then the mass of the earth would still be immaterial to its orbit because it would also be immaterial to its rotational velocity.



Agreed. If you didn't model as a particle I imagine the earth would collapse in around the void and consequentially spin faster on its axis like a figure skater who is bringing in their arms?


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## Cairn (Jan 30, 2013)

Fallowfox said:


> Agreed. If you didn't model as a particle I imagine the earth would collapse in around the void and consequentially spin faster on its axis like a figure skater who is bringing in their arms?


I would image so, and we could possible lose our moon. If for some reason it didn't collapse though, all the air in our atmosphere would still rush to fill the hollow space.


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## Rasly (Jan 30, 2013)

Not much, some people may even survive.


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## Cairn (Jan 30, 2013)

Rasly said:


> Not much, some people may even survive.


If it happened in the way he described (by removing a large column of mass from the middle), then I highly doubt anyone would survive.


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## Kio Snowfyre (Jan 30, 2013)

If the Earth's mass suddenly halved whilst the moon was in the path of its orbit around the sun, the destruction of life on Earth would be inevitable because of the sheer speed of the Earth around the Sun. Orbit itself would be mostly unaffected, except inertia from the actual event of reduction might change the course / give more momentum but the event would likely be destructive, anyway. Also, Earth's rotation would decrease in time causing longer days and this could potentially affect the planet. If the moon wasn't in the Earth's path the moon would move away from the Earth, causing potential climate damage due to lack of pull on the tides. Also, although the theory of "Earth-Moon tilt relation" is rejected it could have an impact on the Earth's tilt (from its orbit around the Sun) as it's possible for the moon to at least slightly affect the momentum of the tilt even if this to a very small degree (i.e. the moon affects the balanced momentum of the Earth's obliquity but does not cause it directly). I'm no astrophysicist, though.


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## Inciatus (Jan 30, 2013)

Fallowfox said:


> We're considering a contrived scenario in which *poof* half the mass of earth is gone.
> 
> The people I was discussing this with specifically used the example of an alien lazer zapping a tunnel through the earth of significant girth that the vapourised rock [which presumeable escapes] would be significant in comparrison to earth's mass.


Well right now, assuming our orbit is pretty well cicular, using ((((((1.9891*10^30)^2)*(6.67*10^-11))/(((5.972*10^24)+(1.9891*10^30))149600000000)))^1/2 gives us roughly a velocity 29780m/s. We divide the mass in half, making ((((((1.9891*10^30)^2)*(6.67*10^-11))/((((5.972*10^24))+(1.9891*10^30))149600000000)))^1/2 we still get the same answer.
Equation 1: 
	

	
	
		
		

		
			




Equation 2: 
	

	
	
		
		

		
		
	


	



Unless I screwed up my math, it would seem the mass of the orbiting body is pretty much irrelevant. It it likely because of the difference in mass between the Sun and Earth. We are six figures smaller and I only have four significant figures.
I suppose the fact that the earth rotates would be more screwed up because now we have a different distribution of the mass so our 'I' isn't going to be .4MR^2 anymore. It would probably sit around .7MR^2 (complete guess but now the mass in going to be closer to the edge so I will get closer to MR^2).
Earth's angular velocity of __, using this equation: .5((7.2921159*10^-5)^2)*(.4*(5.972*10^24)*(6378100^2)), yields an total rotational kinetic energy of 5.172*10^29J. 
Equation 3: [imghttp://www3.wolframalpha.com/Calculate/MSP/MSP39701a52796e80f5645300001f4ci7bi4715ic29?MSPStoreType=image/gif&s=39&w=279&h=36[/img]
If we were to bore out a cylinder from the Earth we would find that it has different layers, with the most dense stuff in the center. Because of the shape of a sphere, the nature of a sine function around pi/2, assuming the radius of the cylinder will not be substantially large as to throw off our sin assumption, the fact that I am too lazy to do the calculus, and that we are assuming so many things as is it isn't worth the effort to be more exact, we can assume that the shape is basically a cylinder. There are four different layers (which will be merged into three for the sake of this), each layer in leading to a greater amount of error. Our mass of the cylinder is going to be roughly 1/2MvE=pi*r^2*2(12800*~1200000+11000*2200000+4000*290000). Moving stuff around we get r=(.25M/(pi(12.8*1200000+11*2200000+4.0*2900000))^.5 (forgot my conversion factor at first, a billion meter diameter cylinder is too big, then forgot another one). This yields a radius of 3050000m or 3050km, which is larger than our core. I'll do more math later to find the actual diameter of the hole or someone else could do it (It will be about ten months before I know how to calculate it. )
Equation 4: 
	

	
	
		
		

		
		
	


	



Keeping the same angular velocity the cylinder would have a rotational kinetic energy of 7.385*10^28 (which being less than one tenth of my old value I fucked up). From what all this says is I made too many assumptions and broke it. We need a much higher math level.

However, I realized that assuming that the the particles didn't gain any kinetic energy from the blast they would still be having the same momentum and energy individually. This would mean that assuming the Earth stayed together all the particles in the area would still have the same net energy. So we wouldn't change the total rotational energy of that part of the Earth because of the equation to find it (which I can't find a good picture of right now)(It says .5 omega squared mulitply by the sum of all the masses multiplied by the sum of all the radii. 

Though since the mantle is pretty plastic there is the chance that everything decides to go a bit more straight and we break apart. Also now we don't have a core so not magnetic shield so we are screwed from that point. Lastly that blast would do a hell of a lot of ionizing to our atmosphere and would probably kill us anyway.

Edit: Well I see Six already got the speed part down during the time I was doing math, writing and eating lunch.


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## BRN (Jan 30, 2013)

Fallowfox said:


> Agreed. If you didn't model as a particle I imagine the earth would collapse in around the void and consequentially spin faster on its axis like a figure skater who is bringing in their arms?


Oh bugger me, that's a civil engineering mindbender.

The eventual outcome depends entirely on the structural integrity of the crust and mantle, but I imagine that at least for a brief while you'd have a torus of earth orbiting around globules of floating displaced outer-core. After that I'd need a migraine pill.


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## RadioactiveRedFox (Jan 30, 2013)

Halving the earths mass would likely cause the moon to be ejected, would it not. If this is so I would think that the change in gravitational forces exerted by the moon as it was being ejected may be enough to destabilize earths orbit, which could cause havoc to the other planets.


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## FrostHusky81 (Jan 30, 2013)

My theory is that the immense amount of gravity lost will cause the earth to collapse upon itself, therefore creating a black hole. The sudden disruption of earths equilibrium leads me to that conclusion. I'm problably wrong anyways, it's just a guess.


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## Inciatus (Jan 30, 2013)

Because the mass of the moon is 5.035*10^21 slug where Earth is 4.092*10^23 slugs the difference in mass wouldn't lead to a huge amount of difference. It would probably slip out a bit faster, but not substantially faster like you are thinking of.

The Schwarzschild radius of normal Earth is about an inch. It will be smaller for half an Earth. That isn't going to happen.


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## RadioactiveRedFox (Jan 30, 2013)

FrostHusky81 said:


> My theory is that the immense amount of gravity lost will cause the earth to collapse upon itself, therefore creating a black hole. The sudden disruption of earths equilibrium leads me to that conclusion. I'm problably wrong anyways, it's just a guess.



The earth's mass is nowhere near what it takes to create a black hole, though it is a far assumption that it would collapse.


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## Inciatus (Jan 30, 2013)

RadioactiveRedFox said:


> The earth's mass is nowhere near what it takes to create a black hole, though it is a far assumption that it would collapse.


Mass is irrelevant to black holes, if you were to squish the Earth's mass into a small enough radius it would be a black hole.

That would depend on the size, distance, and speed of each particle. It could probably be graphed on a three dimensional graph.


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## RadioactiveRedFox (Jan 30, 2013)

Inciatus said:


> Because the mass of the moon is 5.035*10^21 slug where Earth is 4.092*10^23 slugs the difference in mass wouldn't lead to a huge amount of difference. It would probably slip out a bit faster, but not substantially faster like you are thinking of.



Ya, I was kind of afraid of that being the case, I really need to get back into astronomy. But, that being said, wouldn't it still have an effect on earth's orbit over the long term?



Inciatus said:


> Mass is irrelevant to black holes, if you were  to squish the Earth's mass into a small enough radius it would be a  black hole.
> 
> That would depend on the size, distance, and speed of each particle. It  could probably be graphed on a three dimensional graph.



Yes, but you need the mass for a black hole to form naturally, if I remember right you need a star that is 3-4 stellar masses or a black hole to form


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## Kio Snowfyre (Jan 30, 2013)

I think the atmosphere would be affected and definitely the climate, plus gravity-sensitive eco-systems. In lower mass if the size of the Earth is retained, that is, anyway. Also, I heard some get queasy in lower gravity and it can cause blood flow issues. Then there's the magnetic field and if the size of the Earth did reduce with the mass, the Earth could be a bit less closer to the Sun which might cause some environmental problems, that'd also mean with the current speed it'd take less time for the Earth to complete a whole day's worth of rotation.

Black holes did I hear? I wonder what an observer would see when a stream of light particles into black holes. Mmm nothing, I'd guess


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## Inciatus (Jan 30, 2013)

RadioactiveRedFox said:


> Ya, I was kind of afraid of that being the case, I really need to get back into astronomy. But, that being said, wouldn't it still have an effect on earth's orbit over the long term?
> 
> Yes, but you need the mass for a black hole to form naturally, if I remember right you need a star that is 3-4 stellar masses or a black hole to form



It wouldn't be that significant. If I remember correctly we will lose the moon in two-four billion or so years. Instead we would probably lose it just a little bit sooner, our race will likely be long extinct before that is a problem.

Kio, since we are supposing that the center is bored out from pole to pole, there shouldn't be any difference in day period assuming the planet holds intact. Although I is changing, the mass is also changing and the sum of all the masses multiplied by all the radii in the areas that would remain wouldn't change from this so in theory the rotation speed wouldn't change.


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## LizardKing (Jan 30, 2013)

I was going to mention Earth's orbit being unaffected to any real degree, but it seems that's already covered. Things that spring to mind:

Vast swathes of communication are disrupted as satellites are suddenly well above escape velocity. This probably doesn't have too great an impact beyond adding to the chaos. At least, the chaos before they all utterly destroyed.

A sudden, massive drop in atmospheric pressure, and therefore temperature. This would probably affect more things than I can think of. Decompression sickness, for a start. I've no idea how much the temperature would drop, and so much effect it would have. Anything flying - or even floating - in the air would suddenly find themselves stalling.  If they're floating because of a sealed and pressurised chamber, that would probably burst. 

Numerous vehicular accidents as suspensions suddenly spring up because pressure is drastically reduced. Any other machinery and whatnot that have springs under pressure would have similar issues. I don't think this would be too much of an issue though.

I assume the sea would also rise. Not by much I think, as water isn't terribly compressible, but I'd guess a few meters at least. I bet there'd be a massive water hammer effect though. 

This is even discounting the massive gaping hole in the Earth. I don't even know where to begin with that. I guess the molten core would be relatively quick to regain its shape, but the solid crust at the top would probably fold up like tinfoil as the molten layers underneath flow into new shapes. Possibly more water hammer effects as they collide, with shockwaves obliterating anything on the surface. Molten rock erupting all over the place. Entire oceans washing over land as it's distorted. 

Lastly, a hole through the middle of the Earth big enough to halve its mass probably means the entire inner core is gone, maybe most of the outer core. That's the magnetic field gone, so even if people somehow survive all this shit, they're now bombarded by solar winds previously kept out by the magnetosphere.

Yeah.


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## Inciatus (Jan 30, 2013)

RadioactiveRedFox said:


> Yes, but you need the mass for a black hole to form naturally, if I remember right you need a star that is 3-4 stellar masses or a black hole to form


I never claimed it would naturally form. I said it wouldn't. You would need to compress the entirety of Earth to less than an inch to make a black hole out of it.


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## RadioactiveRedFox (Jan 30, 2013)

Inciatus said:


> I never claimed it would naturally form. I said it wouldn't. You would need to compress the entirety of Earth to less than an inch to make a black hole out of it.



I know you didn't say that it would happen naturally, I was just saying  that mass is important in the natural formation of black holes.


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## BRN (Jan 30, 2013)

RadioactiveRedFox said:


> Halving the earths mass would likely cause the moon to be ejected, would it not. If this is so I would think that the change in gravitational forces exerted by the moon as it was being ejected may be enough to destabilize earths orbit, which could cause havoc to the other planets.



This is true!

You might remember the (GMm / r^2) = (mv^2 / r) relationship I posted earlier. By halfing the mass of the earth, which is the big M in this case, the moon's tangential velocity is suddenly around 1.4 times larger than it should be and the moon is flung out of orbit.

However, this shouldn't have much of an impact on the earth's continued orbit of the sun.



FrostHusky81 said:


> My theory is that the immense amount of gravity lost will cause the earth to collapse upon itself, therefore creating a black hole. The sudden disruption of earths equilibrium leads me to that conclusion. I'm problably wrong anyways, it's just a guess.



Nope, never. Inciatus (that smart lad) covered the Schwarzchild Radius in another post.

If you're given some mass - the Earth, for example - the Schwarzchild Radius is the radius of the sphere you'd need to squeeze it all into to create a blackhole. This is just short of one centrimetre for something the mass of the earth, and for something *half* the mass of the earth, it's half that again -- about 0.0045 metres.

[Schwarzchild Radius = (2G * Mass) / c^2 ]

Try to realise that when the mass of the earth is halved, its gravitational exertion on itself is _reduced_, not increased, because there's so much less of it.





LizardKing said:


> I was going to mention Earth's orbit being unaffected to any real degree, but it seems that's already covered. Things that spring to mind:
> 
> Vast swathes of communication are disrupted as satellites are suddenly well above escape velocity. This probably doesn't have too great an impact beyond adding to the chaos. At least, the chaos before they all utterly destroyed.
> 
> ...



All pretty fair! Depending on where the hole is 'shot', the effect might well be like pulling a plug on the oceans.

It makes an amusing Super Mario Galaxy idea to imagine a torus world where a waterfall of water flows through from one side to the other and rejoins the oceans again on the other side. With the Coriolis effect, it's conceivable, but icba to do the maths, and I'm pretty sure it'd all just form in a elliptical globule somewhere in the centre of the hole, among all the scattered flash-frozen segments of core =p

If I could be bothered, I'd work out how large the hole would be and have some fun with that, but it's 1:26am and I'm having a shit week and I haven't been laid in a while so fuck that


ED: Fallowfox it's late, go to bed or buy me a pizza gddmit


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## Furry Anarchy (Jan 30, 2013)

I clicked on this thread and now my brain hurts :v


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## Golden (Jan 30, 2013)

Assuming that the tangential velocity of Earth stays the same, wouldn't Centripetal Force acting on earth drastically decrease? (F=(m(v^2))/r). This would surely eject the planet from its orbit.


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## Fallowfox (Jan 30, 2013)

RaichuOPs said:


> Assuming that the tangential velocity of Earth stays the same, wouldn't Centripetal Force acting on earth drastically decrease? (F=(m(v^2))/r). This would surely eject the planet from its orbit.




Centripetal force decreases by a factor of two, but so does the earth's tangential momentum.

The velocity stays the same just like galileo's bag of feathers and bag of lead shot, which fall at the same speed.


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## RadioactiveRedFox (Jan 30, 2013)

SIX said:


> This is true!
> 
> You might remember the (GMm / r^2) = (mv^2 / r) relationship I posted earlier. By halfing the mass of the earth, which is the big M in this case, the moon's centripetal force is suddenly around 1.4 times larger than it should be and the moon is flung out of orbit.
> 
> However, this shouldn't have much of an impact on the earth's continued orbit of the sun.



Hm, I thought for sure that the ejection of the moon would have an effect on earth's orbit, maybe I was just over thinking the problem.


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## Golden (Jan 30, 2013)

Fallowfox said:


> Centripetal force decreases by a factor of two, but so does the earth's tangential momentum.  The velocity stays the same just like galileo's bag of feathers and bag of lead shot, which fall at the same speed.


  Could you elaborate on "tangential momentum"? And do you thing the earth would be ejected, fall into the sun, or maintain its trajectory?


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## Fallowfox (Jan 30, 2013)

RaichuOPs said:


> Could you elaborate on "tangential momentum"? And do you thing the earth would be ejected, fall into the sun, or maintain its trajectory?



Think of a man spinning around a weight on a rope. If he lets go the weight zooms off on a tangent, at 90 degrees to the direction he was facing when he let go of it. 

The momentum with which the weight flew off is its tangential moment, and is approximated by its mass multiplied by its velocity.



RadioactiveRedFox said:


> Hm, I thought for sure that the  ejection of the moon would have an effect on earth's orbit, maybe I was  just over thinking the problem.



I suspect it may effect the orbit, if the moon weighs about a hundreth of the earth [I think this is right: E22/E24] then as the moon is promoted away from the earth would the earth not also be pushed away from the moon?
although since the two orbit eachother perhaps it cancels out since one week the moon is being pushed towads the sun, the next week away from it.


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## Golden (Jan 30, 2013)

Fallowfox said:


> Think of a man spinning around a weight on a rope. If he lets go the weight zooms off on a tangent, at 90 degrees to the direction he was facing when he let go of it.   The momentum with which the weight flew off is its tangential moment, and is approximated by its mass multiplied by its velocity.    I suspect it may effect the orbit, if the moon weighs about a hundreth of the earth [I think this is right: E22/E24] then as the moon is promoted away from the earth would the earth not also be pushed away from the moon? although since the two orbit eachother perhaps it cancels out since one week the moon is being pushed towads the sun, the next week away from it.


  But, the mass of earth has been halved. If momentum: p = mv, wouldn't momentum be affected? I do think that the moon is already receding away from us, but your ideas give me something to ponder...


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## Kazooie (Jan 30, 2013)

RaichuOPs said:


> But, the mass of earth has been halved. If momentum: p = mv, wouldn't momentum be affected? I do think that the moon is already receding away from us, but your ideas give me something to ponder...


Honestly, momentum is more of a concept than a physical property. If you lose a bunch of mass, you're gonna lose the momentum that mass had, unless that kenetic energy was transmitted to the surrounding mass of the earth.


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## RadioactiveRedFox (Jan 30, 2013)

Fallowfox said:


> I suspect it may effect the orbit, if the moon weighs about a hundreth of the earth [I think this is right: E22/E24] then as the moon is promoted away from the earth would the earth not also be pushed away from the moon?
> although since the two orbit eachother perhaps it cancels out since one week the moon is being pushed towads the sun, the next week away from it.



I suppose that if the moon happened to be headed away from the sun at the time of its ejection the effect may be pretty much canceled out. On the other hand if it was heading towards the sun at the time of its ejection the effect may be amplified.  In theory any ways.


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## Inciatus (Jan 30, 2013)

Fallowfox said:


> Centripetal force decreases by a factor of two, but so does the earth's tangential momentum.
> 
> The velocity stays the same just like galileo's bag of feathers and bag of lead shot, which fall at the same speed.



Actually we can use a different equation to determine this: 
	

	
	
		
		

		
		
	


	




 where m2 is the mass of the body being orbited. Of course, I started to do my math in slugs and there isn't a nice G sitting around I can use.

Using this we find that the Moon moves at 1012m/s.
Equation: 
	

	
	
		
		

		
		
	


	



Now halving the mass of the Earth the moon would need to move at 712m/s to keep that orbit. 
Equation: 
	

	
	
		
		

		
		
	


	



As to where it would eventually land I'm not sure, that would require more calculations and I should be doing physics homework right now.


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## thoron (Jan 30, 2013)

If the Earths mass were cut in half it likely wouldn't cause it be flung out into space since its held by the Sun's gravitation field. For the Earth to be flung out into space something else like a large planet sized body would have to come in close to sling it out much like how we use Earths gravity field to get satelites to Jupiter and beyond.


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## Fallowfox (Jan 30, 2013)

RaichuOPs said:


> But, the mass of earth has been halved. If momentum: p = mv, wouldn't momentum be affected? I do think that the moon is already receding away from us, but your ideas give me something to ponder...



Yes of course the momentum of the earth is affected. That's why the earth stays in its orbit around the sun, ignoring the moon's role. 

The moon might impart momentum to the earth as it is lost to space, but as the moon is a fiftieth of an earth mass in this scenario it may not be significant.


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## Inciatus (Jan 30, 2013)

thoron said:


> If the Earths mass were cut in half it likely wouldn't cause it be flung out into space since its held by the Sun's gravitation field. For the Earth to be flung out into space something else like a large planet sized body would have to come in close to sling it out much like how we use Earths gravity field to get satelites to Jupiter and beyond.


Sorry, what likely wouldn't?

If you are talking about the moon, I agree but for different reasons. As the moon moves along it's going at about 1000m/s. Now since the Earth is less mass, at 1000m/s it will be moving too fast for a circular orbit. It would continue outward where it would slow down and likely return creating an elliptical orbits. Tides would be a bitch. Later I'll do the math but that will be a bunch of stupid integrals.


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## Demensa (Jan 31, 2013)

I always seem to arrive late to the threads I want to post in...

Anyways, everyone here seems to have everything locked down pretty well, so _my _question is:

What would happen if the tunnel was made between _any_ two (roughly) opposite points on the Earth, instead of from pole to pole? What (if anything) would change?


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## BRN (Jan 31, 2013)

Demensa said:


> I always seem to arrive late to the threads I want to post in...
> 
> Anyways, everyone here seems to have everything locked down pretty well, so _my _question is:
> 
> What would happen if the tunnel was made between _any_ two (roughly) opposite points on the Earth, instead of from pole to pole? What (if anything) would change?



You know how the earth tilts on an axis as it rotates, which is what gives us the seasons?

When boring this tunnel, you'd have to imbalance the earth around this axis in order to change what happens. So it doesn't particularly matter which two opposite points you dig the tunnel from -- just so long as they're on opposite points, in this simple model, it wouldn't leave "more" earth on either side of the axis, and nothing should change.

-----






Anyway, I found this thing! From this, you can work out how wide the tunnel would need to be - - and therefore, which parts of the earth structure we're removing. 

I did some of the modelling in a notebook and it looks like the tunnel would be 2500 - 2600km in radius, leaving a remaining Earth halo about 3800km in thickness.

Conveniently this leaves most of the mass of the outer core remaining, and even though we lost the solid inner core, it's the outer core which is generally important for most geologically noticeable processes - such as the magnetic field that keeps us alive.

Funnily enough, since we lost the solid inner core, I'm not even sure how to suggest gravity's going to work anymore.


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## Ricky (Jan 31, 2013)

This is a silly question.

Like someone said, did something happen to the Earth to do this (which would require a lot of force) or did the Earth just suddenly half in mass?

Oh you said suddenly.

Well, this would send a gravitational shock wave that would be of infinite proportions (since it apparently happened instantaneously) and would send the moon and probably all the other planets flying away at infinite speed (would this be c?). This is because gravity was instantaneously changed so anything within it's pull would be moved with infinite force (F=ma where a=âˆž since the planet lies in that distorted spacetime which just changed and put it in another position). They would then stay in motion with this infinite inertia, at c, becoming a singularity (taking into account the relativistic effects a speed of c has on mass of an object) that is without an event horizon (since we have an infinitely fast moving singularity) and this would destroy the universe as we know it.


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## Kazooie (Jan 31, 2013)

SIX said:


> Funnily enough, since we lost the solid inner core, I'm not even sure how to suggest gravity's going to work anymore.


At the center would be weightless. As you walk, on the surface, from the center between the two holes to one of the holes, gravity should steadily decrease as the effective average density of the nearby planet-mass decreases. Surely there's a program out there that can do the integrals; shouldn't be that difficult.



Ricky said:


> Well, this would send a gravitational shock wave that would be of infinite proportions


I don't think gravity shockwaves are actually a thing, sorry.

e: I mean, the Earth's gravitational force would simply suddenly decrease (by exactly half).


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## Fallowfox (Jan 31, 2013)

Demensa said:


> I always seem to arrive late to the threads I want to post in...
> 
> Anyways, everyone here seems to have everything locked down pretty well, so _my _question is:
> 
> What would happen if the tunnel was made between _any_ two (roughly) opposite points on the Earth, instead of from pole to pole? What (if anything) would change?



If an earth tunnel was not pole to pole you couldn't jump through it, because the rock at the centre of the earth rotates slower than rock at the surface, so as you went down you would hit the side. 

You can see this effct in rocket launches, as rockets go up they appear to vear off to one side, because their tangential velocity they had at the ground is different to the tangential velocity of the atmosphere they are flying through.

This change in velocity actually accelerates the rockets, east I believe, which is why rocket launches are done from as close to the equator as possible, where the difference in velocities per unit altitude is greatest, because it helps accelerate them into orbit.


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## Inciatus (Jan 31, 2013)

Fallowfox said:


> If an earth tunnel was not pole to pole you couldn't jump through it, because the rock at the centre of the earth rotates slower than rock at the surface, so as you went down you would hit the side.
> 
> You can see this effct in rocket launches, as rockets go up they appear to vear off to one side, because their tangential velocity they had at the ground is different to the tangential velocity of the atmosphere they are flying through.
> 
> This change in velocity actually accelerates the rockets, east I believe, which is why rocket launches are done from as close to the equator as possible, where the difference in velocities per unit altitude is greatest, because it helps accelerate them into orbit.



Rockets are launched near the equator because in order to get into an orbit is has to achieve a certain velocity tangent to the acceleration of gravity (assuming circular orbit). When launching closer to the equator there is a higher tangential velocity to begin with so the rocket needs to be accelerated less. Most rockets are physically fired east, not because of the atmospheric movement but to take advantage of the tangential velocity. It is for this reason why few satellites orbit retrograde.


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## BRN (Jan 31, 2013)

Inciatus said:


> Rockets are launched near the equator because in order to get into an orbit is has to achieve a certain velocity tangent to the acceleration of gravity (assuming circular orbit). When launching closer to the equator there is a higher tangential velocity to begin with so the rocket needs to be accelerated less. Most rockets are physically fired east, not because of the atmospheric movement but to take advantage of the tangential velocity. It is for this reason why few satellites orbit retrograde.




Kinda sorta. You're both right but you've both muddled things up.

Rockets are launched closer to the equator because of the higher tangential velocity, as you pointed out, but rockets are fired easterly because of the "EÃ¶tvÃ¶s" effect - another function of the earth's spin  that literally decreases the effective weight of an object, which is what Fallowfox was referring to.

EÃ¶tvÃ¶s is like the Coriolis effect, but applied to rising or falling objects, instead of rolling ones. Same principles.


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## Inciatus (Jan 31, 2013)

SIX said:


> rockets are fired easterly because of the "EÃ¶tvÃ¶s" effect - another function of the earth's spin  that literally decreases the effective weight of an object, which is what Fallowfox was referring to.


Okay, thank you. I had never heard of that effect. Though that still doesn't seem to describe what Fallow was saying (but seeing as Fallow agreed it was).


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## Ricky (Jan 31, 2013)

Kazooie said:


> I don't think gravity shockwaves are actually a thing, sorry.
> 
> e: I mean, the Earth's gravitational force would simply suddenly decrease (by exactly half).



Right, but it would decrease suddenly (which in reality, can't happen). You obviously missed the joke but in reality what I said was completely plausible (though I don't know if a black hole moving at the speed of light creates a naked singularity, but one rotating at the speed of light would, and this could possibly destroy the universe as we know it. Or so I read.).

Objects are in a position of space time, which is curved due to gravity, and if the Earth's mass were to just instantaneously half, anything in the field of gravity of that object would feel that force, which took an infinitely small amount of time to move the object. Any motion in an infinitely small amount of time implies an infinitely large force.

Then again, I'm not sure that's considered actual motion. Still, all hell would probably break loose.

Work out the math on *that* ;3


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## Fallowfox (Jan 31, 2013)

The missing mass could be radiated away from the poles at light speed, and cause and effect would remain intact. 

However this rather misses the point of the question.


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## Kazooie (Jan 31, 2013)

Ricky said:


> anything in the field of gravity of that object would feel that force


_What force though?_ This is a hypothetical scenario where the mass is just _gone_. The only thing that Earth's gravitational field suddenly decreasing would achieve is causing its orbiting bodies to fly off into space. I don't understand where this force you claim to exist is coming from.


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## Ricky (Jan 31, 2013)

Kazooie said:


> _What force though?_ This is a hypothetical scenario where the mass is just _gone_. The only thing that Earth's gravitational field suddenly decreasing would achieve is causing its orbiting bodies to fly off into space. I don't understand where this force you claim to exist is coming from.



If an object was moved a distance over time (at a vector and speed, not just from inertia), that implies there was a force.

It takes a force to move an object.

If the spacetime around the object were suddenly warped, you would have a new spacial conformation where the object now resides.

...and this all takes place in an infinitely small amount of time.

The only thing, like I said, is I don't know if this is technically considered "motion."

Still, the instantaneous change in spacetime would obviously cause some weird and potentially cataclysmic effects.

And I don't see the reason this couldn't send a shockwave through the entire universe =P

edit: ** If an object were moved a distance over time (a change of vector and speed; accelerated, whatever)

that is more accurate wording


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## Fallowfox (Jan 31, 2013)

Ricky said:


> If an object was moved a distance over time (at a vector and speed, not just from inertia), that implies there was a force.
> 
> It takes a force to move an object.
> 
> ...



We're not _moving _the mass. 

This is a contrived scenario, afterall.

Imagine it's a computer simulation, and we just changed the mass of earth in the program.


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## Ricky (Jan 31, 2013)

Fallowfox said:


> We're not _moving _the mass.



Distorting the spacetime wouldn't move the mass?

It would change the world line of the object and if you recalculated the position taking this into account would it have moved?

I would like to work out the math, but I'm not that smart 



> This is a contrived scenario, afterall.
> 
> Imagine it's a computer simulation, and we just changed the mass of earth in the program.



I know -- I'm being a dick.

I think SIX outlined it pretty well, as far as any serious answer I read.


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## Kazooie (Jan 31, 2013)

Ricky said:


> I think SIX outlined it pretty well, as far as any serious answer I read.


He stole all the sperg for himself. The jerk.


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## Azure (Jan 31, 2013)

I think if you put a giant hole in the earth that consumed half its mass we are fucked and nobody would be left to debate this silly question. It's sort of like if a tree falls in the forest and nobody is around, does it make a sound?


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## Inciatus (Jan 31, 2013)

Ricky said:


> If an object was moved a distance over time (at a vector and speed, not just from inertia), that implies there was a force.
> 
> It takes a force to move an object.
> 
> ...



I think you might be referring to gravitational waves. Am I correct?


Also I don't think our satellites would fly off. 

Geostationary satellites move at 3070m/s or so. With Earth at half mass, the escape velocity becomes 7875m/s. They aren't going to gain any speed so their speed wouldn't change. Even though the force will be acting at an angle the difference between those two numbers is to large for it to escape. Most of our satellites would go into elliptical orbits.

Now as to the moon. Right now it moves at 1012 m/s. At the distance the moon is from Earth with Earth's mass halved the escape velocity is 1017 m/s. So it is quite possible we could lose the moon. However, the equation I used does not account for the mass of the moon (which at 1/50 the mass of Earth (and I suppose now 1/25) is significant unlike the mass of a satellite) nor does it account for the changing angle of the acceleration of gravity onto the moon. I reckon we would probably still be able to hold onto the moon, though the orbit would be very elliptical.


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## Reviilo Kuro (Jan 31, 2013)

Soo, it's pole to pole? 

This would initialy diruspt the core. Causing it to cool and eventually solidify, disrupting the magnetosphere. Causing the atmopshere to degrade. This would prove fatal, as solar flares would slowly but surely destroy the atmosphere making earth uniinhabitable. 

Eventually over the course of millenia, the earth's rate of descent torwards the sun, would either drag it in or alow it to gradually move further away dependant on whether or not the sun had entered the phase of Red Giant.This could potentially save the earth from total destruction as we could escape the pull. However either the earth is by this point desolate and unhinhabited. 

we woyuld eventually run into the meteor belt and be destroyed anyway, unless the moon had already moved to far away with the increased speed caused by the lack of an atmosphere and mass. The planet will be destroyed by Meteorites.


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## Ricky (Jan 31, 2013)

Inciatus said:


> I think you might be referring to gravitational waves. Am I correct?



Yeah, which would probably be bad if a large amount of mass changed in zero time.

For the rest yeah, I think you're right. As SIX pointed out the mass cancels out and it's really just inertia that moves the object.

With the same velocity, radius and mass of the sun the forces are still equal.

EDIT: oh wait, I thought you meant the Earth.

> Also I don't think our satellites would fly off.

If the mass were changed of the object the satellites are rotating around the orbit would decay.

Thanks for doing the math XD


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## RadioactiveRedFox (Jan 31, 2013)

Reviilo Kuro said:


> Eventually over the course of millenia, the earth's rate of descent torwards the sun, would either drag it in or alow it to gradually move further away dependant on whether or not the sun had entered the phase of Red Giant.This could potentially save the earth from total destruction as we could escape the pull. However either the earth is by this point desolate and unhinhabited.



I think that the earth is already slowly getting further from the sun, but don't quote me on that.



> we woyuld eventually run into the meteor belt and be destroyed anyway, *unless the moon had already moved to far away with the increased speed caused by the lack of an atmosphere and mass.* The planet will be destroyed by Meteorites.




The moon is well beyond earth's atmosphere and thus is unaffected by it.


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## Ricky (Jan 31, 2013)

RadioactiveRedFox said:


> I think that the earth is already slowly getting further from the sun, but don't quote me on that.



I think it depends on the time of year >.>


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## Fallowfox (Jan 31, 2013)

The earth's orbit is an elipse, so it is closest to the sun in January. Over geological time other factors move the earth's orbit slightly, and this is a suspected cause for the initiation and end of ice ages. 

As far as I am aware earth is not drifting away from the sun to an significant or persistant degree.


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## Zaraphayx (Jan 31, 2013)

A 3 page thread about theoretical astrophysics and not a single math in sight.

Edit: Just kidding, there was a math.


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## Inciatus (Jan 31, 2013)

Ricky said:


> If the mass were changed of the object the satellites are rotating around the orbit would decay.
> 
> Thanks for doing the math XD



It certainly wouldn't stay in its current orbit. It would get a new orbit, a very elliptic orbit.


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## Fallowfox (Jan 31, 2013)

Zaraphayx said:


> A 3 page thread about theoretical astrophysics and not a single math in sight.



Six posted the equations he was using I believe. 

I initially drew my conclusion in the OP from Newton's laws of gravitation, but I chose not to add that because I wanted other people's interpretations. 

Essentially 

F=GMm/dd

G d and M are all constant, therefore halving m causes the F, the centripetal force to be halved. 

Centripetal force due to tangential velocity is expressed as F=mVV/r 

the two values for Force need to match to keep the same orbit.

V stays the same, as does r, so the both the gravitational force between earth and sun and the Tangential momentum of earth away from sun decrease by the same factor as mass is subtracted or added within reasonable bounds. 

This means that, without having to check the actual mass of the earth or sun and ignoring the moon's influence, that earth's orbit around the sun would not change, just like the speed of a bag of lead shot and a bag of feathers falling to earth are the same.


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## Ricky (Jan 31, 2013)

Zaraphayx said:


> A 3 page thread about theoretical astrophysics and not a single math in sight.



There was some High School level Physics (sans the calc, which I think was AP when I took it) ;3

I was mostly joking of course, but I'm interested in this stuff and read shit like Brian Greene, Caleb Scharf and all that.

I would love to learn the math but it's beyond me; I only took up to calc and some differential equations and the little else I learned by myself doesn't really apply.

I'm going to learn Linear Algebra very soon because it's just so damn ubiquitous.

Then I can get into stuff like data analysis, signals and maybe even get into Theoretical Physics once I learn a bit more calc.


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## Zaraphayx (Jan 31, 2013)

Eh it would have been more accurate to say that 1-2 people were  giving physics 101 to the rest of the thread and I couldn't think of a  more clever way to bemoan the fact that the thread was filled with twice  twice as much folk physics.



Ricky said:


> There was some High School level Physics (sans the calc, which I think was AP when I took it) ;3
> 
> I was mostly joking of course, but I'm interested in this stuff and read shit like Brian Greene, Caleb Scharf and all that.
> 
> ...



I like mathematical aesthetics which makes me some sort of creepy math pervert, but for some reason physics and I never hit it off.

Took a couple of semesters of it in community college and I never really got into it, different strokes I guess.


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## Ikrit (Jan 31, 2013)

six is so adorkable


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## RadioactiveRedFox (Jan 31, 2013)

Fallowfox said:


> The earth's orbit is an elipse, so it is closest to the sun in January. Over geological time other factors move the earth's orbit slightly, and this is a suspected cause for the initiation and end of ice ages.
> 
> As far as I am aware earth is not drifting away from the sun to an significant or persistant degree.



Ya, I think rate of drift is negligible at best. This thread makes me feel like an idiot, I've forgotten more of this stuff than I though.


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## Inciatus (Jan 31, 2013)

Fallowfox said:


> This means that, without having to check the actual mass of the earth or sun and ignoring the moon's influence, that earth's orbit around the sun would not change, just like the speed of a bag of lead shot and a bag of feathers falling to earth are the same.


I used different equations, mainly the orbital speed equations (though because of the way I wrote the stuff it was a terrible mess to read). I also tried to calculate if the rotation of Earth would change at all, but couldn't, partially because I used so many assumptions I could have made Six = The letter Fish. If it would help I could try to post the equations I was using to be easier to read.

It doesn't matter; because of the huge difference in mass between the sun and earth and the way the equations work. _.__E30 + _.__E24 = _.__E30 when using four significant figures. Earth's mass whether it be E24 or E-32 is pretty much irrelevant so long as it is less than __E26 or so.


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## Golden (Jan 31, 2013)

I'd like to add that if Earth's mass was halved, the magnetic field would be significantly weakened (as the magnetic field is driven by shifting molten rock). Cosmic Rays from the sun will consequently kill the lot of us.


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## Inciatus (Jan 31, 2013)

RaichuOPs said:


> I'd like to add that if Earth's mass was halved, the magnetic field would be significantly weakened (as the magnetic field is driven by shifting molten rock). Cosmic Rays from the sun will consequently kill the lot of us.


That was mentioned back on the first page.

Because of the way the problem was stated it would create roughly a 3200km radius hole through the earth (the calculations are in my post on the first page). This would consume the inner core as well as most of the outer core. We wouldn't have a magnetic field worth mention.


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## M. LeRenard (Jan 31, 2013)

This thread is hilarious.  You know, even if the hole was somehow stabilized, the moment of inertia of the planet would be fucked all to hell and you'd probably end up with some kind of chaotic wobble (if someone wants to do that particular calculation, be my guest) that would play hell with the seasons.  I think in general it's just not a good idea.
And anyway, drilling a hole through the center of the Earth as a gravity train is a dumb idea in the first place.  Everybody knows the quickest route for a gravity train is a hypocycloid.


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## Azure (Jan 31, 2013)

not to mention, where is the ocean going to go if there is a massive hole in the bottom of the sea? not just a silly song anymore :v


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## Demensa (Feb 1, 2013)

Imagine what would happen to the atmosphere...

I assume some would rush in to the center, while some of the outer layers would get flung out... but then again, I'm still doing physics at _high school_ so someone more knowledgeable should correct me.
The wind would be astounding. (Which reminds me of a science fiction plot I once read...)


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