Is what different, exactly? A magical car that goes faster than light? Yes, that’s very, very different from Euclid positing perfectly straight lines.
Sure, that’s an interesting advanced question from somebody who knows some physics. But that wasn’t the OP. Your interesting question had to be dragged kicking and screaming out of some magical gibberish.
Another (very slightly) interesting thing the question raises: what is the observational threshhold for mass in the experiment of dropping two weights from the tower of Pisa? (56.7 meters.)
Suppose you or I went up there, and dropped two weights: one is 40 kg, and the other is 80 kg.
Now, theoretically, per Newton’s laws, the latter falls a tiny bit faster, because of its own gravitational attraction. But nobody is going to observe that with naked eyes and a stopwatch.
How much of a mass is required for the difference to amount to, say, 1/100 of a second?
(I can almost work the math, but, doggone it, not quite.)
You’re right, I’m not an expert in physics, and that’s the whole point of this thread.
My questions were answered with real world physics quite early on. Then I modified the fantasy situation to focus on a very specific part of it - what if the marble was allowed to hit the earth.
If you cannot suspend belief and allow yourself to think outside the box a little, then I thank you for your contributions, but perhaps it’s best if you move along to a different thread.
However if you think my scenario is too outlandish to discuss, then I am open to your suggestions on how to scale down the example so that the same question can be answered without adapting the laws of physics.
The scenario is impossible…but it is not meaningless. I don’t have any problem at all coping with the magical hypothetical. It’s fun!
(It makes me think of “Fairy Chess,” chess with new pieces or new rules. Let’s make a rule that the Knights can only move forward, never backward again. When they get to the top of the board, they can never move again. Whee! Sure, it’s a totally different game now, but it is still a completely playable game.)
Anyway, I agree with TokyoBaker’s model of dropping a bowling ball into a swimming pool full of ping pong balls. SPPPB.
(Also, a SPPPB would be fun to mess around in! Or would I just sink immediately to the bottom? If I cleared a space in front of my mouth with my hands, could I breathe, or would the PPB block air from getting to the bottom of the pool?)
(What if the PPB had the same density as water? Water-filled PPB. How much like water would the overall behavior be?)
Just asking the questions is fun!
The premises in the OP seem better suited to GQ. Thread relocated from IMHO.
They would both fall at exactly the same rate. (ignoring air friction)
However, the earth itself would very likely experience gravitational acceleration towards the super massive marble. So from your perspective, standing on the earth, it might seem like suddenly the gravity of the earth increased, since the earth would actually be accelerating upwards towards the marble. This is all hypothetical and assuming that you personally were somehow shielded from the gravitational effects of this marble.
Yes, because the marble would have such a tremendous density, it would penetrate right through the ground until it reached the earth’s core.
As to whether it would cause catastrophic damage, that would depend on exactly how massive it was. If we are talking about anything anywhere near the same mass as the earth then it would be like a nuclear explosion. But if the marble only had a mass of, say, a couple hundred kilotons, then the damage would not be that catastrophic.
That would likely depend how high you dropped it from. The answer is probably no, but it could be hypothetically possible if you dropped it from a sufficient height and the mass of the marble was comparable to the mass of the entire earth. If you dropped it from a height of 1000 feet, the marble might only be able to shoot out up to a maximum height of 600 feet on the other side before falling back down into the earth again.
Well since the marble itself is already on earth, presumably it’s already in orbit with the earth around the sun, so no, the earth would still maintain its orbit and that would not change.
OK, you do the math and we’ll split the Nobel prize. 
All the serious physicists will have already fled the thread in horror, but assuming Newtonian theory of gravity, no.
With the magic marble, which accepts the gravitational attraction from another object but doesn’t product an attraction itself, it will start at a resting speed of zero when you let go. It then starts to fall toward the center of the Earth at a rate which normally would be calculated from F = G*((m1*m2)/r^2) where F is the force of attraction, G is the constant for gravity on Earth, m1 = mass of the magic marble, m2 = mass of the Earth and r = the distance between the centers of each mass.
You can find the equations and such on the net so I’m not going to do all the work for you, but you can see that the force will become increasing large the closer they are and then become increasingly weaker as it does out.
The gravitational force of attraction will pull the magic marble toward the center of the Earth at all times, just as a pendulum is pulled down. However, because of the speed of the magic marble or pendulum, it will go through the center and out.
Just like adding additional weights to a pendulum will not make it go over the top, the magic marble will never negate the effect.
It would go further away, but would eventually stop. Gravity doesn’t have limits to the distance.
Ummm. We were talking about the effect of friction on the magic marble and if if that friction would slow it down or not. Whatever magic is strong enough to compress the mass of two Earths into a marble is strong enough that a little heat isn’t going to to hurt it.
Alternatively, if we thing about this logically: purple unicorns.
The massive amount of “friction” may not hurt the marble much. (After all, we really don’t understand its properties.) It is going to hurt the Earth! The energy produced is incredible. There will essentially be no Earth as we know it to speak of after a while.
Reality is not the purpose of the OP. They were interested in the behavior of the magic marble.
It’s TokyoBayer.
You wouldn’t sink immediately if you were horizontal because your density isn’t that great.
If you jumped into it, you would sink but friction would slow you down.
You would still be able to breath because the balls don’t block all the air.
I’ll let someone else tackle the PPBs filled with water.
Perhaps this tale told in the dark corners of Physics Department broom closets will help the OP understand …
Let’s imagine a hole all the way through the Earth … and let’s neglect air resistance … 200 miles up we’re holding a marble above the hole AND we have another marble in perfect orbit around the Earth at 200 miles altitude … at the instant the orbiting marble passes the held marble, we release the held marble … this marble starts to accelerate and accelerate until it reaches the center of the Earth … whence it begins to decelerate … and slows slows slows until it exits the hole and reaches up to that 200 mile altitude again …
That marble stops rising at exactly the same instant the orbiting marble passes by …
Anyway … my speculation is that the 2EarthMass marble would initially just poke a small hole in the crust and continue it’s centerward journey … however the shock waves radiating from this teeny tiny hole would subsume the crust material into the frothy mantle … particularly along fault lines the mantle would then “boil” out and cover the surface of Earth in a massive lava flow filling in all the ocean basins …
As the 2EarthMass marble exits the original Earth … quite a bit of original mass would be ejected … what happens to this ejecta depends entire on it’s direction of travel in relation to the Sun … perhaps forming an new planet …
We have a theory about what happens if a 1/2EarthMass planetoid smacks the Earth at a much higher velocity … this would form the Moon …
I was pretty sure Randall has covered almost this exact scenario, but having searched xkcd it seems that if he has, it’s only in the book. I’ll try to remember to look it up when I get home.
You may be thinking of the “What if you touched a bullet made of neutronium?” article in the book. That’s the closest one I can remember.
ETA: Or “What if I fired that neutronium bullet from a gun?” That was in there too.
ETA2: I guess I mentioned this in a previous thread.
It might take a few passes back and forth through the core for that to happen. I imagine there wouldn’t be very much friction relative the intense mass of the marble. It would essentially pass right through the earth like a metal ball bearing going through Jell-O.
(This is assuming the marble has a mass somewhere around half that of the entire earth or more)
I will also add that I just did a calculation and condensing the entire mass of the earth into the size of a marble comes dangerously close to collapsing into a black hole. (compressing it down to a diameter of 18mm it would collapse)
Ah, there is no earth like mass inside the marble - that would be irresponsible. The McGuffin is just that the marble weighs similar to several earths… maybe it’s packed with an Osmiumesque super dense metal…
That just hurts…
But seriously, they should be busy working anyway… perhaps on marble theory!
Don’t be silly, they’re white!
Something the size of a marble with the weight of several Earths is bordering on/going to become a black hole regardless of original composition.
You need to pick an approach here. If it’s a McGuffin with whatever properties you like it to have, such as “doesn’t have mass, just weight”, fine, but that isn’t compatible with “maybe it’s packed with an Osmiumesque super dense metal”.
Yup, I looked it up and it was the latter I was thinking of. Randall calculates that such a bullet would weight about as much as the Empire State Building, and even if you just dropped it, it would speed through the Earth’s crust and only stop at the core. It’s safe to say a bullet with a mass equivalent to the entire planet would do the same, though the difference in mass between the two cases is so great there would probably be other effects too.
I’d suggest submitting it as a question to Randall but he may not want to look at it again given it’s pretty similar.
I donno. At the surface of Earth’s crust, both coming and going, there isn’t going to be much relative speed. The magic marble will only reach extreme speeds well within the crust, then into the magma and then into the core, all of which can handle a lot of temperature and pressure.
But in our case, the magic marble is released from 1,000 ft. Completely different story.
If we go with the just sort of approachable question of a marble the mass of Everest that somehow does not explode back into ordinary matter, the answer is as Randall Munro says.
The Earth is hardly any sort of really solid object. Across the various sorts of things you will find in the universe it is more like marshmallow. But the fate of the Earth and the marble are reasonably easy. The marble will still pass through the rock almost as if it wasn’t there. But there won’t be a huge flash or explosion. The marble will accelerate at exactly the same rate as any other mass, it just doesn’t have any appreciable drag. With such a tiny cross section the entry hole into the Earth is going to kick up a lot of rock, but that is about it. The marble will start to see appreciable drag in the rock, magma and core, so it will impart the potential energy it has to the material it passes through, and won’t really pick up a huge amount of speed. So it won’t exit the other side of the Earth, but will slowly oscillate back and forth a few times and eventually settle in the middle of the core. The total energy it imparts to the Earth is tiny compared to the energy in there already.
If we consider Everest to be about 4000m above the main plain, and roughly conical with base of about 4000, it has a volume of a bit under 2x10[sup]10[/sup]m[[sup]3[/sup]. Its density isn’t huge, about 2.5-2.7. Call it 3. So Everest weighs about 6x10[sup]10[/sup]kg. Distance to the centre of the Earth is 6371km. So,
energy = mgh = 6x10[sup]10[/sup] * 6.4 *10[sup]6[/sup] * 9.8 = about 4 * 10[sup]18[/sup]J
Which is about the same as a 1000 megaton bomb. The thing is, as big and nasty as a bomb that size might be, we are dissipating that energy over a large distance and time inside the Earth.
Energy production from radioactive decay inside the Earth is estimated to be 5 * 10[sup]13[/sup]W.
So our marble is similar to 10[sup]5[/sup] seconds of intrinsic internal energy production. Or about one day’s production. Solar energy hitting the Earth is 1.7 * 10[sup]17[/sup]W. So our marble is similar to two seconds of solar energy hitting the Earth.
The only bit of physics we have to suspend for this question is the lack of any useful binding mechanism to hold the marble together.
The original question was however not of this ilk. It could have been phrased as “what if I teleport an Earth mass black hole to a location 1000 feet above the Earth’s surface?” As described, it would not be a matter of the marble dropping anywhere. The Earth would oblige by tearing itself apart and settling onto the surface of the marble with a flash of energy that would sterilise a good section of the nearby galaxy.