Thought Experiment: Earth Becomes Incredibly Massive

[katiefa]

I'm not sure if I'm posting in the right forum, or if you'll indulge a little mind experiment likely completely outside the possibilities of physics.

Say something on Earth suddenly became incredibly massive, going in seconds from the density of a human body to a density of a planetary body while remaining the size of a human body.

How would such a thing behave? Would it be drawn into orbit around the earth? Would it turn into a black hole or some theoretical phenomenon?

Obviously, this is just for fun and there is no right answer. I am curious if there's a general consensus, though.

Thanks for indulging me!

 

[HallsofIvy]

If it were on earth, as you say, no it would not go into orbit. It would be attracted toward the center of the earth, pressing down into the Earth with the distance depending on the exact mass and density of the soil at that point on earth.

No, it would not "turn into a black hole". "Panetary density" is much too low for that.

 

[LURCH]

I'm pretty sure what you're thinking of is mass, not density. If an object the size of the human body were to suddenly become as massive as a planet, its density would greatly increase (more mass in the same amount of space). Conversely, if the object's density were to increase to "planetary density," the object would then weigh as much as a man-size rock.

So, assuming that the object becomes as massive as a planet, and assuming that that planet is Earth or earth-like:

An object that dense would sink right through the loose topsoil of Earth's crust, and also through the gooey rock of the mantle. This means that the object would immediately begin falling toward the Earth's core. But, because the Earth and the other object are of equal mass, the Earth would also "fall" toward the object. In fact, the planet's center of gravity would move the same distance in the same amount of time as the new object. This will be cataclysmic for anyone inhabiting the planet.

 

[KnowPhysics]

i agree with lurch if the object is already moving, but if the object is at rest it may not penetrate the Earth as well as it may not be traveling with earth, it will be left in space when Earth moves away. because the object of that mass need huge force to start moving. The gravity may not be sufficient for that.

 

[TurtleMeister]

I doubt that the density of the soil near the surface of the Earth would offer much resistance to a man sized object of the same mass as the Earth (even from a stand still). It would travel a maximum of 64 feet into the ground during the first second. It would indeed be a cataclysmic event.

 

[KnowPhysics]

Moon is 1/80 Earth's mass and the distance is about 360000 km and also the moon has surface gravity of 1.62 m/s2. still Earth is unable to attract the moon close. i made above statement by keeping this in mind. i don't know the maximum mass the gravity can disturb its state from rest.

 

[TheSwager]

i agree with lurch if the object is already moving, but if the object is at rest it may not penetrate the Earth as well as it may not be traveling with earth, it will be left in space when Earth moves away. because the object of that mass need huge force to start moving. The gravity may not be sufficient for that.

the object would have its own gravity, and if its mass was the same as Earth using Newtonian gravity it would have the same gravity as Earth and the force between them would be twice what it would have been with just Earth (and some arbitrarily small object). the two objects would accelerate to the center of mass(remember that when excluding air friction all objects accelerate at the same rate because
F(from gravity)=m*g and Fnet=ma so a=g) and the soil at the surface of Earth would not stop something with that much mass. it would be very destructive

Moon is 1/80 Earth's mass and the distance is about 360000 km and also the moon has surface gravity of 1.62 m/s2. still Earth is unable to attract the moon close. i made above statement by keeping this in mind. i don't know the maximum mass the gravity can disturb its state from rest.

the moon is in a rotational motion around the earth. if its linear velocity tangent to its orbit were zero and Earth was at rest they would attract each other and the moon would collide with earth. in fact the moon is accelerating towards the Earth it just also has some velocity so the falling just makes it orbit

 

[KnowPhysics]

Thanks for correcting me. i completely forgot Newtonian gravity when i am thinking the object with that mass, i am sorry for that. In second point i was trying to explain that Earth was unable disturb the "Orbital Motion" of the moon but i do agree "if the moon linear velocity tangent to its orbit were zero and Earth was at rest they would attract each other".

 

[M Grandin]

Interesting hypothetical question. First I thought of the "planetstone" making a tunnel through earth, passing Earth center and continuing up opposite side almost up to surface there. And continue (like a pendelum) oscillate passing Earth center at decreasing amplitude.
Of course Earth at the same time is oscillating correspondingly around common mass center.
If you look at it "theoretically".

But in "practice" that may not occur, because of the extreme attraction gravity from "planetstone" in its vicinity. For instance a kilogram (a litre of water) at a distance of 1 meter from the "planetsatone" is attracted by a force 4 x 10 exp 13 kp (corresponding to the weight of a several kilometer cube of water), and maybe everything up to a distance
of some kilometers rather immediately will be attracted to "planetstone" and becoming some fuzzy melting ball - making the "planetboll" not very small any longer and not simply piercing
the Earth but more resembling a giant meteor sinking into earth. Maybe it results in a fuzzy
pulsating oscillating mix of heated and melting matter.

 

[LURCH]

It should also be mentioned that an object on the surface of the Earth (unless it is at the polls) will have a rotational velocity around the Earth's center. The object falls toward the center, it continues to progress along this lateral path, slightly missing the exact center of the planet. So, the object falls into a highly elliptical orbit around Earth's center of gravity, and the Earth goes into a highly elliptical orbit around the object (both orbiting around a common center of gravity, as has been mentioned).

However, M Grandon has an excellent point about the newly massive object accreting material as it falls. Not only could this slow the objects progress through the dancer regions near Earth's core, but it would also go a long ways towards following a planet.

A very bad day, indeed, my fellow terrestrials!