A strict proof of "why the Earth is a ball"

[graphking]

TL;DR

Do you laugh when see the title?
I imitate the proof of "why bubbles are ballshpe"(due to the surface tension energy)
to generate a proof and make an essay.

"bubbles are ball" is called isoperimetric problem in serious mathematic. In this topic, many essay were written. Here's my serious essay about "why earth ball", which has been rejected by arxiv and my mentors...... I would want to know if physicists are interest?
I really think that is something worth to proof, but in fact my work is basic imitation of the isoperimetric problem (why bubbles are ball)

 

[jedishrfu]

I would show your paper to your profs to get their feedback on your math.

The common consensus is that through measurement and experiment the Earth is roughly an oblate spheroid with a gravitational acceleration of about $9.8 m/s^2$.

Its also likely that someone has gone through these same calculations before using Classical Mechanics and Calculus to model an oblate spheroid and considering the Earth’s rotational speed and pull of gravity from the Sun, Moon, and planets.

This modeling is valuable info for space agencies such as NASA and the Indian, Eurpean, Russian and Chinese Space Agencies for orbital mechanics.

Sadly, we cant review your work until its been published in a peer reviewed journal. I had to remove the link for that reason.

 

[Orodruin]

This to me sounds more like something I would hand out as an assignment in first year rather than something new that merits publishing.

 

[hutchphd]

Doe your theory explain why smaller accretion objects are not spheres and does it define what "smaller" means?

 

[graphking]

Doe your theory explain why smaller accretion objects are not spheres and does it define what "smaller" means?

that is a new view to me, I only pretty sure it must be sphere when the object is convex, adding small part maybe not convex?

 

[Vanadium 50]

The earth is not a ball. A ball is a toy. The word you are looking for is 'sphere'.

However, the earth is not a sphere either. It is, as has been mentioned, approximately an oblate sphereoid. Since it is not a sphere, any "rigorous proof" that it is a sphere is wrong.

If you have a proof that the earth is kindof-sortof spherical, how can such a mushy statement be rigorous?

In any event, you have not done what you set out to do, so it is unsurprising that it's been rejected by everyone who has seen it.

 

[hutchphd]

that is a new view to me, I only pretty sure it must be sphere when the object is convex, adding small part maybe not convex?

Most asteroids are not spheres. They are potatos. Phobos and Deimos are not spheres. Yet Luna is ~a sphere. Size matters.

 

[graphking]

using Classical Mechanics and Calculus to model an oblate spheroid and considering the Earth’s rotational speed and pull of gravity from the Sun, Moon, and planets.

I have seen some of them, but I can't fully strctly understand the calculate using legendre polynomials.
And as for the begining of all calculation base on small disturbing from sphere, I haven't found the proof of sphere in google, not so sure whether some journal has it

 

[Bandersnatch]

The earth is not a ball. A ball is a toy. The word you are looking for is 'sphere'.

And here I thought there was some stuff below the infinisetimaly thin boundary consisting of a set of points at radius R from the centre. Why, I thought it might even be a closed ball (to the first approximation).

 

[Baluncore]

Is this thread an attempt to debunk all possible Flat Earth hypotheses ?

 

[Orodruin]

Most asteroids are not spheres. They are potatos. Phobos and Deimos are not spheres. Yet Luna is ~a sphere. Size matters.

I am not certain OP understands the gravity of the situation …

 

[Orodruin]

that is a new view to me, I only pretty sure it must be sphere when the object is convex, adding small part maybe not convex?

The Earth is provably not a sphere (as has already been pointed out, it is an oblate spheroid to good approximation).

 

[Bystander]

Really?

 

[sophiecentaur]

Most asteroids are not spheres. They are potatos. Phobos and Deimos are not spheres. Yet Luna is ~a sphere. Size matters.

And also, the asteroid belt would probably have been a planet (another oblate spheroid) in an orbit between Mars and Jupiter if it hadn't been for the disturbance of nearby Jupiter's enormous mass. Instead of forming a planet, they never got together and formed billions of rocks.

 

[Vanadium 50]

I am not certain OP understands the gravity of the situation

Down with gravity! Up with levity!

 

[graphking]

I am not certain OP understands the gravity of the situation …

what is the situation here? if it's not rotating, the gravity formula is modified?

 

[Ibix]

what is the situation here? if it's not rotating, the gravity formula is modified?

What? No.

Small bodies do not have strong enough gravity to overcome the structural strength of the rock they're made of. Large bodies (about the size if Ceres) simply collapse under their own weight into a nearly spherical configuration, with only small departures from sphericity such as mountain ranges and oceans. If such large objects spin they gain an equatorial bulge from the centrifugal force, as well.

 

[sophiecentaur]

simply collapse under their own weight into a nearly spherical configuration,

Also the temperature of the eqarly solar system would have been a lot higher so many of the early clumps of matter would have been hot enough to melt together into spheroids. Spinning could have limited their final size before cooling. But it's all very complicated and largish objects can melt due to tidal friction forces from nearby large objects. Io (a jovian moon) has active vulcanism due to this tidal effect.
There is a vast range of situations for astronomical objects that produce a whole range of different final results.

 

[Baluncore]

Here's my serious essay about "why earth ball", which has been rejected by arxiv and my mentors

In your draft paper, you refer to the planet "earth".
Yet "Earth" is a proper noun, so it should be capitalised.
Soil or "earth", is the material in which plants grow.

Why earth is ball shape? That is an old question. To find out why earth is ball,
there’s two perspective:

Your failure to capitalise the proper noun "Earth", may explain why the paper was quickly rejected.

 

[graphking]

Thank you all for more information from physics! I understand the real situation better.

What I can provide is an interesting fact that gravity maybe fail to exist in a 2-dimension world, because it cannot be the form of r^-2, and due to bertrand theorem, if you want a force can make 2 point rotate around each other periodically (when their distance over all time are bounded, that is just the situation of elliptic moving, not
Hyperbolic/parabola), the force must be r^-2 or r^1(spring force f=kx).

 

[Orodruin]

Thank you all for more information from physics! I understand the real situation better.

What I can provide is an interesting fact that gravity maybe fail to exist in a 2-dimension world, because it cannot be the form of r^-2, and due to bertrand theorem, if you want a force can make 2 point rotate around each other periodically (when their distance over all time are bounded, that is just the situation of elliptic moving, not
Hyperbolic/parabola), the force must be r^-2 or r^1(spring force f=kx).

This is a gross and faulty representation of what Bertrand’s theorem actually says and its implications.

 

[graphking]

This is a gross and faulty representation of what Bertrand’s theorem actually says and its implications.

I know my expression is bad, I should google it, but what do you say about bertrand thm?

 

[berkeman]

What I can provide is an interesting fact that gravity maybe fail to exist in a 2-dimension world, because it cannot be the form of r^-2

El thread-o es cerrado por un momento...

 

[berkeman]

Since this thread is heading into personal speculation territory, it will remain closed. Thanks to everybody who tried to help the OP.