B What would it be like on Earth if it were not a sphere?

[AZFIREBALL]

Since I was very young I have wondered what life would be like if the Earth was a different shape.

For example, what if Earth were two spheres stuck together rather than just a single sphere?Say the Earth consisted of two, same size, spheres connected at what is now our north pole with a contact diameter of 1500 miles. The orbital plane is the same and the great axis is tilted the same from the orbital plane (about 29 degrees). The North pole is now on top of the attached sphere. The South pole remains were it is currently.Has anyone else thought about this scenario? Any ideas?

 

[Bandersnatch]

Depends on what laws of physics you want to turn off, and where. Because if you were to leave them as they are, the two spheres would just get crunched together under their mutual gravity to form one larger sphere.

 

[russ_watters]

For example, what if Earth were two spheres stuck together rather than just a single sphere?

Say the Earth consisted of two, same size, spheres connected at what is now our north pole with a contact diameter of 1500 miles. The orbital plane is the same and the great axis is tilted the same from the orbital plane (about 29 degrees). The North pole is now on top of the attached sphere. The South pole remains were it is currently.

Are we to assume the Earth is somehow structurally capable of this shape?

Has anyone else thought about this scenario?

Probably not, since it is physically impossible.

 

[DrStupid]

For example, what if Earth were two spheres stuck together rather than just a single sphere?

Say the Earth consisted of two, same size, spheres connected at what is now our north pole with a contact diameter of 1500 miles.

Something similar is actually possible if the two bodies are attached at the equator. Such configurations are known for stars (contact binaries) and should also be possible for planets.

 

[Janus]

Something similar is actually possible if the two bodies are attached at the equator. Such configurations are known for stars (contact binaries) and should also be possible for planets.

For fluid objects like stars, the Roche Limit is:

$$ R = 2.433 R \left ( \frac{\rho M}{\rho m} \right )^{\frac{1}{3}}$$

where R is the radius of the primary and $\rho M$ and $\rho m$ are the densities of the primary and secondary respectively. If the two densities are equal, then this puts the Roche limit more than twice the radius of the primary away, and you can't have a contact binary. If you increase the density of the secondary in order to decrease the ratio of the densities, you can drive the Roche limit down to being less than the sum of the two radii and you get a contact binary. This is possible with stars, as you can have hot larger star of low density paired with a smaller less massive star of greater density.

Now while the Earth is considered a "rocky" planet, it is not rigid and behaves more fluid (its shape is subject to outside forces like tidal forces).
Two Earth-sized planets of equal density touching each other would be within Each other's Roche limits. You are not likely to find the larger, less dense planet paired with a smaller High density planet, as planets like the Earth tend to increase in density with size. ( Such a pairing could theoretically happen between a gas giant and rocky world, but that is not what we are talking about here.)

As you reduce the size of the objects involved, the structural strength of the objects begin to overcome gravitational forces, and they can hold together against tidal forces, so you once again can form contact binaries.

 

[DrStupid]

For fluid objects like stars, the Roche Limit is:

$$ R = 2.433 R \left ( \frac{\rho M}{\rho m} \right )^{\frac{1}{3}}$$

This equation is derived for M>>m, for a size of the satellite much smaller than its distance from the central body and under the assumption that the satellite is a rotational ellipsoide. A contact system of two similar bodies doesn't meet this conditions. What makes you sure that the Roche Limit still applies?

 

[rootone]

Earth not an exact sphere.
It is spheroidal, and with a lot of surface features.
While that might not seem to be much different to an exact sphere,
it is enough different that the range of environments and climates varies hugely,
in some places within very short distances.

 

[Vanadium 50]

What makes you sure that the Roche Limit still applies?

Maybe since it's your claim...

Something similar is actually possible if the two bodies are attached at the equator.

...you should show why it's possible?

 

[DaveC426913]

If the bodies are small enough, they don't coalesce.

https://en.wikipedia.org/wiki/Contact_binary_(small_Solar_System_body)
https://www.google.com/search?q=con...q1kKHXGtAUsQ_AUIDigB&biw=1600&bih=796#imgrc=_Someone did a really cool visual analysis of what gravity is like on/near such a body. Wish I'd bookmarked it.

 

[OmCheeto]

If the bodies are small enough, they don't coalesce.

https://en.wikipedia.org/wiki/Contact_binary_(small_Solar_System_body)
https://www.google.com/search?q=con...q1kKHXGtAUsQ_AUIDigB&biw=1600&bih=796#imgrc=_Someone did a really cool visual analysis of what gravity is like on/near such a body. Wish I'd bookmarked it.

I did a rather simple analysis of gravity on Ultima Thule.
The only interesting area is between F & G.

Probably not habitable, being only 34 km from end to end. But fun to think about.

 

[DaveC426913]

The only interesting area is between F & G.

Cool. So starting at G, you'd be on the side of a hill, sloping sharply (feeling like about 45 degrees) down toward F.
As you "walked" (gently bounced) downhill, you'd feel the slope under your feet rapidly becoming vertical - more so than expected, until you'd just drift off in the direction of C, eventually bumping into the larger mass.

It would be interesting to visualize the walk from the stroller's POV. The apparent horizontal would not be where you expect.
Standing at H, it would feel like a 15 degree slope, and it would look like the horizon of the larger mass is directly horizontal to your line of sight (i.e. perpendicular to the direction of "down" for you at H.)

I wonder, if you stood at F, could you push the masses apart...

 

[OmCheeto]

Cool. So starting at G, you'd be on the side of a hill, sloping sharply (feeling like about 45 degrees) down toward F.
As you "walked" (gently bounced) downhill, you'd feel the slope under your feet rapidly becoming vertical - more so than expected, until you'd just drift off in the direction of C, eventually bumping into the larger mass.

It would be interesting to visualize the walk from the stroller's POV. The apparent horizontal would not be where you expect.
Standing at H, it would feel like a 15 degree slope, and it would look like the horizon of the larger mass is directly horizontal to your line of sight (i.e. perpendicular to the direction of "down" for you at H.)

I wonder, if you stood at F, could you push the masses apart...

I think you've got it.
Though Ultima Thule is kind of weird, as the surface gravity is 3600 times less than here on Earth. Probably feels effectively weightless.

Perhaps I'll make another spreadsheet, doing the same thing, by tying a rope to the moon, and pulling it to the Earth's surface.
Might work. Might not.
You never know, till you do the maths.

Hmmm... According to everyone at Quora, the two would coalesce into a sphere.
But I wonder what would happen to the rotational speeds during the process.
Would it be like an ice skater, who brings their arms in while spinning, and speeds up?

Hmmm... Sounds like a lot of maths. Perhaps I'll look at what Janus was talking about in post #5 before I start any of this.

 

[DaveC426913]

Hmmm... According to everyone at Quora, the two would coalesce into a sphere.

I think the Moon would start to break up at about 10,000km altitude (Earth's Roche limit) and become rings for a while.

 

[DrStupid]

Maybe since it's your claim...
[...]
...you should show why it's possible?

I don’t see how my claim proves the Roche Limit under this conditions. However, as that seems to be OK for you let’s start with it:

Two equal bodies with distance of 2.433·R would almost form a contact binary if they would remain spheres with radius R. But they don’t remain spheres due to tidal forces and centrifugal forces in the co-rotating system. Even with the conservative assumption that the mass is mainly concentrated in the centers the resulting deformations are sufficient to bridge the small gap between the original spheres. This is the result for two Earth-sized bodies (shown from the side):

As real or even homogeneous mass distributions would result in even larger deformations and therefore allow for contact binaries with a larger distance the Roche Limit actually supports my claim.

 

[AZFIREBALL]

Research results:
CONTACT BINARY SYSTEMShttps://phys.org/news/2014-12-binary-terrestrial-planets.html

Can binary terrestrial planets exist?

December 3, 2014, California Institute of TechnologyThe possible existence of Earth-like binary planets is being described today at the American Astronomical Society's Division for Planetary Sciences meeting in Tucson, AZ. Two bodies, each of mass similar to Earth, can form a closely orbiting pair under certain conditions present during the formation of planetary systems. 201.02 – Binary Planets Can a bound pair of similar mass terrestrial planets exist? We are interested here in bodies with a mass ratio of ~ 3:1 or less (so Pluto/Charon or Earth/Moon do not qualify) and we do not regard the absence of any such discoveries in the Kepler data set to be significant since the radeal decay and merger of a close binary is prohibitively fast well inside of 1AU. SPH simulations of equal mass “Earths” were carried out to seek an answer to this question, assuming encounters that were only slightly more energetic than parabolic (zero energy). We were interested in whether the collision or near collision of two similar mass bodies would lead to a binary in which the two bodies remain largely intact, effectively a radial capture hypothesis though with the radial distortion being very large. Necessarily, the angular momentum of such an encounter will lead to bodies separated by only a few planetary radii if capture occurs. Consistent with previous work, mostly by Canup, we find that most impacts are disruptive, leading to a dominant mass body surrounded by a disk from which a secondary forms whose mass is small compared to the primary, hence not a binary planet by our adopted definition. However, larger impact parameter “kissing” collisions were found to produce binaries because the dissipation upon first encounter was sufficient to provide a bound orbit that was then rung down by tides to an end state where the planets are only a few planetary radii apart. The long computational times for these simulation make it difficult to fully map the phase space of encounters for which this outcome is likely but the indications are that the probability is not vanishingly small and since planetary encounters are a plausible part of planet formation, we expect binary planets to exist and be a non-negligible fraction of the larger orbital radius exoplanets awaiting discovery. Author(s): Keegan Ryan , Miki Nakajima , David J. Stevenson Institution(s): 1. Caltech, Pasadena, CA.
Read more at: https://phys.org/news/2014-12-binary-terrestrial-planets.html#jCp

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https://phys.org/news/2012-05-capturing-planets.html#nRlv

(Phys.org) -- The discovery of planets around other stars has led to the realization that alien solar systems often have bizarre features - at least they seem bizarre to us because they were so unexpected. For example, many systems have giant planets closer to their star than Mercury is to the Sun, while other have the opposite - giant planets more than ten times farther way from their star than Jupiter is from our Sun. Astronomers think they understand how planets could end up close to the star: they gradually drift in from more customary orbits. But how can planets end up so far away?

Read more at: https://phys.org/news/2012-05-capturing-planets.html#jCp

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https://phys.org/news/2012-04-stars-capture-rogue-planets.html#nRlv

(Phys.org) -- New research suggests that billions of stars in our galaxy have captured rogue planets that once roamed interstellar space. The nomad worlds, which were kicked out of the star systems in which they formed, occasionally find a new home with a different sun. This finding could explain the existence of some planets that orbit surprisingly far from their stars, and even the existence of a double-planet system.

Read more at: https://phys.org/news/2012-04-stars-capture-rogue-planets.html#jCp

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[DrStupid]

Research results:
CONTACT BINARY SYSTEMS

The results are actually not about contact binaries. However, it is interesting that there is at least a possible way for the formation of binary planets.

 

[AZFIREBALL]

Assuming Earth size contact binaries where possible:

What fascinates me is the image (prospective) one would see while traveling on one of the objects toward the interface of the two objects and what possible gravity shifts would be experienced as you approached the junction interface. What strange things would you think one might see; especially if the contact interface area were in an ocean. Would there be a vertical wall of water, perpendicular to the water surface you were traveling on? Would the water form a radius between the two objects that could be navigated? So many images!

 

[DaveC426913]

What fascinates me is the image (prospective) one would see while traveling on one of the objects toward the interface of the two objects and what possible gravity shifts would be experienced as you approached the junction interface. What strange things would you think one might see; especially if the contact interface area were in an ocean. Would there be a vertical wall of water, perpendicular to the water surface you were traveling on? Would the water form a radius between the two objects that could be navigated? So many images!

Review the image in post 10 and my description of it in post 11.

Mostly what happens is that you feel like you are standing on a hillside, no matter where on the body you are (except the poles, it'll feel normally flat there). Near the poles, it'll be a gentle slope getting steeper and steeper as you near the mid latitudes.

As you approachet the waist, the last few metres would feel like a rapdily steepening slope, until you were slipping down a vertical cliff, with another cliff rising opposite you.

All free water would run toward - and pool at - the waist.
It would be kind of cool to swim from G to E. The water's surface in front of you would rise up like a vertical 90 degree wall. But as you swam toward it, you'd always feel the surface is flat where you are - while the wall in front of you flattened out, and the water behind you rose up to a wall.

 

[Nik_2213]

https://en.wikipedia.org/wiki/Rocheworld

Robert Forward & Co. explored a plausible scenario for a 'contact' terrestrial binary in a series of SciFi books. I haven't read the later spin-offs, but the early volumes were fun.
YMMV...

 

[DaveC426913]

Here is what it would look like walking from pole to pole. Thanks to @OmCheeto for providing the template.

I'm not too happy with the water line. The water will always be horizontal, wherever he is in it.
But I think he falls straight down into it from the left, whereas he is able to walk out of the surf on the right.

Bah. Too small to see.

Here it is in all its glory.

It'd be cool to zoom in on just the waist, but I'd need Omcheeto to add a few more vectors.

 

[DrStupid]

What fascinates me is the image (prospective) one would see while traveling on one of the objects toward the interface of the two objects

You would see the other world sit up and then bend down again.

and what possible gravity shifts would be experienced as you approached the junction interface.

In case of my example in #14 gravity has a maximum of 1.3 g on the poles and a minimum of 0.3 g on top of the junction. At the outer points it is 0.7 g.

Would there be a vertical wall of water, perpendicular to the water surface you were traveling on? Would the water form a radius between the two objects that could be navigated?

The water will always be horizontal with respect to the local gravity. In the result oceans on one world as seen from the other will not look like a wall of water but reather like oceans on Earth as seen from space. Just imagine each world as a big tower standing on the other.

The different gravity also affects the atmosphere. On the outer points it will be around twice as high as on the poles and at the junction even four times as high.

 

[OmCheeto]

Here is what it would look like walking from pole to pole. Thanks to @OmCheeto for providing the template.

I'm not too happy with the water line. The water will always be horizontal, wherever he is in it.
But I think he falls straight down into it from the left, whereas he is able to walk out of the surf on the right.

View attachment 237417
Bah. Too small to see.

Here it is in all its glory.

It'd be cool to zoom in on just the waist, but I'd need Omcheeto to add a few more vectors.

Like this?

I made the one arrow red, as it was almost invisible resting on the surface of Thule.

I've only found a couple of other graphics of the surface gravity, and they don't seem to match mine.
This is why I had a bit of a panic the other day, and asked someone to check my math.

This one is purportedly by James Tuttle Keane, posted by Emily Lakdawalla on Twitter. I can't find where James posted it, so I think he shared it with her.

It appears the local slopes don't come even close to mine, maxing out at around 30 degrees, while mine max out at 90 degrees.
I'm guessing he used a thicker neck.

 

[DaveC426913]

Thanks, Om.

Hmph. Not quite as exciting as I'd hoped.

The lake would look saddle-shaped - curving up a little toward the far shore, while simultaneously curving down to your left and right.

Keep in mind, you couldn't swim in this. Gravity is so slight that even on land you'd be bouncing around.

So the water is equally light. Water in low-G tends to get VERY sloshy, with high, slow waves creeping far up the shores, and large depressions forming as well.
It would slosh around like oil in water.

A little like this:


You'd bob up and down very gently and slowly, resulting in you being constantly overwhelmed by slow, easy glob/waves. If you didn't have a scuba tank, you'd surely drown.

 

[stefan r]

...
Hmph. Not quite as exciting as I'd hoped.You'd bob up and down very gently and slowly, resulting in you being constantly overwhelmed by slow, easy glob/waves. If you didn't have a scuba tank, you'd surely drown...

The weather should be dramatic. Normally Earth is radiating into space. The trench has less space to radiate into. The trench is also eclipsed so it may not be much hotter on average. The distance from the arctic to the equator is smaller and all of the heating occurs in a short burst. The atmosphere is higher so a rising column of hot humid air rise much further.

The Coriolis forces move rising air anti-spinward and sinking air spinward. Can we expect most of the hurricanes and biblical flooding on the trailing sphere at the equator and polar vortex on the leading sphere at mid latitudes? .

Any thoughts on tides?

 

[diogenesNY]

Other non-spherical habitations that could host a large population that are fun to imagine and envision include:

A ringworld:

https://www.popularmechanics.com/space/deep-space/a11183/could-we-build-a-ringworld-17166651/
http://news.larryniven.net/concordance/content.asp?page=Ringworld Appendix

and a Dyson Sphere (well, technically a sphere, but one where you live on the inside):

https://en.wikipedia.org/wiki/Dyson_sphere
https://Earth'sky.org/space/what-is-a-dyson-sphere

There is some debate whether these would be physically possible. The engineering would be quite a challenge.

diogenesNY

 

[DrStupid]

Any thoughts on tides?

There can be tides from the sun and maybe from a moon. But in order to keep the system stable they must not be strong enough to slow down the rotation significantly. In that case tidel forces wouldn't be sufficient to increase vulcanic activity directly (in contrast to Io) but maybe for plate tectonics. That leads to the next question: How would plate tectonics looks like on such a planet?

 

[DrStupid]

and a Dyson Sphere (well, technically a sphere, but one where you live on the inside):

Dyson Spheres are solar power plants and not a place to live in or on (at least not for life as we know it).

There is some debate whether these would be physically possible.

That depends on the type. Some types are possible (e.g. Dyson bubbles) others are not (e.g. rigid spheres).

 

[DaveC426913]

The weather should be dramatic.

The problem is that this particular solution can only exist below a certain scale. Small enough to keep the masses spherical.
So, I tried not to cheat by pretending this could be a planet-sized object.

 

[AZFIREBALL]

Do you think the water surface would appear flat or would you see the radius out in front of you; with the water on the far side almost over head or as a vertical wall?

 

[dschlink]

A more likely situation would be if it was rotating rapidly. Gravity at the equator would countered by the spin and the effective gravity could be an order of magnitude lower.

 

[rootone]

Do you think the water surface would appear flat or would you see the radius out in front of you

I think it would appear flat in your immediate locality, but beyond that it could be just about anything,
depending on what topology your planet has if it isn't a sphere.
A donut shaped planet is gravitationaly feasible, even if it is extremely unlikely.
In this case the water in the distance could appear to be at a higher elevation than you are, and the most distant water above your head.

 

[DaveC426913]

Do you think the water surface would appear flat or would you see the radius out in front of you; with the water on the far side almost over head or as a vertical wall?

Thing is, in order have such strong surface curvature you need large gradients (otherwise you wouldn't have two surfaces at different angles so close together), and thus there's got to high gravity in there somewhere.

Which makes it more problematic to have solid structures so tenuous.

You sortta can't have your cake and eat it too.

 

[DrStupid]

A donut shaped planet is gravitationaly feasible, even if it is extremely unlikely.

Is such a donut shaped hydrostatic equilibrium stable? Otherwise it would not only be unlikely but impossible.

 

[gfwhell]

There can be tides from the sun and maybe from a moon. But in order to keep the system stable they must not be strong enough to slow down the rotation significantly. In that case tidel forces wouldn't be sufficient to increase vulcanic activity directly (in contrast to Io) but maybe for plate tectonics. That leads to the next question: How would plate tectonics looks like on such a planet?

It would seem the gravitational effects on our planet from the rest of our solar system and beyond are proving to be irregular.
This is due to our short period of record keeping.
The tidal effects, torture the tectonic plates causing the eruption of volcano’s above and below sea level.
This means that 7/5ths of the worlds volcano’s are underwater. When they erupt they don't seem to effect us very much, other than raising the temperature a degree or two and poison the ocean, killing the coral and sea life, not forgetting the warming of the atmosphere.

 

[DaveC426913]

... 7/5ths of the worlds volcano’s are underwater.

 

[davenn]

It would seem the gravitational effects on our planet from the rest of our solar system and beyond are proving to be irregular.
This is due to our short period of record keeping.
The tidal effects, torture the tectonic plates causing the eruption of volcano’s above and below sea level.
This means that 7/5ths of the worlds volcano’s are underwater. When they erupt they don't seem to effect us very much, other than raising the temperature a degree or two and poison the ocean, killing the coral and sea life, not forgetting the warming of the atmosphere.

I'm seriously trying to figure out how to make sense of that post ?

 

[Vanadium 50]

This means that 7/5ths of the worlds volcano’s are underwater.

And the other negative 2/5ths?

 

[pinball1970]

Review the image in post 10 and my description of it in post 11.

Mostly what happens is that you feel like you are standing on a hillside, no matter where on the body you are (except the poles, it'll feel normally flat there). Near the poles, it'll be a gentle slope getting steeper and steeper as you near the mid latitudes.

As you approachet the waist, the last few metres would feel like a rapdily steepening slope, until you were slipping down a vertical cliff, with another cliff rising opposite you.

All free water would run toward - and pool at - the waist.
It would be kind of cool to swim from G to E. The water's surface in front of you would rise up like a vertical 90 degree wall. But as you swam toward it, you'd always feel the surface is flat where you are - while the wall in front of you flattened out, and the water behind you rose up to a wall.

That is crazy! They should make a film based on a binary planet, the CGI people would have a blast.

 

[AZFIREBALL]

In relationship to gfwhell's post of 8/13/2019 at 7:29 PM
davenn said: "I'm seriously trying to figure out how to make sense of that post ? "
I am having the same problem understand what it is he is trying to say related to the original proposition.
@gfwhell: Care to enlighten us?

 

[Umang Soni]

Something similar is actually possible if the two bodies are attached at the equator. Such configurations are known for stars (contact binaries) and should also be possible for planets.

but then Earth would still be sphere ...please clear your question

 

[Bystander]

https://www.physicsforums.com/threa...s-with-your-what-if-question-comments.975547/

 

[DrStupid]

but then Earth would still be sphere

No, it wouldn't. See in #14 how that reather looks like.
I am currently working on a solution for somewhat realistic mass distributions. But that will take some more time.

...please clear your question

Which question?

 

[DrStupid]

Now my calculation got a step forward. The shape in #14 is the isosurface of the effective potential of two orbiting point masses in their common rest frame. Of course it makes not much sense that the entire mass of the body is concentrated in two centers, but it was easy to calculate. Now I managed to describe a system where only a part of the mass is located in the centers (representing large spherical iron cores) and the rest is homogeneous distributed inside the isosurface. Here is a comparison of the two resulting shapes:

In order to get a stable equilibrium I increased the size of the cores by 500 km (compared to Earth). Stability requires that the surface potential increases with the size. In case of a non rotating sphere this would be the case when the surface density is below 1/3 of the average density. For a fast rotating system there seems to be another limit but the basic principle is the same: the bigger the cores the better.