# 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.

#### 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

Mentor
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?
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

Staff Emeritus
Gold Member
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.

Staff Emeritus
What makes you sure that the Roche Limit still applies?

Something similar is actually possible if the two bodies are attached at the equator.
...you should show why it's possible?

Gold Member

#### OmCheeto

Gold Member
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.

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#### DaveC426913

Gold Member
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 - moreso 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

Gold Member
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 - moreso 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.

Gold Member

#### DrStupid

[...]
...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.

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#### AZFIREBALL

Research results:
CONTACT BINARY SYSTEMS

https://phys.org/news/2014-12-binary-terrestrial-planets.html

Can binary terrestrial planets exist?

December 3, 2014, California Institute of Technology

The 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.

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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?

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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.

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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

Gold Member
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

Gold Member
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.

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