# Can a planet with variable gravity have constant atmospheric pressure over the surface

This earth has roughly three to five times the radius and ten to twelve times the surface area of our earth

And it lies in the center of toroidal planet (their equatorial planes line up perfectly). This would cause a low gravity upto 0.6 G at equators and high gravity of upto 2.4 G at poles

This would also make oceans “deeper” near equator and earth’s shape more “squished”at poles.

So, at same height relative to sea level, would the atmospheric pressure be the same?

Also, don’t worry about insanity of a planet system like this being formed naturally.

Edit: Though atmospheric pressure changes places to places on account of various factor, what I’m concerned with whether it’ll too high or low to make humans rather “uncomfortable”

• Three times of what? What is a teroidal planet?
– L.Dutch
Commented Jun 8, 2022 at 16:57
• @L.Dutch /What is a teroidal planet?/ I think there is a round something suspended in the center of a larger hollow something, so perhaps the proverbial "teroid in the punchbowl?" Commented Jun 8, 2022 at 17:04
• But I am curious if the large planet in question and the substantially larger planet surrounding it share their atmospheres. Commented Jun 8, 2022 at 17:04
• Do you mean toroidol planet? Like a literal discworld? Commented Jun 8, 2022 at 17:16
• "This earth has roughly three to five times the radius and ten to twelve times the surface area of our earth": Those numbers don't go together. If it has 3 to 5 times the radius, then it has 9 to 25 times the surface area. If it has 10 to 12 times the surface area, then it has 3.16 to 3.46 times the radius. Commented Jun 9, 2022 at 2:10

Correct answer is yes, especially in the form of:

• So, at same height relative to sea level, would the atmospheric pressure be the same?

As there is no difference between isobar surface formed by liquid or gas, it will be the same surface.

One of the reasons for strict yes is that because if not, then we will have flow of mass of liquid or gas, as result of what pressure is(kinetic movement of molecules in essence) and it allows us to have perpetuum mobile or break second thermodynamic law, or conservation of energy or mass - which obiviously won't happen by magic of donout shaping planet size amounts of mass - magic is not strong enough in this one.

It is not an answer to q, or it is a half baked answer, because the actual shape of that equipotencial surface should be part of such answer, maybe, but I'm not prepared to answer that part, and this answer is more to counterweigth JBH present answer. Sure there are fluctuations of pressure on earth, for a number of reasons (not that many reasons btw), but pressure deviations are just that deviation, and it seems those deviations are not the subject of the q, at least not before first order of the problems is shown/solved.

PS I can't comment cuz some funky changes to wb javascrips, so it is - answer comment.

## PPS

There is such work The exterior gravitational potential of toroids, unfortunatly no nice pictures for us to easy understand things, except fig2. Probably okay work, but for pictures for the absence of general view picture it 2 points out of 10. But formulas there, so potencially gourging one to plug in some plot producing thing is here.

This work is better, to some degree, fig8 in it, Gravitational potential of a homogeneous circular torus: new approach

Yes-but-no. The no: obviously a real planet, whether surface gravity is uniform or wildly variable, will not have exactly equal surface pressure everywhere, unless it doesn't have any atmosphere so the pressure is just zero everywhere. Wind, after all, exists, as do heating differentials and sound waves.

But, that is clearly ignoring the spirit of the question. Averaging over the variations due to weather, Earth has approximately constant sea level pressure everywhere on the surface that is at sea level--where the theoretical sea level in places far from the sea is the gravitational equipotential surface that water would follow. And the same goes for all other equipotential surfaces

The fact that Earth's gravity is very close to uniform means that the spacing of equipotential surfaces is also roughly uniform, and the pressure lapse rate is roughly uniform, which is nice because it means we can use barometers as altimeters. This will not be true of your world of highly variables surface gravity--different equipotential surfaces will not be geometrically similar, or have constant spacing at all points, and the atmosphere as a whole will be deeper in some place and shallow in others. But if you choose a specific equipotential surface--like the planet's sea level--as a place to measure "surface air pressure", it will be approximately constant (modulo weather) across that entire surface. When it isn't, you get wind.

I can't decide to down vote or close, so I'll post an answer instead

No

Earth doesn't have a constant air pressure over its surface, so why would your toroidal planet?

Air pressure varies for an insane number of reasons. Your planet's shape would simply make that worse.

Atmospheric pressure dependency

Atmospheric pressure depends on

• Temperature
• Altitude
• Moisture or water vapor in air
• Gravity

At different points on the planet, the values of above factors vary, therefore atmospheric pressure will also vary.

Oceans

If all the oceans are connected, their level will be somewhat different from global level depending on tide or specific gravity (which depends on salinity). But if some seas or lakes are disconnected, their level can be very different from global level. So atmospheric pressure will be different at different points in oceans.

• @AlexP I edited the answer. Thanks Commented Jun 9, 2022 at 14:55