Indian Ocean "Gravity hole" - a visual explanation

[DaveC426913]

TL;DR Summary

A lot of people on Facebook thinking that lower local gravity should equal higher sea levels

https://www.livescience.com/planet-...ield-created-by-the-death-of-an-ancient-ocean

This article has popped up on FB. A lot of people can't get their head around the idea that a localized low gravity area would cause a drop in sea level. Many, many seem to think the sea level would rise in a low gravity area (I guess they think water would ballooon up, like air).

I got fed up with trying to explain how gravity can certainly act laterally (such as standing near a mountain - or near Cavendish's steel balls ), and how we can only treat the Earth as a point source of gravity when it is nominally spherical and far away.

So I drew a diagram. I hope this puts an end to gravity hole doubters.

 

[Hornbein]

Yep, surface gravity should be everywhere the same on a liquid planet. Known to Isaac Newton. He even calculated the shape of the Earth though without the relativistic factor.

If surface gravity is less somewhere then water will flow away until it equalizes.

But doesn't the Moon attract water even though it decreases surface gravity? I'm too lazy to figure it out but suspect it has to do with the center of mass of the earth-moon system being not that far beneath the surface of the earth. So the moon actually increases surface gravity? Dunno.

 

[Orodruin]

If surface gravity is less somewhere then water will flow away until it equalizes.

This is incorrect. In absence of other effects, water will flow until its surface represents a level surface of the gravitational potential. In that case, a fluid parcel at the surface will have no force component tangent to the surface. There is no requirement that the field strength should be the same on the surface.

 

[AlexB23]

TL;DR Summary: A lot of people on Face thimnig that lower local gravity should equal higher sea levels

https://www.livescience.com/planet-...ield-created-by-the-death-of-an-ancient-ocean

This article has popped up on FB. A lot of people can't get their head around the idea that a localized low gravity area would cause a drop in sea level. Many, many seem to think the sea level would rise in a low gravity area (I guess they think water would ballooon up, like air).

I got fed up with trying to explain how gravity can certainly act laterally (such as standing near a mountain - or near Cavendish's steel balls ), and how we can only treat the Earth as a point source of gravity when it is nominally spherical and far away.

So I drew a diagram. I hope this puts an end to gravity hole doubters.

View attachment 354124

Thus makes sense, the water is attracted by gravity, so higher gravity would pull the water away from lower gravity areas. Would this have a compounding effect, as when there is more water in a higher gravity region, then there would be more mass of water as well to attract even more water, or is that impact negligible?

 

[davenn]

Yep, surface gravity should be everywhere the same on a liquid planet.

A totally liquid planet, yes, but the Earth isnt a totally liquid planet
Because of density variations within the crust and mantle there are gravity anomalies right across the planet.
This was in my basic Geology 101

The problem with that article that @DaveC426913 linked to is it doesnt give any into on the gravity field strength variations

Dave

 

[D H]

Yep, surface gravity should be everywhere the same on a liquid planet.

That is not quite correct. Note that surface gravity by definition implicitly includes acceleration due to the fictitious centrifugal force as surface gravity g is measured with respect to an Earth-fixed frame.

What is correct is that surface gravitational potential, including potential due to the fictitious centrifugal force, should be everywhere the same on a liquid planet. This means that surface gravity will not be the same everywhere if the planet is rotating. The equatorial bulge, which is caused by rotation, sees to that. The acceleration due to gravity (including the equatorial bulge) and rotation (fictitious centrifugal acceleration) is not everywhere the same. We can see this on the Earth: gravitational acceleration at sea level is greatest at the poles, weakest at the equator.

 

[D H]

Adding to the above, Saturn's equatorial bulge is obviously visible due to Saturn's extremely fast rotation rate. (The Earth's equatorial bulge is visible, but to a lesser extent). Simplifying, Earth surface gravity at sea level, in order of effect, is

• Higher at the poles than at the equator because the poles are closer to the center of the Earth than is the equator due to the equatorial bulge. This $GM/r^2$ contribution is by far the dominant effect.
• Slightly lower at the poles than at the equator due to the equatorial bulge. This is the $J_2$ effect, where $J_2$ is the Earth's second dynamic form.
• Slightly higher at the poles than at the equator because there is no centrifugal acceleration at the poles while centrifugal acceleration is outward at the equator.

Aside: I'm having technical difficulties regarding my use of LaTeX (MathJax, actually). I ghosted this site quite a while ago. I forgot how to use it. (Markdown with MathJax extensions is so much easier than is BB Code.)