The relevant reference surface would be a sphere. Relative to a sphere, the Mississippi flows uphill towards the Equator.
Fascinating! This smart ass learned something today.
Thank you all very much.
Is there any astronomical object that is not rotating? I’d venture to say that not only isn’t there one, there cannot be one (conservation of momentum, rotational inertia, etc.)
Using some notes I made when I last did some calculations, the source of the Mississippi is 450 meters above sea level (with sea level defined as the equipotential ellipsoid) at about 42 degrees latitude, while the mouth of the river is at sea level at about 30 degrees latitude. So the average slope relative to the ellipsoid is about 0.002% (really small - resulting in an average ). If you calculate the gravitational force for a non-rotating ellipsoidal earth, you get an effective slope of about 0.17% in the northward direction. However, the average centrifugal force (along the surface of the Earth) is almost exactly the same amount in the southward direction. So the flow of the Mississippi is driven by three effects (overall shape of the Earth, centrifugal force, and local shape of the terrain) with the first two effects being much larger than the third - but with the first two effects cancelling each other out (not by coincidence).
So it is not correct to say that the southerly flow of the Mississippi is due to the centrifugal force of the rotating Earth, is it? Your last three words point out that the north-facing slope (and south-facing in the Southern Hemisphere) is almost exactly due to the centrifugal force of the Earth’s rotation, without which no equatorial bulge, leaving local topography to rule.
I’m not sure how it could not be correct. Some force is acting on the water in the river, causing it to flow from Minnesota to Louisiana. That force cannot be gravity, because the gravitational force on the water is pointing in the other direction. What else, besides centrifugal force, would it be?
The original singularity? That which erupted into the big bang? As a single point, “rotation” would be meaningless. However, if you mean an objects larger than a baseball, I’d guess at any given time, somewhere in the universe there’s an object not rotating. Perhaps an object that has never rotated does not exist.
When you put it that starkly, okay - there is no other appreciable force acting on the water. It just seems so counter-intuitive.
There is a downslope measured relative to sea level, which means there is a component of gravity pulling the water in the river southward.
Sea level isn’t defined by gravity alone, but includes the influence of the centrifugal force.
I was bored …
Considering only gravity, I have New Orleans at 5,400 m about sea level, St Louis at 2,400 m and Minneapolis/St Paul at sea level. However, the Earth as a whole is liquid enough that she would try become spherical herself, crumpling crust at the equator and splitting open at the poles letting mantel material gush out into deep ocean water … woot …
Let’s cut the Gordian knot with respect to the Mississippi or any other river on the planet “flowing uphill”.
Forget the earth being an oblate spheroid, forget sea level.
Let’s imagine that we have a long water level … a flexible tube filled with water with a vial at each end which allows you to see the meniscus of the water at each end. By long , I mean as long as it needs to be …4000 miles long if necessary .
Let’s imagine that we take this water level and attach it to two poles stuck into the river bed , one nearer the source and one nearer the mouth. We measure the height of the meniscus above the river surface for each vial. Let us call the height nearer the source hS and the height nearer the mouth hM.
In order for the river to be flowing uphill, then that would mean that there are at least two points along the river at which hS > hM.
In order to exclude any freak local turbulence let us assume that the minimum distance between any two readings would be , arbitrarily, one mile.
I do not believe for one microsecond that any such two points could be found, and would be prepared to bet the farm on the outcome.
If we’re forgetting sea level, then your water level won’t work. Both exist for the exact same reasons. As a thought experiment, put a pie pan full of water on a potter’s wheel. If you spin the wheel fast enough, all the water will be flung out of the pan, in defiance of the Law of Gravity. But there it is, water flowing uphill.
When you take the deed to your farm down to the escrow office, make sure you put “love and affection” in the blank for selling price, gambling is illegal where you live …
How so? The water level*** is*** the datum … what the sea level might be is irrelevant… we are measuring the "slope " of the water … we know that the water in the water level is level at both ends … the contention to be affirmed or refuted is that at some point (or rather between two given points) the river flows uphill … the only conceivable way to measure this accurately is with a water level, as I described.
The water level is being affected by centrifugal force in exactly the same way that the river is.
I remain sceptical.
If all this centrifugal force has that much effect, then it follows that a given mass at the equator is going to weigh measurably more at the North or South Pole.
As far as I know, this is not the case.
Although I confess I haven’t done the experiment myself.
It’s a small amount, but yes, a given mass will indeed weigh more at the poles than at the equator.
Eh- I’ll have to concede defeat - rotation of a planet isn’t affected by friction to any meaningful extent. Curiously enough, I already knew that was true for gas giants - but didn’t extend it to terrestrials.
Gas giants do contract, though, which causes them to speed up- everything else being equal.
Here’s what NASA’s poetry department has to say about that … although it doesn’t rhyme very well …
A given mass weighs 0.5% more at the poles. 60% of this change is due to centrifugal force, the rest is due to being closer to Earth’s center of gravity. But since this is due to the Earth’s flattened shape, and that shape is due to the rotation, I suppose a case could be made for this too to be an effect of the centrifugal force.