Under General Relativity what is commonly called gravity is a fictitious force or pseudo force and is purely an artifact of being in a non-inertial frame of reference.
While a very useful in most use cases, and accurate for most needs even Newton was bothered that under his model gravity acts Instanously. This superluminal communication makes the math work but is a spherical cow :)
As a direct comparison under Newtonian mechanics, the centrifugal force is a "inertial" or "fictitious" or "pseudo" force. Due to Einstein's equivalence principle, and under General Relativity gravity is also a "inertial" or "fictitious" or "pseudo" force.
To quote John Wheeler. "Mass tells space-time how to curve, and space-time tells mass how to move."
I think we should dump the "fictitious force" and "pseduo force" nonsense and say what we mean: "frame-dependent force", as in this force depends on the observer being in a specific, non-inertial frame of reference. These forces are real, and observable, and their existence distinguishes inertial from non-inertial frames, which is a useful thing to do.
The non-sphericity of the cow applies only at distances comparable to the size of the cow. The corrections would be meaningful for the "Jupiter" and "Venus" results, but negligible otherwise.
Sorry for nitpicking, but a cow to represent Mars should be 10m away, and the length of a typical cow is about 2m (1m~=1yd=3ft). So I expects a 4% correction, because the main part of gravity goes like 1/d^2 and the first correction like 1/d^4 (with some constants that mix theoretical numbers with the details of the shape of the cow).
So if the cow is 5 cows away, you can get something like a get a 4% correction, that perhaps is measurable if you can measure the pull form the cow.
The cow representing Regulus is 4000 cows away, so the correction is less than 1/1000000 and it's safe to take it as a spherical cow.
[Side question: Can LIGO "hear" a nearby cow? It has filters to try to see the chirp of the merge of two black holes, and another filter to only consider the signals that appear in both detectors, so you probably need to train two synchronized dancing cows to fool LIGO. But, do they have enough precision?]
You are absolutely correct. I'd somehow parsed the Mars number as in miles, rather than meters. Some part of my brain was surprised, but didn't pull the fire alarm.
On the LIGO question: Two GPS-synchronized cows, standing near the end-masses, that mooed in the appropriate chirp (correcting amplitude for polarization) would make people nervous enough to do a few calculations and, out of an abundance of caution, put up a fence. I expect the gravitational effect from any mooing (it's a tiny quadrupolar deformation of the cow) to be extremely small.
In practice, even the end-station buildings are large enough to keep cow-moos from happening close-enough to bother the instrument gravitationally. Furthermore, there are no cows at Hanford, and I doubt that there are any near Livingston.
Just to be 100% sure, I don't expect LIGO to detect the sound waves of the moowing cow, or the deformation of the cows while moowing. But can it detect the movement of a cow nearby?
Which, as we know at least since Alan Turings 1952 paper ”The Chemical Basis of Morphogenesis”, might possibly not even exist.
"a system which has spherical symmetry, and whose state is changing because of chemical reactions and diffusion ... cannot result in an organism such as a horse, which is not spherically symmetrical.”
I was going to try to crack a joke about cows being spherically homomorphic, but apparently I'm way too late because spherical cows have quite a history in physics...
Under General Relativity what is commonly called gravity is a fictitious force or pseudo force and is purely an artifact of being in a non-inertial frame of reference.
While a very useful in most use cases, and accurate for most needs even Newton was bothered that under his model gravity acts Instanously. This superluminal communication makes the math work but is a spherical cow :)
As a direct comparison under Newtonian mechanics, the centrifugal force is a "inertial" or "fictitious" or "pseudo" force. Due to Einstein's equivalence principle, and under General Relativity gravity is also a "inertial" or "fictitious" or "pseudo" force.
To quote John Wheeler. "Mass tells space-time how to curve, and space-time tells mass how to move."