Next question, what is the smallest object whose gravitational field could reliably be measured by the accelerometer in your phone? We know that it can measure the field of the Earth at more or less sea level, how much less heavy/further away could something get for your phone to feel it?
my attempt:
diameter of earth = 12742 km
sea level = distance from earth = 12742/2
weight of empire state building = 331000000 kg
resolution of BMA280 in the iPhone 6: 1/4096 g
mass of earth = 5.972e+24 kg
gravity of earth = 1 g
km to m = 1000x
(12742/2. * sqrt(331000000 / (5.972e+24 / 4096.))) * 1000
= 3 meters
So your phone should be able to register 1 bit of resolution when the empire state building is 3 meters away or less, otherwise it would be too far away to detect. Of course the empire state building would need to be compressed into a single point but that's a minor practical concern.
That is an amazing effect, which I'd never considered, before seeing it on HN some months ago. It's a nontrivial contribution to sea level rise after ice sheets melt.
I wondered whether "17 miles" is a good estimate for how far I am from a cow, and now I'm trying to do a sort of Fermi problem in my head and realizing I'm out of practice for bad job interviews.
Actually we are in free fall relative to these astronomical bodies. Meaning that the Earth and you are both pulled together and so in your local reference frame it is not detectable.
The locally detectable force is tidal. Which follows a cube law.
It turns out that every cow on Earth creates larger tidal forces on you than any star except the Sun. :-)
Since they're not really islands, more like a heap of suspended particles in the upper layer of water, they should have the same density as the water. So they should have the same gravitational effect as water.
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...
I'm a physics teacher, and we just did Universal Gravitation last week. I whimsically explained it as "the longing of everything for everything". (They liked it, but devolved into a giggle fest about being attracted to each other.)
Other easily romantic notions in physics:
* we are all born of star stuff
* every breath we take has elements of the same breath as every human who ever lived (excluding some currently living ones, due to diffusion rates, but eventually...)
* (The current grav force between my partner and me is 1.9159965e-15 N)
> every breath we take has elements of the same breath as every human who ever lived (excluding some currently living ones, due to diffusion rates, but eventually...)
Is it conceivable that some of the oxygen and nitrogen, etc, in the atmosphere today wasn’t present in the atmosphere, say, 40,000 years ago due to it being bound up in minerals or biological matter?
I know gravity has a speed limit, but does it have a upper distance limit or lower magnitude limit?
As in, are we really feeling gravitational effects of mass that is 14 light years away, even if they are insignificantly tiny and we probably can't measure it, or is there a point where a force is so miniscule that the universe truncates the force to 0?
If one arbitrarily defines "zero force" as less than the force sufficient to accelerate one proton at one planck length per age-of-universe^2, I come up with a distance of 10^12 meters between two protons (+/- an order of magnitude).
However, (and if I didn't screw up the math) since gravity scales linearly with mass, and the size of the visible universe is about 10^27 meters, then anything with mass greater than 10^15 protons -- or about the mass of a human cell -- has a "non zero" gravitational effect on you.
No, but neither does the EM force, it all just asymptotically approaches zero. Don’t let that fool you though, in that it really approaches zero to a high degree.
Well.... I'm pretty sure the field interpretation of EM also applies across the universe. So you could, on a dark night, with the electrons in the atoms of your body, feel the movement of electrons in a star, millions of light years away in space and time...
Yeah, but the electrons in the star are pushing on your electrons, not pulling. I think bluetwo called gravity romantic because it is bringing together, not driving apart.
I hesitate to say this because I dont entirely grasp it at the moment but I think when electrons are travelling parallel to each other they can stop repelling... their repulsive force is overtly effected by their relative movement, as well as their position and charge - due to how charges in motion modify and follow the magnetic field.
I believe that if we were just dealing with electrons, the repulsion from the electric field would be much much stronger than the attraction from the magnetic field.
We only see a net attraction between current carrying parallel wires because the wires contain both electrons and protons in almost perfect balance, so that the electron/electron repulsions and proton/proton repulsions between the wires are almost perfectly canceled by the electron/proton attractions between the wires, leaving no net electrical attraction or repulsion.
That lets the weak magnetic attractions (or repulsions, depending on the directions of the currents) dominate.
This is the first calculation of the gravitational forces for small objects that I can actually understand intuitively. Much better than trying to specify in newtons the actual force of gravity between me and said cow.
I somehow feel you're not going to divest an astrologer of their belief in the power of Jupiter by comparing it with standing within touching distance of a massive cow.
The only somewhat reasonable hypothesis I've ever heard about how astrology might work (if it did) is the clock hypothesis. The idea is that the stars have nothing to do with it in a causal sense. Ancient people just noticed certain patterns and correlated them with the stars because stars were what they used to keep time. The real causal mechanism could be some kind of biological cycle or something else.
What this article overlooks is the indirect effect of this gravitation. Yes, the moon's effect on only my body is tiny, but the moon's cumulative effect on every particle on Earth adds up to substantial cycles which we observe as tides. If it affects the whole, then it also affects the parts.
Also, being in free-fall relative to the earth isn't locally distinguishable from being in free-fall relative to both the earth and the moon.
Tidal effects are caused by the gradient of the gravitational field across significant distances. And the gradient drops off in proportion to the inverse cube of the distance, not the inverse square. Which is why tidal effects are only observable from the moon and sun, not from other celestial bodies. (Jupiter's gravitational influence on the Earth is about 1% that of the moon, but it's so far away that the tidal effects are infinitesimal.)
The gravitational pull of nearby, mundane objects is just as strong, if not stronger, than the pull of the stars and planets. If the gravitational pull of the stars and planets impacts human behavior, as astrology posists, then so should a cow several miles away.
I think astrology only posits that human behavior is somehow correlated with the positions of the various heavenly bodies. This could be via an intermediate correlation with the weather, etc.
Isn’t there a quantum theory of entanglement that says something like once two electrons meet then separate they are still ‘bound’ and influencing each other ? I wonder since, as carbon based life forms , we are all just made up of stardust , how and on what string theoretical levels we are quantum entangled with all the atoms known as planets moving around ?
Jupiter is pulling on your body right now (a little bit). You would experience the same amount of pull from a cow standing half a meter away (since it is much closer, but much less massive).
my attempt:
So your phone should be able to register 1 bit of resolution when the empire state building is 3 meters away or less, otherwise it would be too far away to detect. Of course the empire state building would need to be compressed into a single point but that's a minor practical concern.