
Gravitational attraction of stars and cows - weinzierl
https://www.johndcook.com/blog/2018/03/28/cow-astrology/
======
nerfhammer
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.

~~~
dx034
But wouldn't all of the mass need to be <3 meters away from you?

~~~
nerfhammer
I called this out as a minor practical concern

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amelius
What I find more interesting is the gravitational pull of ice sheets on the
sea, e.g. [1].

[1] [http://sealevelstudy.org/sea-change-science/whats-in-a-
numbe...](http://sealevelstudy.org/sea-change-science/whats-in-a-
number/attractive-ice-sheets)

~~~
mirimir
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.

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CobrastanJorji
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.

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btilly
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. :-)

~~~
eismcc
Wonder what the effects of the great plastic islands in the oceans are.

~~~
ben-schaaf
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.

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vincentchu
Calculation only holds for spherical cows. :D

~~~
nyrikki
It actually is :)

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."

~~~
msla
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.

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bluetwo
Gravity is the most romantic force in all of nature.

The idea that everything in the universe is connected and pulling is mind
blowing.

~~~
oh_sigh
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?

~~~
Treblemaker
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.

~~~
Treblemaker
Ah, one little slip of the pen and everything changes. It's more like 3.6 *
10^16 meters.

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coryfklein
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.

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pmontra
It reminds me of this page I created a few years ago
[https://connettiva.eu/newton/](https://connettiva.eu/newton/)

Select a planet, then touch the objects below. Eventually read the text at the
end for the implementation details.

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EvilTerran
Randall Munroe's done an edition of "What If" on a similar question:

 _" Which has a greater gravitational pull on me: the Sun, or spiders?"_

[https://what-if.xkcd.com/136/](https://what-if.xkcd.com/136/)

The main conclusion is sadly not that exciting, but the digressions are fun as
always.

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hanoz
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.

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api
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.

~~~
jakeogh
Certain old but powerful gangs like to flash their signs by doing things in
sidereal time, so the same stars are overhead.

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sxv
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.

~~~
teraflop
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.)

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jacinabox
Whoa, leading with astrology in a physics article, strong choice.

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roywiggins
I wonder what the implications are for cow-based astrology.

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cjg
I think that if I was standing 0.57m from a cow all day, that might have some
significant impact - just not in a gravitational sense.

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alberto_ol
something related [https://xorshammer.com/2016/05/18/gravity-is-stronger-
than-i...](https://xorshammer.com/2016/05/18/gravity-is-stronger-than-i-
thought/)

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mirimir
In my experience, astrologers aren't readily tempted into physical
explanations.

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kang
The entire universe is having measurable("infinite" but countable)
gravitational effect. You need to prove that "cumulative" effect is
negligible.

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amriksohata
I don't get it

~~~
cowboysauce
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.

~~~
mikeash
Does astrology actually posit a mechanism? I thought that part was left
unspecified.

~~~
baddox
According to the first sentence of the article, gravity is one suggested
mechanism.

~~~
mikeash
Sure, but there’s potentially a large gulf between “some people attempt to
rationalize astrology by saying” and “astrology says.”

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jpmoyn
He is just addressing the people who rationalize it by gravity, then.

~~~
godzilla82
Exactly. Side question: If you really believe something, do you feel the need
to rationalize it?

