For Questions That Don't Merit Their Own Thread

[FleshJeb]

15 minutes ago, Gargamel said:

So let me rephrase to a hypothetical.    In degrees, how much would a fixed plane vary from truly level due to the wobble of the barycenter?

I think it's more of a force vector problem. Take the force of gravity on an object on the surface of the Earth, and then the force of gravity imposed on that object by the Moon set at 90 degrees to the Earth vector. Then it's just arctan(F_m/F_e).

Speaking as a surveyor, I can set an instrument up on a tripod, on dirt, in the sun, and expect it to hold about 5 arcseconds in the vertical all day.  (The moon will have moved several degrees during this time.) This is presuming I've let everything heat up to thermal equilibrium first, and then leveled it. In practice, I usually see a 20 arcsecond drift because I don't have time for that, and it's got an internal compensator to apply corrections to to my angular measurements. In the worst-case scenarios, on a surface with a lot of thermal expansion (like asphalt), it can get to 2-3 arcminutes. Even then, the compensator can correct that if I'm doing lower-accuracy work.

[Gargamel]

Soooo.... a noticeable amount then?   Not just a rounding error amount.   Interesting. 

[kerbiloid]

https://en.wikipedia.org/wiki/Barycenter

Quote

 This is the case for the Earth–Moon system, in which the barycenter is located on average 4,671 km (2,902 mi) from Earth's center, 75% of Earth's radius of 6,378 km (3,963 mi).

***

But the gravity force doesn't point at the E-M barycenter.
Otherwise the rocks would fly from the Moon surface up to the Earth.

g ~M/r²

Earth: 5.97*10²⁴ / (6.371*10⁶)² ~= 1.47*10¹¹

Moon: 7.35*10²² / (384.4*10⁶)² ~= 5*10⁵

Acceleration ratio from-Earth / from-Moon = 1.47*10¹¹ / 5*10⁵ = 300 000 times.

Max angle ~ arctan(1 / 300 000) ~= 0.7 ".

Edited November 17, 2021 by kerbiloid

[FleshJeb]

42 minutes ago, Gargamel said:

Soooo.... a noticeable amount then?   Not just a rounding error amount.   Interesting. 

Sorry, I left the wrong impression due to my mental frame of reference. It’s not the moon doing that. I’m saying my best non-lab bench results have negligible drift over an 8+ hour day. Any drift I get is from differential heating as the sun moves.

Comparison of forces involved: https://www.quora.com/How-does-the-Moons-gravity-affect-humans

Hmm, check my math, I’m on my phone: arctan(0.0034/981) =0.000199 degrees. The best I can measure is 1/3600 degrees = 0.000278. Theoretically, if the moon moved 180 degrees relative to your position, you’d double the 0.000199, so I might be able to detect it with a bench test…provided I didn’t breathe, the building foundation was thermally isolated, and no mosquitoes farted.

@kerbiloid You ninja’d me and we agree!

Thats actually a significant amount. I wonder how astronomers maintain sub-arcsecond pointing? Gyros? Reference stars?

[Gargamel]

1 hour ago, kerbiloid said:

 

But the gravity force doesn't point at the E-M barycenter.
Otherwise the rocks would fly from the Moon surface up to the Earth.

Ahhha!    I knew I smelled a logical fallacy in my thinking somewhere.  

[JoeSchmuckatelli]

I like the idea of floating the table in mercury to get it as level as possible... But once you did, what work could you do on it?  If I set my coffee cup on one corner - the table's surface would no longer be level. 

Thank God I'm only a carpenter - level enough is good enough for me 

[TheSaint]

9 hours ago, JoeSchmuckatelli said:

I like the idea of floating the table in mercury to get it as level as possible... But once you did, what work could you do on it?  If I set my coffee cup on one corner - the table's surface would no longer be level. 

Thank God I'm only a carpenter - level enough is good enough for me 

Oh, wait, you wanted a solution with practical applications? Sorry, those cost extra.

(Actually, floating things on pools of liquid metal does have practical application, just not in carpentry. It is how they create panes of glass, which have to cool at a perfectly level attitude otherwise they wind up with variations in thickness. But I digress.)

Taking a step back, for a work surface what you need to do is level it during construction. If it is a process which requires ultra-fine leveling, you use an extremely precise measure of level (such as @FleshJeb's equipment) combined with jack screws on the actual work surface to periodically re-level the surface to account for any variations due to heat, wear, or vibration. And you wind up barking at the guys who drive the forklifts a lot.

Edited November 17, 2021 by TheSaint

[kerbiloid]

But didn't we miss another significant factor?

We took as presumption that the table is flat.
But the Earth is not flat ^{(citation needed)}.  It's more or less spherical.

So, the table surface must be a segment of sphere, to match the Earth gravity field curvature.

[TheSaint]

7 minutes ago, kerbiloid said:

But didn't we miss another significant factor?

We took as presumption that the table is flat.
But the Earth is not flat ^{(citation needed)}.  It's more or less spherical.

So, the table surface must be a segment of sphere, to match the Earth gravity field curvature.

The industrial engineer:

Really, for most surfaces, it would be difficult to prove that it isn't a segment of the proper sphere, considering how slight the variation of the surface would be to conform to the sphere, and how much the curvature of the surface is going to vary simply because of differential heating. You would have to make the surface a massively thick slab of metal, and hone it with the precision of a telescope lens. But if you are moving away from the practical to the absolute, then yes, you are correct.

[kerbiloid]

5 minutes ago, TheSaint said:

Really, for most surfaces, it would be difficult to prove that it isn't a segment of the proper sphere, considering how slight the variation of the surface would be to conform to the sphere, and how much the curvature of the surface is going to vary simply because of differential heating.

They are multicurvature spheres, while this table should be a monocurvature one.

Maybe, we could approximate this with a kind of parabola by casting the table top from liquid glass and rotating it while it's freezing.

Then using this as a casting form to cast the surface itself.

Just the rotation speed should be calculated.

[JoeSchmuckatelli]

1 hour ago, kerbiloid said:

They are multicurvature spheres, while this table should be a monocurvature one.

Maybe, we could approximate this with a kind of parabola by casting the table top from liquid glass and rotating it while it's freezing.

Then using this as a casting form to cast the surface itself.

Just the rotation speed should be calculated.

Except, if you are rotating it wont the edges end up thicker than the center?

If you have a perfectly still pool of liquid metal, then its surface should already conform to 'level' at any given point - but if you have a big enough pool, then you should notice with a straight edge or laser that while level, it is not flat - right?

Edited November 17, 2021 by JoeSchmuckatelli

[wumpus]

1 hour ago, TheSaint said:

The industrial engineer:

Really, for most surfaces, it would be difficult to prove that it isn't a segment of the proper sphere, considering how slight the variation of the surface would be to conform to the sphere, and how much the curvature of the surface is going to vary simply because of differential heating. You would have to make the surface a massively thick slab of metal, and hone it with the precision of a telescope lens. But if you are moving away from the practical to the absolute, then yes, you are correct.

Fun fact: the runway at KSP's KSC is flat, and doesn't follow the curvature of Kerbin.  Presumably you can tell this by noting the difference in the size of the banks needed to "raise" the runway between the ends and the middle.  But Kerbin is much smaller than Earth, and the runway is designed for spacecraft (so presumably more on the scale of Shuttle landing runways, although expect Kerbal aircraft to cheat a lot).

On Earth, I'd be curious if the difference of such a table (let's say round, with a 2.4m radius) matching the curvature  vs. non-matched would be more or less than difference between the Hubble mirror and the specs for the mirror (sans spherical aberration).  And yes, you'd need to polish the table like such a mirror to get the measurement to be meaningful.

[kerbiloid]

42 minutes ago, JoeSchmuckatelli said:

Except, if you are rotating it wont the edges end up thicker than the center?

If you have a perfectly still pool of liquid metal, then its surface should already conform to 'level' at any given point - but if you have a big enough pool, then you should notice with a straight edge or laser that while level, it is not flat - right?

It should get concave and form a quasi-spherical surface.

[TheSaint]

1 hour ago, wumpus said:

Fun fact: the runway at KSP's KSC is flat, and doesn't follow the curvature of Kerbin.  Presumably you can tell this by noting the difference in the size of the banks needed to "raise" the runway between the ends and the middle.  But Kerbin is much smaller than Earth, and the runway is designed for spacecraft (so presumably more on the scale of Shuttle landing runways, although expect Kerbal aircraft to cheat a lot).

On Earth, I'd be curious if the difference of such a table (let's say round, with a 2.4m radius) matching the curvature  vs. non-matched would be more or less than difference between the Hubble mirror and the specs for the mirror (sans spherical aberration).  And yes, you'd need to polish the table like such a mirror to get the measurement to be meaningful.

So, here is what I learned today:

The sagitta is the height underneath an arc.

To calculate an approximate sagitta (s) when you know the radius of the arc (r) and the length of the arc's chord (l), (if the sagitta is very small in relation to the radius) you can use the following formula:

So, using the formula, with a chord of 2.4m and the radius of the Earth being roughly 6,360,000m, the sagitta of our table would be approximately 1.13 x 10^-7 meters, or roughly 113 nanometers. That is to say, the center of the table would be 113 nanometers higher than the edges, consistently and uniformly. For a sense of scale, the spherical aberration error in the Hubble mirror was 2200 nanometers. So, yeah, you're talking about the same order of magnitude as polishing a telescope mirror.

[JoeSchmuckatelli]

11 minutes ago, TheSaint said:

So, using the formula, with a chord of 2.4m and the radius of the Earth being roughly 6,360,000m, the sagitta of our table would be approximately 1.13 x 10^-7 meters, or roughly 113 nanometers. That is to say, the center of the table would be 113 nanometers higher than the edges, consistently and uniformly. For a sense of scale, the spherical aberration error in the Hubble mirror was 2200 nanometers. So, yeah, you're talking about the same order of magnitude as polishing a telescope mirror.

Cool - thanks for doing that work!

 

[JoeSchmuckatelli]

When I add a touch of water to my Scotch... how fast does the water and alcohol mix?

(Actual scientific inquiry behind this: some guy at a distillery told a bunch of us that stirring was useless, as alcohol and water mixed 'instantly'.  News to me, but then I'm not a chemist).

Edited November 18, 2021 by JoeSchmuckatelli

[TheSaint]

2 hours ago, JoeSchmuckatelli said:

When I add a touch of water to my Scotch... how fast does the water and alcohol mix?

(Actual scientific inquiry behind this: some guy at a distillery told a bunch of us that stirring was useless, as alcohol and water mixed 'instantly'.  News to me, but then I'm not a chemist).

Can't help you, I'm drinking cognac tonight.

[kerbiloid]

5 hours ago, JoeSchmuckatelli said:

When I add a touch of water to my Scotch... how fast does the water and alcohol mix?

What a strange recipe.

A reverted "Admiral's Tea" ?

Spoiler

1. Take a cup of tea.
2. Do several drinks.
3. Add cognac to keep it full.
4. Repeat pp. 2 and 3 until the pure cognac in the cup.
5. Drink the cup.

 

2 hours ago, TheSaint said:

Can't help you, I'm drinking cognac tonight.

Navy can into Admiral's Tea.

***

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Edited November 18, 2021 by kerbiloid

[lrd.Helmet]

8 hours ago, JoeSchmuckatelli said:

When I add a touch of water to my Scotch... how fast does the water and alcohol mix?

(Actual scientific inquiry behind this: some guy at a distillery told a bunch of us that stirring was useless, as alcohol and water mixed 'instantly'.  News to me, but then I'm not a chemist).

Depends on how you pour it in. A container with water and alcohol would slowly dissolve the alcohol into the water at the boundary layer, this would be a fairly slow process as the only point of contact is in that contact layer. However, if you poured the water in like you normally would you'd also agitate the liquids quite a bit. This would greatly impact the time it takes to fully dissolve the alcohol. The same would be true for stirring.

If you're talking about mixing water into scotch, I'm not really sure they would mix by themselves. Scotch will actually float on top of water due to the difference in density.

Edited November 18, 2021 by lrd.Helmet
whiskey to scotch

[magnemoe]

1 hour ago, lrd.Helmet said:

Depends on how you pour it in. A container with water and alcohol would slowly dissolve the alcohol into the water at the boundary layer, this would be a fairly slow process as the only point of contact is in that contact layer. However, if you poured the water in like you normally would you'd also agitate the liquids quite a bit. This would greatly impact the time it takes to fully dissolve the alcohol. The same would be true for stirring.

If you're talking about mixing water into scotch, I'm not really sure they would mix by themselves. Scotch will actually float on top of water due to the difference in density.

Simply filling in water will mix it well enough. And should be visible even if its much easier to see if you water out concentrated juice. 
having the two liquids at an even level and remove an separating wall it will mix much slower. 
Alcohol and water mix unlike water and oil who separates. 

16 hours ago, wumpus said:

Fun fact: the runway at KSP's KSC is flat, and doesn't follow the curvature of Kerbin.  Presumably you can tell this by noting the difference in the size of the banks needed to "raise" the runway between the ends and the middle.  But Kerbin is much smaller than Earth, and the runway is designed for spacecraft (so presumably more on the scale of Shuttle landing runways, although expect Kerbal aircraft to cheat a lot).

On Earth, I'd be curious if the difference of such a table (let's say round, with a 2.4m radius) matching the curvature  vs. non-matched would be more or less than difference between the Hubble mirror and the specs for the mirror (sans spherical aberration).  And yes, you'd need to polish the table like such a mirror to get the measurement to be meaningful.

I noticed the very helpful drop at the end but thought this was simply because the terrain dropped off towards the sea. 

In practice I assume an table or an flat floor suspended from the walls will sag more in center than the curvature but in the opposite direction, an concrete floor will follow the curvature but other factors are more important. 

[AHHans]

[P.S. I'm a bit late to the party, but now I already typed it, so you can damn well take the time and read it! (Or just ignore it, whatever.)]

On 11/17/2021 at 6:27 AM, Gargamel said:

“Down” is basically pointing to the barycenter of the Earth/Moon system, but that wobbles around slightly over time.  

I don't think so. The Earth-Moon barycenter is about 75% of the Earth's radius away from the Earth's center. That means that as the Earth rotates the direction from any point on the surface to the barycenter changes by tens of degrees each day. I guess we would have noticed if that was also how the gravitation changes.

The thing is we are not in an orbit around the Earth-Moon barycenter, but more ore less stationary on the Earth's surface. Which is in a complex motion around the barycenter. So I guess what matter in the end is the tidal force that the Moon effects on the Earth's surface. According to the Wikipedia article the corresponding acceleration is:  g_tidal = 1.10×10⁻⁶ m⋅s⁻²
Compare to Earth's gravity:  g_tidal / g_Earth = 1.10×10⁻⁶ / 9.81 =1.121×10⁻⁷  Which corresponds to a maximum angle of about 0.02 arcsec

This ignores all the more Earthly effects to the local gravity, like the mountain range over there, or variation in density of the Earth's crust (and mantle?), or whatever. If I remember the late night discussions in my student dormitory correctly (back when I still lived in one) then these variations can be quite significant and need to be taken into account by civil engineers. (Which IIRC they do by defining elevation in terms of local gravity.)

On 11/17/2021 at 10:41 AM, FleshJeb said:

Hmm, check my math,

Your math is fine. But the force actually changes less than the value you used, because you move around relative to the Moon .

21 hours ago, wumpus said:

Fun fact: the runway at KSP's KSC is flat, and doesn't follow the curvature of Kerbin.  Presumably you can tell this by noting the difference in the size of the banks needed to "raise" the runway between the ends and the middle.

You can also notice that by the fact that any wheeled craft that you "launch" from the SPH will roll forwards (towards the middle) on the runway. Because the ends of the runway are tilted with regards to the local gravitational field.

Edited November 18, 2021 by AHHans

[magnemoe]

On 11/17/2021 at 10:34 AM, kerbiloid said:

https://en.wikipedia.org/wiki/Barycenter

***

But the gravity force doesn't point at the E-M barycenter.
Otherwise the rocks would fly from the Moon surface up to the Earth.

g ~M/r²

Earth: 5.97*10²⁴ / (6.371*10⁶)² ~= 1.47*10¹¹

Moon: 7.35*10²² / (384.4*10⁶)² ~= 5*10⁵

Acceleration ratio from-Earth / from-Moon = 1.47*10¹¹ / 5*10⁵ = 300 000 times.

Max angle ~ arctan(1 / 300 000) ~= 0.7 ".

Still gravity is pretty strong, I assume the moon affect the orbit of satellites require high accuracy like the ones measure ocean height to map the ocean floor or gravity wave detection satellites, but the moon position is pretty well known
Does it have more down to earth effect like does it have an practical effect an long range artillery shell so you might want to add it to an digital fire computer?
ICBM is more affected but they have an inertial guidance system but they have much longer flight time and spend much of it in space. 

[aziazukra]

If you had 1kg of antimatter (safely contained), what would you do?

You can have any sort of technology you want to use it with, as long as its possible within our current understanding of physics.

[Shpaget]

There aren't many choices, apart from energy and death generation.

[FleshJeb]

10 hours ago, AHHans said:

This ignores all the more Earthly effects to the local gravity, like the mountain range over there, or variation in density of the Earth's crust (and mantle?), or whatever. If I remember the late night discussions in my student dormitory correctly (back when I still lived in one) then these variations can be quite significant and need to be taken into account by civil engineers. (Which IIRC they do by defining elevation in terms of local gravity.)

Gravitational anomalies:

What GPS equipment reports is latitude, longitude, and a height above a reference ellipsoid.

To turn an ellipsoid height into a useful height, you compare it to the Geoid, which is a height map of the gravitational anomalies relative to the reference ellipsoid. It's basically a big database of values keyed to lat/long.
"All points on a geoid surface have the same geopotential (the sum of gravitational potential energy and centrifugal potential energy). The force of gravity acts everywhere perpendicular to the geoid"

2 is the ellipsoid, 5 is the geoid:

"the geoid's deviation from an ellipsoid ranges from +85 m (Iceland) to −106 m (southern India)"

If you know your US geography, these geoid heights make sense:

Here are some of the later steps in how GPS equipment shows a useful elevation (Orthometric Height):

11 hours ago, AHHans said:

Your math is fine. But the force actually changes less than the value you used, because you move around relative to the Moon .

I'll think about that some more on a day when I haven't been building and measuring a network of very large triangles at a sewage treatment plant.
Bonus: It's for deformation monitoring, so it's time-dependent. My brain (and the rest of me) hurts.