So, I learned in physics class at school in the UK that the value of acceleration due to gravity is a constant called g and that it was 9.81m/s^2. I knew that this value is not a true constant as it is affected by terrain and location. However I didn’t know that it can be so significantly different as to be 9.776 m/s^2 in Kuala Lumpur for example. I’m wondering if a different value is told to children in school that is locally relevant for them? Or do we all use the value I learned?
I just learned ‘about 9.8’ which is true anywhere in the world.
Yeah. 9.8 is what I learned. I was generally aware that locality made a difference, but I had no idea that there was that much of a spread. For anything not involving millions of dollars of rocketry and actual satellites a simplified number is likely good enough. Much like Pi, where a couple digits is good enough for most everything and calculating out past 6 digits or so is infinitesimally small.
Standard gravity is 9.80665 m/s2. That the number defined by the metric people who set all the world’s units. In schools in the united states of america, we used 9.8. I don’t recal using any more precision than that. Gravity at the surface does vary, but you don’t need more presision than that for most academic purposes.
Is that so? I wonder what the story behind that is. Maybe it’s a surface average?
Most people would probably guess this, but meters and seconds are defined independently of Earth’s gravity, so it doesn’t have a true value, just apparently a standard nominal one.
The value of g depends on altitude. You can define it easily at the earth average 0m altitude.
It also depends on latitude, and local geology and…
Maybe it is just weighted by surface area, you’re right, and that’s what I meant by “surface average”.
Standard gravity was adopted as a standard in 1901. That was at the 3rd meeting of the General Conference on Weights and Measures. They redefined a litre as 1 kilogram of water, but the volume of water depends on the pressure, and the pressure depends on the local gravity, so they had to come up with standard values for both standard atmosphere and standard gravity. You also need a standard value for gravity to define a standard for weight measurements which was also done.
Standard gravity is the acceleration at sea level at 45 degrees latitude. The official number was based on measurements made by Gilbert Étienne Defforges in 1888. I can’t find details about his methodology without going to a library or something, and that’s not worth the effort for an internet comment.
No, it’s not worth it. Honestly that’s great all on it’s own. I guess they never had a reason to update it, then, since anybody that needs a more accurate value would just measure it themselves.
It looks like they went back to the original litre definition a few decades later. I’m not sure why they thought defining volume by mass rather than geometry was better in 1901, anyway. Some fun facts about the kilogram itself, since I never get to talk about this stuff:
Since 2019 the kilogram has been based on a “Kibble balance”, which is a contraption that precisely measures the force produced by electromagnetism. The necessary electricity is provided by circuit with a material that has quantised resistance near absolute zero, and a superconducting junction which produces oscillation exactly tied to the current flowing through, which is itself timed by atomic clock. This allows you to measure it out using just the new fixed value of Plank’s constant.
Before 2019 there was just a chunk of metal the was the kilogram, which is hilariously low-tech.
This is why you have so many Russians being thrown out of windows in high buildings. They’re testing the local value of g.
Dimitri, come to the window! I have a stopwatch and questions about the local density of the Earth’s crust!
We learned 9.82 m/^2. But in the classes I have as an engineering student we use 10 m/s^2. And I wish I was kidding when I say it’s because it easier to do the math in your head. Well obviously for safety critical stuff we use the current value for wherever the math problem is located at
9.8 is close enough to 10 for most human scale calculations. No need to have extra sig figs
Pi = 3
Sin(x) = x
And now, g = 10. Smh.
I have a “pi^2 = g” shirt, and every engineer I know loves it, every friend with a scheme background needs to point out that it’s wrong.
I’ve seen engineers use all of these. Bridges still work
Yeah air resistance is a stronger factor than those .2 m/s2. If we can ignore it we can ignore both
Interesting that I learned 32.2 ft/s, but only 9.8 m/s - one less significant figure, but only a factor of two in precision (32.2 vs 32 = .6%; 9.81 vs 9.8 is only 0.1%). Here’s the fun part - as a practicing engineer for three decades, both in aerospace and in industry, it’s exceedingly rare that precision of 0.1% will lead to a better result. Now, people doing physics and high-accuracy detection based on physical parameters really do use that kind of precision and it matters. But for almost every physical object and mechanism in ordinary life, refining to better than 1% is almost always wasted effort.
Being off by 10/9.81x is usually less than the amount that non-modeled conditions will affect the design of a component. Thermal changes, bolt tensions, humidity, temperature, material imperfections, and input variance all conspire to invalidate my careful calculations. Finding the answer to 4 decimal places is nice, but being about to get an answer within 5% or so in your head, quickly, and on site where a solution is needed quickly makes you look like a genius.
Even then, once you figure in a safety factor of 2 or 3 as a minimum, the extra precision really gets lost in the fog anyway.
I gotta say, that explanations sounds way better than shrugging and saying “close enough”. But then again our teachers usually say “fanden være med det” meaning “devil be with that” actually meaning “Fu*k it” when it comes to those small deviations
our teachers usually say “fanden være med det”
There’s a lot of wisdom in that. ;-)
Going to guess civil. I work on space systems and we don’t have one number. We have the g0 value, which is standard gravity out to some precision, but gravity matters enough we don’t even use point mass gravity, we use one of the nonspherical earth gravity models. It matters because orbits.
Nope. Mechanical engineering. So usually we say g=10 and then make the steel a bit thicker and call it a day
Well, g is not a real constant, it depends mostly on altitude. The true constant is G. g=9.8 is usually more than enough for your calculations, to the point we often round it to 10 for simplicity, or you remove it completely is the mass is too low. But actual numbers is only the very last step usually. The calculations will be made with letters. The value you use at the end for g depends on the precision you need, so it depends on the precision of the other parameters.
In grade school i learned it was about 32 ft/s2, but by high school on it was all 9.8[1/06] m/s2. Then in engineering school it was sometimes 10. None of that had anything to do with local gravity and everything to do with Americans having to be special at first, followed by the fact that our science classes are actually in metric (statics and dynamics were in both as some fields of engineering haven’t metricated yet here). And the 10 is because you can round to a round number by barely even touching your fudge factor so why not.
Interesting - what part of the US are you from?
I was going to say that even here in the US it was 9.81 m/s^2. I don’t remember ever being taught the number in feet (in NYS) nor seeing it for my kids (in MA). Science was always metric
Ohio, and Catholic schools. It was clearly on its way out. In retrospect it was definitely a strange situation where different teachers had different opinions on metric. Some clearly thought it’s fine for science, and others clearly just wanted to quit our two measurement system that does nothing but prolongs the inevitable.
I learned 9.81 m/s2 and 32.2 ft/s2 with the qualifier being at sea level.
This doesn’t change the issue presented by OP. Sea level is not level across the world. In fact there are much larger differences than most people expect. The Earth is not perfectly round. Earth rotation causes the equator to be affected by a centrifugal force, making it wider there ( more distance to earth core means less gravity ) than at the poles. Overall, gravity at Earth surface level varies by 0.7%, ranging from 9.76 in Peru to 9.83 in the Arctic Ocean, but it’s absolutely not linear. In addition, the Earth is full of gravity anomalies. These cause localized dips and spikes in gravity. Two of the big dogs lips lie in the Indian ocean and the Caribbean. Because water is fluid, sea level is very much affected by local gravity (as well as other factors such as air pressure, salinity, temperature…). Which is also why the moons gravity can cause tides. The permanently lower gravity on these anomalous spots mean that the average sea level here is lower than it would be on a perfect sphere. This difference can be up to two meters in sea level.
I figured they took the best average at sea level across the planet that they could measure.
In freshman college physics we had a lab to measure gravity then had to use our lab result for the rest of the course.
Just don’t make the same mistake as one physics lab did. They made a series of measurements and their results showed that gravity quickly increases in fall, falls slowly over winter, and back to about pre-fall levels very slowly in summer. It took quite a while to figure out the reason of this unexpected result. They turned their equipment inside out to find a mistake to no avail. Then they realized that the university stored coal for the central heating and hot water in the basement under the lab…
Could you explain to me why that last part matters?
I’m assuming they’re indicating that the mass below the apparatus increased in fall (when storage was filled) and decreased slowly through the winter, leading them to measure a changed graviational constant. A back of the napkin calculation shows that in order to change the measured gravitational constant by 1 %, by placing a point mass 1 m below the apparatus, that point mass would need to be about 15 000 tons. That’s not a huge number, and it’s not unlikely that their measuring equipment could measure the gravitational acceleration to much better precision than 1 %, I still think it sounds a bit unlikely.
Remember: If we place the point mass (or equivalently, centre of mass of the coal heap) 2 m below the apparatus instead of 1 m, we need 60 000 tons to get the same effect (because gravitational force scales as inverse distance squared). To me this sounds like a fun “wandering story”, that without being impossible definitely sounds unlikely.
For reference: The coal consumption of Luxembourg in 2016 was roughly 90 000 tons. Coal has a density of roughly 1500 kg / m3, so 15 000 tons of coal is about 10 000 m3, or a 21.5 m x 21.5 m x 21.5 m cube, or about four olympic swimming pools.
Edit: The above density calculations use the density of coal, not the (significantly lower) density of a coal heap, which contains a lot of air in-between the coal lumps. My guess on the density of a coal heap is in the range of ≈ 1000 kg / m3 (equivalent to guessing that a coal heap has a void fraction of ≈ 1 / 3.)
Thank you for the very well detailed explanation, as well as the visual. Much appreciated!
À better question is why is a university still using coal heating in the modern age?
This observation further compounds the hypothesis of “fun wandering story that has been told from person to person for a long time”
Fits in with the sinking library and Native American graveyard (though i believe that the exact second one may be regionally locked)
How much was the variation?
Can’t be that big, as the difference in mass close to the instrument only varied in the several tons category, but obviously enough to puzzle the scientists.
Well yeah. I was just curious if the difference was on the order of millimeters or microns /m².
I also learned 9.8.
This reminds me of the story of magnetic detonators for torpedos they tried to use in the early days of WW2. They detect the slight disturbance in the Earth’s magnetic field caused by a gigantic hunk of floating metal, and that triggers the detonation.
However, they did not yet know that the Earth’s magnetic field is not consistent over the whole planet, so while they calibrated it to the local field, it functioned very badly in other regions with different field strengths. Torpedo would either detonate far too early, doing minimal damage, or not detonate at all, just hitting the target ship with a loud thunk.
This was largely responsible for the ineffectiveness of American submarines in the early days of our WW2 involvement. Took us a couple years to sort too.
It was called the Mk 42 in case anyone wanted to read a little more. It’s an amusing story. They never wanted to actually properly test them, because they were so damn expensive. So they just didn’t. lol It wasn’t until enough sailors complained and got a high ranking admiral on their side that it got sorted.
People learned different values for g for a number of reasons, but as far as I understand local variability is not one of them. The primary root cause seems to be accuracy of the measurement over time and the age of textbooks/course material.
Over time we have gotten better at measuring the true value of g through advances in technology and this has caused the taught value to shift a little. The value when initially measured had fairly large error margins, meaning that we were sure it was near a specific value but not sure of the exact value. As the tools improved we have reduced the uncertainty, getting to a more accurate and also more precise value, meaning more digits after the decimal as well as higher confidence in each digit. We have also changed what we mean by g over time, bringing it in line with the metric system and basing it on fundamental values and constants. From my understanding the most recent method relies on how much the repulsive force of an electromagnet with a specific number of culombs passing through is overcome by gravity at a specific distance from the center of the mass of Earth, so a little more removed from backyard science than measuring if things drop at the same speed at the top of a mountain and sea level.
Part 2 is the differences in how recent your material is. In my primary school in a relatively affluent area of an affluent country we had textbooks from the last 10 years. My partner went to a school in the same country but a worse area about 5km away from mine. Their school had textbooks literally 20 years old. In that time the measurements had changed, understandings had changed, and they were therefore taught things that were untrue. These sorts of differences based on geography reproduce the impacts of racism and inequality from the past into the future.
I’ve learned it as 9.81 but we usually round up to 10 for calculations. (this is for highschool. I haven’t gotten to college yet)
We just use 9.8 at my high school for calculations. Also its cool to see another young person on the fediverse (Assuming you are still in highschool).
Close enough I graduated last year 2023. I couldn’t get in to the college I wanted so I decided to try it a second time. There’s a countrywide exam that gives you a score. It’s called yks. I’m currently studying for that exam.
You round it to 10? Do you also round PI to 3 for simplicity? Kids these days.
Rounding of constants always depends on what you are calculating. Getting a rocket into orbit is a case to use the actual local value of g with a bunch of digits (and the change with height, too). If you build a precision tool, some more digits of PI are no bad idea.
But to calculate the lenght of fence to buy to surround a round pond, I actually used 10/3 for “PI plus safety margin” once.
I was just kidding but good example with the fence.
yeah :/ in physics class we do round pi to 3
9.81 in Scotland.
Whoa, thats heavy
Seeing as the British invented gravity, most places just use our gravity rather than making their own.
g = 9.80665 m/s^2 at sea level. Higher than sea level lowers the value due to GR (General Relativity).
Newtonian physics also has gravity decreasing with height, no need to get out the big guns.
say what now?
citation needed.
Newton’s law of gravitation. F = G m1*m2/r^2
Ah, I see. I thought we were talking about the constant.
G is also fixed in GR, although it’s not guaranteed to manifest in a neat relation like that in every situation because spacetime curvature has a lot of components at every point, and they interact super nonlinearly.
F=Gm1m2/r2
G is the gravitational constant, the m’s are the masses in question, and F is the force generated. The r is radius from the center of one body to the other; that is, height. If it didn’t decrease, orbits wouldn’t exist the same way and astronomers would have laughed Newton out of the room.
I could give you a link if you really want, but it’s the Newtonian gravity equation, so it’s probably just going to be “Gravity” on Wikipedia.
“Mom! Canada’s picking on me again…”
See Wikipedia for this.
