Questions tagged [order-of-magnitude]

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39
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3answers
6k views

Why is 7 TeV considered as a big amount of energy?

Considering that $7$ TeV is more or less the same kinetic energy as a mosquito flying, why is it considered to be a great amount of energy at the LHC? I mean, a giant particle accelerator that can ...
38
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3answers
6k views

Can the solar system really fit in a thimble?

Almost every time somebody talks about atoms, at some point they mention something like this: If we remove the spaces between the atoms and atomic components, we can fit the solar system in a ...
28
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4answers
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If an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple

Quoting from the Feynman Lectures on Physics - Vol I: The atoms are 1 or $2 \times 10^{−8}\ \rm cm$ in radius. Now $10^{−8}\ \rm cm$ is called an angstrom (just as another name), so we say they are ...
23
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5answers
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Is there a rigorous definition of 'much greater than'?

I have encountered $\gg$ in many physics text books where it's used as a relation between constants or functions but in none of the text books I have read is it properly defined anywhere. If $A \gg ...
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9answers
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In dimensional analysis, why the dimensionless constant is usually of order 1?

Usually in all discussions and arguments of scaling or solving problems using dimensional analysis, the dimensionless constant is indeterminate but it is usually assumed that it is of order 1. What ...
18
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1answer
3k views

Turned to steel in the great magnetic field

This is obviously a "fun" question, but I'm sure it still has valid physics in it, so bear with me. How great of a magnetic field would you need to transmute other elements into iron/nickel, if that'...
13
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3answers
659 views

“Weakness” of gravitational force [duplicate]

I often hear that gravitational force is much "weaker" than electroweak and strong forces. But how can you compare the strength of interactions without the parameters like mass, charge on which it ...
10
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2answers
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How cold does it need to be for spit to freeze before hitting the ground?

What is the dominant form of heat transfer between warm water and cold air? If a $100 mg$ drop of water falls through $-40 C$ air, how quickly could it freeze? Is it credible that in very cold ...
9
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5answers
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How does the temperature of the triple point of water depend on gravitational acceleration?

Suppose I do two experiments to find the triple point of water, one in zero-g and one on Earth. On Earth, water in the liquid or solid phase has less gravitational potential per unit mass than water ...
9
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2answers
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How did Enrico Fermi calculate the classical Fermi Problem?

From Wikipedia: Fermi was known for his ability to make good approximate calculations with little or no actual data, hence the name. One example is his estimate of the strength of the atomic bomb ...
9
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2answers
3k views

Why do mirages only appear on hot days?

A previous question asked why the road sometimes appears wet on hot days. The reason is that when there's a temperature gradient in the air, it causes a gradient in the index of refraction, causing ...
8
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3answers
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How can we make an order-of-magnitude estimate of the strength of Earth's magnetic field?

The source of Earth's magnetic field is a dynamo driven by convection current in the molten core. Using some basic physics principles (Maxwell's equations, fluid mechanics equations), properties of ...
8
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5answers
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Planck mass is about the mass of one eyebrow hair

Unlike most Planck units named after "Planck" such as Planck length, Planck temperature, etc, the Planck mass seems more closed to daily life. It is about $10^{-5}$g, same order of magnitude of one ...
7
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3answers
355 views

Is there a number that describes a gas's departure from the ideal gas law?

When judging if relativity is important in a given phenomenon, we might examine the number $v/c$, with $v$ a typical velocity of the object. If this number is near one, relativity is important. In ...
7
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2answers
675 views

Why is the string length around the Planck length?

In string theory, it is assumed that a string is about the size of a Planck length, $$\ell_{string} \sim \ell_{Pl} \simeq 10^{-35}\,\text m.$$ Why that length? Why not for example a hundred times ...
6
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5answers
713 views

What's the greatest range of orders of magnitude?

There's a famous claim along the lines of "40 dp of PI are sufficient to calculate the circumference of the Observable Universe to the width of a hydrogen atom" I don't know the accuracy and detail ...
6
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2answers
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A Fermi-question: Are there more stars than grains of sand?

This claim is pretty popular in the web and obviously cannot be answered by counting grains or stars. Thats what physicists call a Fermi-question. It deals with problems/questions where we dont have ...
6
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5answers
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Why don't the relative positions of stars and other objects in a galaxy change over the year?

Though the identifiable stars in a constellation (say Andromeda) and a galaxy (say the Andromeda galaxy) are situated light years apart, why doesn't the galaxy appear at different positions with ...
5
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2answers
277 views

Dimensionless numbers or parameters that are $\ll 1$ or $\gg 1$

Many times, in various fields, authors use the notation: $$C\ll 1$$ or $$C\gg 1,$$ where $C$ is some parameter related to the system being studied. I know this is highly dependent on application, ...
5
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2answers
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Is there scale by size of all discovered particles?

Atom: Neutron: Elementary particles: Is there scale by size of all discovered particles? From neutron and proton to electron and to boson? Compare to each other, like this I have found many ...
5
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1answer
127 views

Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
4
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3answers
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How much would the LHC beam be attenuated by the atmosphere?

As I understand it, the completed Large Hadron Collider (LHC) will ultimately have a proton beam with $2,808$ bunches of $1.15 \times 10^{11}$ protons each at $7$ TeV, giving a total beam energy of $(...
4
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3answers
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How many photons enter our eyes per second when looking at the blue sky on a sunny day?

How many photons enter our eyes per second when looking at the blue sky on a sunny day? Say the sun is directly over head and you are looking at the blue sky on the horizon. Say that the pupil is 2mm ...
4
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1answer
178 views

For how long must a molecule remain stable to be considered “stable”?

In the Star Trek: Voyager episode The Omega Directive, Seven of Nine says that the Borg synthesized a molecule which was "kept [] stable for one trillionth of a nanosecond before it destabilized". ...
4
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1answer
810 views

Why is Planck mass much larger than the smallest mass that we actually know about? [duplicate]

The three fundamental constants $h$, $c$ and $G$ are manipulated and rearranged in different ways to get the Planck time, Planck mass etc. The Planck time is said to be the smallest time possible and ...
4
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2answers
497 views

Magnitude of Black hole entropy

I was looking with a friend of mine through time travel related stuff, and for some reason we ended up at the Hawking equation for black hole entropy which is: $$S= \frac{\pi Akc^3}{2hG}$$ where: A:...
4
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1answer
211 views

Data requirement to determine proportionality

A common result of theoretical analysis in physics is some sort of relation derived from physical parameters and typically expressed in the form of a non-dimensional parameter. These scale relations ...
3
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4answers
375 views

How do you quantify the “much greater” operator “$\gg$”?

I'm specifically asked to compute the charge in the Earth-Moon system knowing that the gravitational force between the two bodies is much greater ($\gg$) than the electrostatic one. However, I don't ...
3
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2answers
886 views

Heuristics for specific heat capacities of solids

A didactic question publish in The Physics Teacher (http://tpt.aapt.org/resource/1/phteah/v41/i1/p8_s1) asks which will melt more ice: 100g of metal at 100C or 100g of wood at 100C. (The particular ...
3
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2answers
3k views

Newton's Third Law Of Motion: Earth Falling to an Apple?

I 'get' Newton's third law of motion, except for one thing. We know that if we let an apple fall to the Earth, the earth will fall to the apple, because the Earth must experience the same force in the ...
3
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1answer
112 views

When do you use Quantum Mechanics? [duplicate]

Given a problem, how does one know whether to use quantum mechanics or classical mechanics? Take for example electron scattering from a nucleus. The electrons are given a wavefunction in this case. ...
3
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1answer
674 views

What is a “scale length”, and how do I calculate it for galaxies?

I'm trying to work through, understand, and apply concepts regarding mass models of galaxies. Looking at the Hernquist model, I'm finding the equation $$Φ(r)=−\frac{GM}{r+a},$$ where a is the scale ...
3
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2answers
2k views

Measuring the nearest order of magnitude [closed]

The world's largest ball of a string is about $R=2 m$ in radius. To find the nearest order of magnitude, what is the total length $L$ of the string in the ball? I have tried this in the following way ...
3
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2answers
20k views

Temperature on the surface of the sun calculated with the Stefan-Boltzmann-rule

In a German Wikipedia page, the following calculation for the temperature on the surface of the Sun is made: $\sigma=5.67*10^{-8}\frac{W}{m^2K^4}$ (Stefan-Boltzmann constant) $S = 1367\frac{W}{m^2}$ ...
3
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2answers
165 views

Kolmogorov scale why $d\sim \left( \frac{\nu^3}{\epsilon} \right)^{1/4}$ and not $d\propto \left( \frac{\nu^3}{\varepsilon} \right)^{1/4}$?

I am looking at the Kolmogorov scale and in numerous sources (e.g. this one). I have seen the following: $$d\sim \left( \frac{\nu^3}{\epsilon} \right)^{1/4}$$ for the Kolmogorov scale. I can see why ...
3
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1answer
150 views

Mammal Population Estimates as a Fermi problem [closed]

Can We estimate the order of magnitude of number of mammals on earth? Can this be treated as Fermi problem or not?
3
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1answer
806 views

Can we really neglect gravitational strength?

In an atomic and particle physics model, the gravitational force is ignored or neglected. Physicists might have freedom of ignoring such minute scale value. But can we really avoid it in calculations? ...
3
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0answers
340 views

Pressure inside a typical white dwarf

Does any one know the order of magnitude of pressure inside a typical white dwarf (better with reference)? Thanks! I think it should be $m_e^4c^5/h^3$ (may be multiplied by $\pi$), which is $10^{22} \...
2
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2answers
3k views

What's smaller: a neutrino, or a string from string theory [closed]

I've recently read an article that stated "If an atom were as big as the solar system, a neutrino would be the size of a golf ball". I watch the science channel, and on (I believe) the show How the ...
2
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3answers
215 views

Will my car consume more if I plug in my laptop?

I drive a Volvo v40 with a 110hp diesel engine. It usually use 4.6L/100km. If I plug my laptop which is 85W, will this change the fuel need? If so, by how much?
2
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2answers
125 views

Do you create gravitational waves by clapping your hands?

I was thinking that given that GW's can be created by the merger of both black holes and neutron stars I don't see why any two colliding objects wouldn't also be able to create gravitational waves, ...
2
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1answer
672 views

How much water is destroyed in photosynthesis, relative to the world's supply?

Water is involved in the photosynthesis. How much water are we talking about compared with the total amount on water on Earth? Is it enough to have an effect on the average age of water molecules?
2
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1answer
118 views

Forces: Worth worrying anything?

I am a general physics student, I had a question in my text-book and according to it two students having gravitational attraction between them = ($6.67\cdot10^-8\ \mathrm{Nm}^2/\mathrm{kg}^2$) is not ...
2
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1answer
36 views

Sun's energy and grand unification

According to Wikipedia, The approximate grand unification energy value is equal to $1×10^{25}$ eV or $10^{16}$ GeV This is equal to $1602176$ J. Now, The Earth receives 174 petawatts (PW) ...
2
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2answers
61 views

What is the point of generalizing a more specific result to an order of magnitude?

In my textbook, an example wants me to find an estimate of the number of cells in a human brain. It gives the volume of the brain as $8 \times 10^{-3}\ \rm m^3$ which it then estimates further as $...
2
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1answer
45 views

How much faster is the chain reaction in a power plant than that of natural uranium ore? What about a nuclear bomb?

How much faster does the fissile uranium in a power plant 'break down' than an equivalent amount of naturally decaying U-235? How much faster is the chain reaction in a bomb compared to a power plant?...
2
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2answers
87 views

In geometrical optics, how can we say that rays coming from a distant object are parallel to one another?

If two rays are not parallel in the start, how can they become parallel at the instant when they strike the lens of a telescope? If they don't become parallel, why do we consider them to be, in the ...
2
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2answers
307 views

Modeling galactic colonization

I found a really cool sounding order-of-magnitude modeling question but am a bit at a loss on how to approach this: The Milky Way contains 100 billion stars and has a radius of 250,000 light years. ...
2
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1answer
56 views

Why does the universe manifest scale?

I'll try outline my question in clear terms, articulating specific aspects that are its primary motivators. I'm just beginning in my exploration of physics as a student, but a persistent question that ...
2
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1answer
35 views

Different approch on Order of magnitude confusion [closed]

My problem: How many orders of magnitude larger is the sun $(1.99$ x $10^{30} kg)$ than the moon $(7.32$ x $10^{22} kg)$. Justification 1: So according to my teacher, we can do this question by ...