# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2015-10-17 12:58:51

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Micro / Macro numbers in Science

Micro / Macro numbers in Physics and Chemistry :

Planck's Constant :

Last edited by Jai Ganesh (2015-10-17 15:09:27)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #2 2015-10-17 14:34:30

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Electron Rest Mass :

kilograms.
Mass of Neutron :
kilograms.
Mass of Proton :
kilograms.

Boltzmann Constant :

.

Charge of an Electon :

coulumbs.
Charge of a Proton :
coulumbs.

Last edited by Jai Ganesh (2015-10-27 12:11:25)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #3 2015-10-17 17:40:45

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Coulumbs per kilogram.
Mass of Earth
kilograms.
Mass of Sun
kilograms.
Age of Earth, Sun
years.

Last edited by Jai Ganesh (2015-10-19 15:50:47)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #4 2015-10-19 15:48:44

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Gravitational Constant

.

Last edited by Jai Ganesh (2015-10-26 19:53:28)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #5 2015-10-19 16:09:04

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Standard acceleration due to gravity, in vaccum

near of the surface of the earth.

Last edited by Jai Ganesh (2015-10-19 16:14:13)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #6 2015-10-19 16:41:58

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,995
Website

### Re: Micro / Macro numbers in Science

Please add speed of light, fine structure constant and gas constant too

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #7 2015-10-19 16:53:35

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Certainly, comrade... In a few hours...

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #8 2015-10-19 17:39:39

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Velocity of light :

.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #9 2015-10-19 17:57:18

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Fine structure constant : charectering the strangth of the electromagnetic interaction beween elementary charged particles also known as Sommerfeld's constant denoted by

is a fundamental physical constant charecterizing the strength of the electromagnetic interaction between the elementary charged particles. Value :
.

No unit.

Last edited by Jai Ganesh (2015-10-19 18:01:25)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #10 2015-10-19 18:05:17

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Gas constant :

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #11 2015-10-20 14:44:42

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Heaviest Metal : Osmium : Density :

Second Heaviest Metal : Iridium : Density :
.

Last edited by Jai Ganesh (2015-10-20 14:48:22)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #12 2015-10-20 15:17:30

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Lightest gas : Hydrogen : Density at STP : 0 degrees Centigrade and 101.325 kPa :

When liquid at melting point

Second lightest gas : Helium : Density at STP : at 0 degrees Centigrade and 101.525 kPa :

When liquid at Melting Point

Last edited by Jai Ganesh (2015-10-20 15:25:09)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #13 2015-10-23 11:55:57

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Planetary Data Distance Table
Planet     : Distance      (from Sun)         :    Diameter
Mercury     : 57,910,000 km :0.387 A.U.   : 4,800 km
Venus     : 108,200,000 km :  0.723 A.U. : 12,100 km
Earth     : 149,600,000 km :  1.000 A.U  : 12,750 km
Mars             : 227,940,000 km : 1.524 A.U.  : 6,800 km
Jupiter     : 778,330,000 km : 5.203 A.U.  : 142,800 km
Saturn        : 1,424,600,000 km : 9.523 A.U.: 120,660 km
Uranus      : 2,873,550,000 km: 19.208 A.U. : 51,800 km
Neptune       : 4,501,000,000 km :  30.087 A.U. : 49,500 km
Pluto      : 5,945,900,000 km : 39.746 A.U. :    3,300 km

Last edited by Jai Ganesh (2015-10-26 20:03:11)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #14 2015-10-23 14:07:29

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Helium gas has a density of 0.164g/liter It is 0.139 times as dense as air.
Air has a density of 1.18g/liter.

Material : Specific Gravity
Balsa wood : 0.2
Oak wood  : 0.75
Ethanol : 0.78
Water : 1
Table salt : 2.17
Aluminium: 2.7
Iron     : 7.87
Copper : 8.96
Mercury : 13.56
Depleted uranium : 19.1
Gold     : 19.3
Osmium : 22.59

(Samples may vary, and these figures are approximate.)
Urine normally has a specific gravity between 1.003 and 1.035.
Blood normally has a specific gravity of ~1.060.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #15 2015-10-23 14:58:56

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Heat capacity or thermal capacity is a measurable physical quantity equal to the ratio of the heat added to (or removed from) an object to the resulting temperature change. The SI unit of heat capacity is joule per kelvin

and the dimensional form is
. Specific heat is the amount of heat needed to raise the temperature of a certain mass 1 degree Celsius.

Last edited by Jai Ganesh (2015-10-23 15:11:04)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #16 2015-10-23 15:50:35

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Mass heat capacity of building materials

(Usually of interest to builders and solar designers)
Mass heat capacity of building materials Substance  : Phase : cP :

Asphalt : solid  : 0.920
Brick  : solid  : 0.840
Concrete :    solid : 0.880
Glass, silica : solid : 0.840
Glass, crown : solid : 0.670
Glass, flint : solid : 0.503
Glass, pyrex : solid : 0.753
Granite : solid :     0.790
Gypsum : solid  : 1.090
Marble, mica  : solid  : 0.880
Sand : solid : 0.835
Soil : solid :  0.800
Water : liquid  : 4.1813
Wood : solid : 1.7 (1.2 to 2.9)
Substance     : Phase  : cP :

Last edited by Jai Ganesh (2015-10-23 16:05:10)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #17 2015-10-23 20:40:28

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

In optics the refractive index or index of refraction n of an optical medium is a dimensionless number that describes how light, or any other radiation, propagates through that medium. It is defined as. where c is the speed of light in vacuum and v is the phase velocity of light in the medium.

Some representative refractive indices Material     :  λ (nm)     :  n
Vacuum         : 1 (by definition)
Air at STP         : 1.000277
Gases at 0 °C and 1 atm
Air : 589.29     : 1.000293
Carbon dioxide     : 589.29 : 1.00045
Helium : 589.29     : 1.000036
Hydrogen     589.29 : 1.000132
Liquids at 20 °C
math trisulfide and sulfur in methylene iodide :    1.9
Benzene : 589.29 : 1.501
Carbon disulfide    :589.29 : 1.628
Carbon tetrachloride :    589.29  : 1.461
Ethanol (ethyl alcohol) : 589.29 : 1.361
Silicone oil :     1.336-1.582
Water : 589.29     : 1.3330
10% Glucose solution in water :    589.29  :    1.3477
20% Glucose solution in water :     589.29  :  1.3635
60% Glucose solution in water :    589.29  : 1.4394
Solids at room temperature
Titanium dioxide (rutile phase) :589.29 :  2.614
Diamond :  589.29 :    2.419
Strontium titanate  :    589.29 : 2.41
Amber : 589.29     : 1.55
Fused silica (also called fused quartz)     : 589.29 : 1.458
Sodium chloride : 589.29 :     1.544
Other materials
Liquid helium :    1.025
Water ice     : 1.31
Cornea (human) : 1.373/1.380/1.401
Lens (human)      : 1.386 - 1.406
Acetone         : 1.36
Ethanol         : 1.36
Glycerol         : 1.4729
Bromine         : 1.661
Polytetrafluoroethylene (Teflon AF) : 1.315
Polytetrafluoroethylene (Teflon) :    1.35 - 1.38     :
Cytop         : 1.34
Sylgard 184 (polydimethylsiloxane) : 1.4118
Polylactic acid     :1.46
Acrylic glass     : 1.490 - 1.492
Polycarbonate     :    1.60
Poly(methyl methacrylate) (PMMA) :    1.4893 - 1.4899
PETg         : 1.57
Polyethylene terephthalate (PET) : 1.5750
Kerosene      : 1.39
Crown glass (pure) :    1.50 - 1.54
Flint glass (pure) :    1.60 - 1.62
Crown glass (impure) : 1.485 - 1.755
Flint glass (impure)     : 1.523 - 1.925
Pyrex (a borosilicate glass)     : 1.470
Cryolite :     1.338
Halite (rock salt) : 1.516
Sapphire     : 1.762–1.778
Sugar solution, 25% :     1.3723
Sugar solution, 50%     : 1.4200
Sugar solution, 75%     :    1.4774
Cubic zirconia :    2.15 - 2.18
Potassium niobate (KNbO3) : 2.28
Silicon carbide (moissanite)     : 2.65 - 2.69
Cinnabar (mercury sulfide)     : 3.02
Gallium(III) phosphide : 3.5
Gallium(III) math :3.927
Zinc oxide : 390 : 2.4
Germanium     3000 - 16000     4.05 - 4.01
Silicon     1200 - 8500     3.48 - 3.42

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #18 2015-10-24 01:57:46

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Table of Specific Heats for Various Substances
Substance
Air (50 degrees C) : 1046 : 0.250
Aluminum, Al :     900 :     0.215
Benzene, C6H6     : 1750  :    0.418
Copper, Cu :    387 :     0.0924
Glass     : 837 :    0.200
Gold, Au     : 130 : 0.0310
Ice, H2O (-10 degrees C to 0 degrees C) :    2093 :    0.500
Iron, Fe      : 452 : 0.108
Lead, Pb     : 128  : 0.0305
Marble     : 858 :    0.205
Methanol or methyl Alcohol, CH3OH : 2549     : 0.609
Mercury, Hg     : 138  : 0.0330
Silver, Ag     : 236 : 0.0564
Soil     : 1046 :    0.250
Steam, H2O (100 degrees C)  :2009 :    0.480
Water, H2O (0 degrees C to 100 degrees C)     : 4186 : 1.000
Wood     : 1674 :    0.400

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #19 2015-10-24 06:24:31

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 700 nm. In terms of frequency, this corresponds to a band in the vicinity of 430–770 THz.

Color     : Wavelength     : Frequency     : Photon energy
violet     : 380–450 nm     : 668–789 THz     : 2.75–3.26 eV
blue             : 450–495 nm     : 606–668 THz     : 2.50–2.75 eV
green        :495–570 nm    :526–606 THz     : 2.17–2.50 eV
yellow     : 570–590 nm     : 508–526 THz     : 2.10–2.17 eV
orange     : 590–620 nm     : 484–508 THz     : 2.00–2.10 eV
red             : 620–750 nm     : 400–484 THz     : 1.65–2.00 eV

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #20 2015-10-24 07:02:44

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Tables

In the standard atmosphere:

T0 is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m/s (= 1086.9 ft/s = 1193 km/h = 741.1 mph = 644.0 kn). Values ranging from 331.3-331.6 may be found in reference literature, however;
T20 is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m/s (= 1126.0 ft/s = 1236 km/h = 767.8 mph = 667.2 kn);
T25 is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m/s (= 1135.6 ft/s = 1246 km/h = 774.3 mph = 672.8 kn).

In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure or density (since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere—actual conditions may vary.
Effect of temperature on properties of air Temperature
T (°C)     : Speed of sound
c (m/s)     : Density of air
ρ (kg/cubic meters)     : Characteristic specific acoustic impedance
z0 (Pa·s/m)
35      : 351.88     : 1.1455     : 403.2
30       : 349.02     : 1.1644     : 406.5
25       : 346.13     : 1.1839     : 409.4
20       : 343.21     : 1.2041     : 413.3
15       : 340.27  : 1.2250     : 416.9
10       : 337.31  : 1.2466     : 420.5
5       : 334.32      : 1.2690     : 424.3
0       : 331.30      : 1.2922     : 428.0
−5       : 328.25      : 1.3163     : 432.1
−10       : 325.18      : 1.3413     : 436.1
−15       : 322.07   : 1.3673     : 440.3
−20       : 318.94      : 1.3943     : 444.6
−25       : 315.77      : 1.4224     : 449.1

Last edited by Jai Ganesh (2015-10-26 20:19:08)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #21 2015-10-24 12:46:38

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

Modern classification

The modern classification system is known as the Morgan–Keenan (MK) classification. Each star is assigned a spectral class from the older Harvard spectral classification and a luminosity class using Roman numerals as explained below, forming the star's spectral type.

Harvard spectral classification

The Harvard classification system is a one-dimensional classification scheme using single letters of the alphabet, optionally with numeric subdivisions, to group stars according to their spectral characteristics. Main-sequence stars vary in surface temperature from approximately 2,000 to 50,000 K, whereas more-evolved stars can have temperatures above 100,000 K. Physically, the classes indicate the temperature of the star's atmosphere and are normally listed from hottest to coldest.
Class     Effective temperature     Conventional color description     Actual apparent color     Main-sequence mass
(bolometric)     Hydrogen
lines     Fraction of all
main-sequence stars

O     ≥ 30,000 K     blue     blue     ≥ 16 M☉     ≥ 6.6 R☉     ≥ 30,000 L☉     Weak     ~0.00003%
B     10,000–30,000 K  blue white     blue white     2.1–16 M☉     1.8–6.6 R☉     25–30,000 L☉     Medium     0.13%
A     7,500–10,000 K     white     blue white     1.4–2.1 M☉     1.4–1.8 R☉     5–25 L☉     Strong     0.6%
F     6,000–7,500 K     yellow white     white     1.04–1.4 M☉     1.15–1.4 R☉     1.5–5 L☉     Medium     3%
G     5,200–6,000 K     yellow     yellowish white     0.8–1.04 M☉     0.96–1.15 R☉     0.6–1.5 L☉     Weak     7.6%
K     3,700–5,200 K     orange  pale yellow orange     0.45–0.8 M☉     0.7–0.96 R     0.08–0.6 L☉ Very weak     12.1%
M     2,400–3,700 K     red     light orange red     0.08–0.45 M☉     ≤ 0.7 R☉     ≤ 0.08 L☉     Very weak     76.45%

The spectral classes O through M, as well as other more specialized classes discussed later, are subdivided by Arabic numerals (0–9), where 0 denotes the hottest stars of a given class. For example, A0 denotes the hottest stars in the A class and A9 denotes the coolest ones.

Fractional numbers are allowed; for example, the star Mu Normae is classified as O9.7. The Sun is classified as G2.

The solar mass (M☉) is a standard unit of mass in astronomy that is used to indicate the masses of other stars, as well as clusters, nebulae and galaxies. It is equal to the mass of the Sun, about two nonillion kilograms:

M☉ =

Solar radius is a unit of distance used to express the size of stars in astronomy equal to the current radius of the Sun:

The solar luminosity, L☉, is a unit of radiant flux (power emitted in the form of photons) conventionally used by astronomers to measure the luminosity of stars. It is defined in terms of the Sun's output. One solar luminosity is

, or
. This does not include the solar neutrino luminosity, which would add 0.023 L☉. The Sun is a weakly variable star, and its luminosity therefore fluctuates. The major fluctuation is the eleven-year solar cycle (sunspot cycle) that causes a periodic variation of about ±0.1%. Other variations over the last 200–300 years is thought to be much smaller than this.

Last edited by Jai Ganesh (2015-10-24 12:50:35)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #22 2015-10-24 16:38:46

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

The Sun in visible wavelength with filtered white light on 8 July 2014. Characteristic limb darkening and numerous sunspots are visible.
Observation data
Mean distance
from Earth

8 min 19 s at light speed
Visual brightness (V)     -26.74
Absolute magnitude     4.83
Spectral classification     G2V
Metallicity     Z = 0.0122
Angular size     31.6–32.7′

Orbital characteristics
Mean distance from Milky Way core

27200 light-years
Galactic period
Julian Year (a)
Velocity
(orbit around the center of the Milky Way)
≈ 20 km/s (relative to average velocity of other stars in stellar neighborhood)
≈ 370 km/s (relative to the cosmic microwave background)
Physical characteristics
= 109 × Earth.
Equatorial circumference
= 109 × Earth
Flattening

Surface area =
square kilometers.
12000 × Earth
Volume =
cubic kilometers = 1300000 × Earth
Mass =
=
333000 × Earth
Average density     1.408 grams per cubic centimeters.
0.255 × Earth
Center density (modeled) = 162.2 grams per cubic centimeters = 12.4 × Earth
Equatorial surface gravity =
meters per second square = 27.94 g
27542.29 cgs
28 × Earth
Escape velocity = (from the surface)     617.7 km/s = 55 × Earth
Temperature     = Center (modeled):

Photosphere (effective): 5778 K
Corona:

Luminosity (Lsol) =

efficacy
.
Age
billion years
Rotation characteristics
Obliquity     7.25°
(to the ecliptic)
67.23°
(to the galactic plane)
Right ascension
of North pole     286.13°
19 h 4 min 30 s
Declination
of North pole     +63.87°
63° 52' North
Sidereal rotation period
(at equator)     25.05 days
(at 16° latitude)     25.38 days
25 d 9 h 7 min 12 s
(at poles)     34.4 days
Rotation velocity
(at equator)

Photospheric composition (by mass)
Hydrogen     73.46%
Helium     24.85%
Oxygen     0.77%
Carbon     0.29%
Iron             0.16%
Neon     0.12%
Nitrogen     0.09%
Silicon     0.07%
Magnesium     0.05%
Sulfur     0.04%

Last edited by Jai Ganesh (2015-10-24 23:25:48)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #23 2015-10-25 01:39:40

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of speed is the metre per second (m/s). In dry air at 20 °C, the speed of sound is 343.2 metres per second (1,126 ft/s). This is 1,236 kilometres per hour (768 mph; 667 kn), or a kilometre in 2.914 s or a mile in 4.689 s.

Sir Isaac Newton computed the speed of sound in air as 979 feet per second (298 m/s), which is too low by about 15%, but had neglected the effect of fluctuating temperature; that was later rectified by Laplace.

During the 17th century, there were several attempts to measure the speed of sound accurately, including attempts by Marin Mersenne in 1630 (1,380 Parisian feet per second), Pierre Gassendi in 1635 (1,473 Parisian feet per second) and Robert Boyle (1,125 Parisian feet per second).

In 1709, the Reverend William Derham, Rector of Upminster, published a more accurate measure of the speed of sound, at 1,072 Parisian feet per second. Derham used a telescope from the tower of the church of St Laurence, Upminster to observe the flash of a distant shotgun being fired, and then measured the time until he heard the gunshot with a half second pendulum. Measurements were made of gunshots from a number of local landmarks, including North Ockendon church. The distance was known by triangulation, and thus the speed that the sound had travelled could be calculated.

Practical formula for dry air

The approximate speed of sound in dry (0% humidity) air, in meters per second, at temperatures near 0 °C, can be calculated from

,

where

is the temperature in degrees Celsius (°C).

In the standard atmosphere:

is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m/s (= 1086.9 ft/s = 1193 km/h = 741.1 mph = 644.0 kn). Values ranging from 331.3-331.6 may be found in reference literature, however;

is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m/s (= 1126.0 ft/s = 1236 km/h = 767.8 mph = 667.2 kn);

is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m/s (= 1135.6 ft/s = 1246 km/h = 774.3 mph = 672.8 kn).

In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure or density (since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere—actual conditions may vary.

Last edited by Jai Ganesh (2015-10-25 01:44:01)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #24 2015-10-25 07:03:56

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #25 2015-10-25 14:50:09

Jai Ganesh
Registered: 2005-06-28
Posts: 47,752

### Re: Micro / Macro numbers in Science

In SI units, thermal conductivity is measured in watts per meter kelvin

. The dimension of thermal conductivity is
. These variables are (M)mass, (L)length, (T)time, and (Θ)temperature. In Imperial units, thermal conductivity is measured in BTU/(hr·ft⋅°F).

Thermal Conductivity :  k : W/(m K)
Material/Substance :    Temperature :

25    125    225
Acetals     : 0.23
Acetone     : 0.16
Acetylene (gas) : 0.018
Acrylic     : 0.2
Air, atmosphere (gas) : 0.024
Air, elevation 10000 m : 0.020
Alcohol     : 0.17
Aluminum     : 205     : 215     : 250
Aluminum Brass : 121
Aluminum Oxide :30
Ammonia (gas)     : 0.022
Antimony     : .5
Apple (85.6% moisture) :     0.39
Argon (gas):  0.016
Asbestos-cement board :    0.744
Asbestos-cement sheets : 0.166
Asbestos-cement : 2.07
Asbestos, loosely packed :     0.15
Asbestos mill board     : 0.14
Asphalt     : 0.75
Balsa wood : 0.048
Bitumen     : 0.17
Bitumen/felt layers :     0.5
Beef, lean (78.9 % moisture) :     0.43 - 0.48
Benzene     : 0.16
Beryllium     : 218
Bitumen     : 0.17
Blast furnace gas (gas) :    0.02
Brass     : 109
Breeze block :     0.10 - 0.20
Brick dense :1.31
Brick, insulating : 0.15
Brickwork, common (Building Brick)     : 0.6 -1.0
Brickwork, dense : 1.6
Bromine (gas)  : 0.004
Bronze     : 110
Butter (15% moisture content) :    0.20
Calcium silicate     : 0.05
Carbon  : 1.7
Carbon dioxide (gas) : 0.0146
Carbon monoxide :    0.0232
Cellulose, cotton, wood pulp and regenerated : 0.23
Cellulose acetate, molded, sheet : 0.17 - 0.33
Cellulose nitrate, celluloid :    0.12 - 0.21
Cement, portland : 0.29
Cement, mortar     : 1.73
Chalk     : 0. 09
Charcoal     : 0.2
Chlorinated poly-ether :    0.13
Chlorine (gas)     : 0.0081
Chrome Nickel Steel (18% Cr, 8 % Ni)     : 16.3
Chromium : 94
Clay, dry to moist : 0.15 - 1.8
Clay, saturated     : 0.6 - 2.5
Coal     : 0.2
Cobalt : 69
Cod (83% moisture content) :     0.54
Concrete, lightweight     : 0.1 - 0.3
Concrete, medium  : 0.4 - 0.7
Concrete, dense : 1.0 - 1.8
Concrete, stone     : 1.7
Constantan : 22
Copper     :  401     : 400     : 398
Corian (ceramic filled) : 1.06
Cork board     : 0.043
Cork, re-granulated :     0.044
Cork     : 0.07
Cotton  :    0.04
Cotton wool : 0.029
Carbon Steel :     54 :    51 :    47
Cotton Wool insulation : 0.029
Diamond     : 1000
Diatomaceous earth (Sil-o-cel) : 0.06
Diatomite : 0.12
Earth, dry     : 1.5
Engine Oil     : 0.15
Ethane (gas) : 0.018
Ether : 0.14
Ethylene (gas) : 0.017
Epoxy : 0.35
Ethylene glycol     : 0.25
Feathers     : 0.034
Felt insulation : 0.04
Fiberglass     : 0.04
Fiber insulating board : 0.048
Fiber hardboard     : 0.2
Fire-clay brick
1.4
Fluorine (gas) : 0.0254
Foam glass  : 0.045
Freon R-12 (gas) :  0.007
Freon R-12 (liquid) : 0.09
Gasoline : 0.15
Glass : 1.05
Glass, Pearls, dry : 0.18
Glass, Pearls, saturated : 0.76
Glass, window : 0.96
Glass, wool Insulation : 0.04
Glycerol  : 0.28
Gold     : 310  : 312  : 310
Granite  : 1.7 - 4.0
Gravel : 0.7
Ground or soil, very moist area :  1.4
Ground or soil, moist area     : 1.0
Ground or soil, dry area : 0.5
Ground or soil, very dry area : 0.33
Gypsum board     : 0.17
Hairfelt  : 0.05
Hardboard high density : 0.15
Hardwoods (oak, maple..) : 0.16
Helium (gas) : 0.142
Honey (12.6% moisture content) : 0.5
Hydrochloric acid (gas) : 0.013
Hydrogen (gas)     : 0.168
Hydrogen sulfide (gas) : 0.013
Ice (0 degrees C, 32 degrees F)     : 2.18
Insulation materials  : 0.035 - 0.16
Iridium  : 147
Iron     : 80     : 68 : 60
Iron, wrought : 59
Iron, cast     : 55
Kapok insulation : 0.034
Kerosene     : 0.15
Krypton (gas) : 0.0088
Leather, dry : 0.14
Limestone     : 1.26 - 1.33
Magnesia insulation (85%) :  0.07
Magnesite     : 4.15
Magnesium : 156
Marble : 2.08 - 2.94
Mercury, liquid : 8.3
Methane (gas)  : 0.030
Methanol     : 0.21
Mica     : 0.71
Milk     : 0.53
Mineral wool insulation materials, wool blankets .. : 0.04
Molybdenum :     138
Monel     : 26
Neon (gas)     : 0.046
Neoprene     : 0.05
Nickel     : 91
Nitric oxide (gas) :     0.0238
Nitrogen (gas)     : 0.024
Nitrous oxide (gas)     :0.0151
Nylon 6, Nylon 6/6 :    0.25
Oil, machine lubricating SAE 50 :    0.15
Olive oil     : 0.17
Oxygen (gas) :    0.024
Paper     : 0.05
Paraffin Wax  : 0.25
Perlite, atmospheric pressure :     0.031
Perlite, vacuum     : 0.00137
Phenolic cast resins     0.15
Phenol-formaldehyde moulding compounds :    0.13 - 0.25
Plaster light     : 0.2
Plaster, metal lath : 0.47
Plaster, sand     : 0.71
Plaster, wood lath :    0.28
Plasticine     : 0.65 - 0.8
Plastics, foamed (insulation materials) : 0.03
Platinum     : 70     : 71     72
Plutonium     : 6.7         :
Plywood     : 0.13
Polycarbonate :    0.19
Polyester     : 0.05
Polyethylene low density, PEL : 0.33
Polyethylene high density, PEH :     0.42 - 0.51
Polyisoprene natural rubber : 0.13
Polyisoprene hard rubber     : 0.16
Polymethylmethacrylate : 0.17 - 0.25
Polypropylene, PP : 0.1 - 0.22
Polystyrene, expanded styrofoam : 0.03
Polystyrol     : 0.043
Polyurethane foam : 0.03
Porcelain     : 1.5
Potato, raw flesh : 0.55
Propane (gas)     : 0.015
Polytetrafluoroethylene, Teflon, PTFE :    0.25
Polyvinylchloride, PVC : 0.19
Pyrex glass     : 1.005
Quartz mineral     : 3
Rock, solid :     2 - 7
Rock, porous volcanic (Tuff) : 0.5 - 2.5
Rock Wool insulation :  0.045
Rubber, cellular     : 0.045
Rubber, natural     : 0.13
Salmon (73% moisture content) : 0.50
Sand, dry     : 0.15 - 0.25
Sand, moist     : 0.25 - 2
Sand, saturated :     2 - 4
Sandstone :1.7
Sawdust     : 0.08
Sheep wool     : 0.039
Silica aerogel     : 0.02
Silicone cast resin : 0.15 - 0.32
Silicone oil :0.1
Silver     : 429
Slag wool     : 0.042
Slate     : 2.01
Snow (temp <
C     0.05 - 0.25
Sodium     : 135 (solid)     : 86 (liquid)
Softwoods (fir, pine ..) : 0.12
Soil, clay     : 1.1
Soil, with organic matter :     0.15 - 2
Soil, saturated :     0.6 - 4
Steam, saturated : 0.0184
Steam, low pressure     : 0.0188
Steel, Carbon 1%     : 43
Stainless Steel     : 16     : 17     : 19
Straw slab insulation, compressed : 0.09
Styrofoam:      : 0.033
Sulfur dioxide (gas) :     0.0086
Sugars     : 0.087 - 0.22
Teflon     : 0.25
Timber     : 0.14
Tin Sn     : 67
Titanium     : 22
Tungsten     : 174
Uranium     : 27.6
Urethane foam     : 0.021
Vacuum :    0
Vermiculite granules :     0.065
Vinyl ester     : 0.25
Water     : 0.58
Water, vapor (steam) :        0.016
Wheat flour :0.45
Wood across the grain, white pine :     0.12
Wood across the grain, balsa :    0.055
Wood across the grain, yellow pine, timber : 0.147
Wood, oak :    0.17
Wool, felt :    0.07
Wood wool, slab :     0.1 - 0.15
Xenon (gas) :    0.0051
Zinc Zn :    116

Last edited by Jai Ganesh (2015-10-27 15:54:04)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline