Constants

From HvWiki

1 Physical Constants
2 Mathematical Constants

Physical Constants

Gravitational constant

The gravitational constant is a physical constant which appears in Newton's law of universal gravitation and in Einstein's theory of general relativity.

$G = \left(6.67428 \plusmn 0.0007 \right) \times 10^{-11} \ \mbox{m}^3 \ \mbox{kg}^{-1} \ \mbox{s}^{-2} \,$

$= \left(6.67428 \plusmn 0.0007 \right) \times 10^{-11} \ \mbox{N} \ \mbox{m}^2 \ \mbox{kg}^{-2} \,$

$= \left(6.67428 \plusmn 0.0007 \right) \times 10^{-8} \ \mbox{cm}^3 \ \mbox{g}^{-1} \ \mbox{s}^{-2} \,$

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Electron Charge

The absolute charge of an electron.

$e = 1.60 \times 10^{-19} C$

Of course, that means $1/e = 6.25 \times 10^{18}$ is the number of electrons in a coulomb.

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Permeability and Permittivity of Free Space

The permeability of free space is the permeability of a vacuum.

$\mu_0 = 4\pi \times 10^{-7} Tm/A \approx 1.257 \times 10^{-6}Tm/A$

This is an exact value. A value by definition.

Likewise is the permittivity of free space.

$\epsilon_0 = 1/\mu_0c^2 \approx 8.85 \times 10^{-12} C^2Nm^2$

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Speed of Light

In vacuum: $c = 299792458 m / s$

According to Special Relativity, this really is a constant. Now matter how quickly you run towards or away from a light source, the light will come at you at exactly $c$ .

In any medium in general, the speed of light is $\sqrt\frac{1}{\mu\epsilon}$

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Avagadro's Number

The number of particles in 1 mole of any substance.

$N_A = 6.02 \times 10^{26}$

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Mathematical Constants

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Pi

This is most commonly defined as the ratio of the circumference of any circle to its diameter. It is, however, useful in situations seemingly unrelated to circles.

$\pi \approx 3.141593 \approx 355/113 \approx 22/7$

The approximation $22 / 7$ is good enough for a lot of engineering work. In practice, some approximation must be used since $π$ cannot be written as a finite expression.

A convenient mnemonic to remember the first 20 decimal places of pi (more than you need for double precision reals) is

I wish I could determine pi,
Eureka! cried the great inventor,
Christmas pudding, Christmas pie,
Is the problem's very centre.

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