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# Formula Sheet

## Meaning of the characters

An alphabetical list of the characters and their meanings on our webpage:

a: (A constant) acceleration

d: Distance

E: Energy

f: Frequency

F: Force

L: Luminosity

: Wavelength

m: Mass

M: Mass (of the black hole)

P: Power

r: Distance

t: Time

T: Temperature

v: Velocity

## Important constants

A list of all constants we used on our webpage:

c: Speed of Light;

G: Gravitational constant;

h: Planck constant;

k: Boltzmann constant;

: Stefan-Boltzmann constant;

## Important values

Here are some values you might want to look up:

The mass of the earth is about

The mass of the black hole in "The Hole Man" is about

The mass of the sun is about

The frequency of orange light:

The frequency of visible light lies between and

The luminosity of the sun:

## Initial formulas

Here is a list of those formulas we used, but didn't derive, on our webpages:

1. Classical kinetic energy equation:

2. Heisenberg's principle of uncertainty:

3. Planck's equation:

4. Kinetic energy of a mass after being constantly accelerated over a certatin distance:

5. Distance light moves within a certain time:

6. Mass-energy equivalence relation:

7. Average energy of a photon of black body radiation:

8. Stefan-Boltzmann formula:

9. Newton's second law of motion:

F = ma

## Derived Formulas

Here is a list of formulas we derived on our webpages:

Derivation

Derivation

3. Energy of a photon of Hawking radiation:

Derivation

4. Temperature of a black hole:

Derivation

5. Luminosity of a black hole:

Derivation

6. Lifetime of a black hole:

; where .
Derivation

7. Gravitational potential energy:

Derivation

8. Newton's law of gravitation:

Derivation

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"Black holes aren't black - After Hawking they shine!"
Presented by Angie, Matthias and Thorsten
Team C007571,ThinkQuest Internet Challenge 2000.