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

R: Schwarzschild radius

t: Time

T: Temperature

v: Velocity

Important constants

A list of all constants we used on our webpage:

c: Speed of Light; c = 3 * 10^8 m s^-1

G: Gravitational constant; G = 6.67 * 10^-11 m^3 kg^-1 s^-2

h: Planck constant; h = 6.626 * 10^-34 J s

k: Boltzmann constant; k=1.38*10^-23JK^-1

sigma: Stefan-Boltzmann constant; sigma=5.67*10^-8 W*m^-2*K^-4

Important values

Here are some values you might want to look up:

The mass of the earth is about 6*10^24kg

The mass of the black hole in "The Hole Man" is about 10^11kg

The mass of the sun is about M=1.99*10^30kg

The frequency of orange light: f=5810^14Hz

The frequency of visible light lies between f1=4*10^14Hz and f2=8.2*10^14Hz

The luminosity of the sun: L=3.86*10^26W

Initial formulas

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

1. Classical kinetic energy equation:

E=1/2 m*v^2

2. Heisenberg's principle of uncertainty:

dE*dt=h/(4*pi)

3. Planck's equation:

E=h*f

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

E = m * a * d

5. Distance light moves within a certain time:

d = c * delta t

6. Mass-energy equivalence relation:

E=m*c^2

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

<E>=2.821*k*T

8. Stefan-Boltzmann formula:

L=sigma*A*t^4

9. Newton's second law of motion:

F = ma

Derived Formulas

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

1. Schwarzschild radius:

R=(2*G*M)/c^2
Derivation

2. Lifetime of virtual photons:

delta t = 1/ (8*pi*f)
Derivation

3. Energy of a photon of Hawking radiation:

E=(h^5*c^3)/(16*pi*G*M)
Derivation

4. Temperature of a black hole:

T=(h*c^3)/(16*pi^2*k*G*M)
Derivation

5. Luminosity of a black hole:


Derivation

6. Lifetime of a black hole:

t1=M nout^3/3K; where K:=h*c^4/30720*pi^2*G^2=3.98*10^15.
Derivation

7. Gravitational potential energy:

E=G*M*m/r
Derivation

8. Newton's law of gravitation:

F=(G*m1*m2)/r^2
Derivation 

From: "Black holes aren't black - After Hawking they shine!"
/C007571
Presented by Angie, Matthias and Thorsten
Team C007571, ThinkQuest Internet Challenge 2000 (http://www.thinkquest.org).
Last modified: 2000-08-13.