# Introduction to Astrophysics/Laws and Formulae

## Contents

## Gravitation[edit]

### Kepler's Laws[edit]

- The orbit of each planet is an ellipse which has the sun at one of its foci.
- Each planet moves in such a way that the line joining it to the sun sweeps out equal areas in equal times.
- The squares of the periods of revolution of the planets about the Sun are proportional to the cubes of their mean distance from it.

### Newton's gravitational law[edit]

F = |
The gravitational force between two bodies. |

G = |
Universal gravity constant, 6.67 x 10^{−11} N m^{2} kg^{−2} |

m =_{1} |
The mass of the first body. |

m =_{2} |
The mass of the second body. |

r = |
The distance between the centres of mass of two bodies. |

## Black body radiation[edit]

temperature of the black body.

*w*= 2.90 × 10^{−3}m K

### Stefan's Law[edit]

E = |
Rate of energy radiated from the surface of a black body per unit area. |

σ = |
Stefan's constant, 5.67 × 10^{−8} W m^{−2} K^{−4} |

T = |
Surface temperature of the black body. |

## Stellar Magnitude[edit]

### Apparent Magnitude[edit]

m = |
Apparent magnitude of star. |

I = |
Intensity of light received. |

K = |
a constant |

### Pogson's Formula[edit]

m =_{1} |
Apparent magnitude of first star. |

m =_{2} |
Apparent magnitude of second star. |

I =_{1} |
Intensity of light received from first star. |

I =_{2} |
Intensity of light received from second star. |

### Absolute Magnitude[edit]

m = |
Apparent magnitude of star. |

M = |
Absolute magnitude of star. |

d = |
Distance to star in parsecs. |