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The Cosmic Velocities Calculator will calculate:

- The first cosmic velocity of an object, i.e. the minimum velocity it must have when launched from the surface of a planet of mass M, which has a radius R, to become an artificial satellite.
- The second cosmic velocity of an object, i.e. the minimum velocity it must have when launched from the surface of a planet of mass M, which has a radius R, to get away from the planet but still rotate around the Sun.
- The third cosmic velocity of an object, i.e. the minimum velocity it must have when launched from the surface of a planet of mass M, which has a radius R, to leave our solar system.

The Cosmic Velocities Calculator includes examples for each of the planets within our solar system, click on the name of the planets to automatically update the mass of the planet, radius of the planet and distance of the planet from the sun. Alternatively you can enter your own values and adjust the gravitational constant and mass of the sun as required to test theory.

Examples [click to see formula and calculations for each planet within our solar system] | |
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The first cosmic velocity of an object launched from the surface of a planet is m/s |

The second cosmic velocity of an object launched from the surface of a planet is m/s |

The third cosmic velocity of an object launched from the surface of a planet is m/s |

The first cosmic velocity of an object launched from the surface of a planet calculations |
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v_{1} (cosmic) = √G × M_{p}/R_{p}v _{1} (cosmic) = √ × /v _{1} (cosmic) = √/v _{1} (cosmic) = √v _{1} (cosmic) = |

The second cosmic velocity of an object launched from the surface of a planet calculations |

v_{1} (cosmic) = √2 × G × M_{p}/R_{p}v _{1} (cosmic) = √2 × × /v _{1} (cosmic) = √/v _{1} (cosmic) = √v _{1} (cosmic) = |

The third cosmic velocity of an object launched from the surface of a planet calculations |

v = √2 × G × M_{Sun}/R_{Sun-planet}v = √ 2 × × /v = √ /v = √ v = |

Input Values |

Mass of the planet (M_{p}) kg |

Radius of planet (R_{p}) m |

Distance of the planet from the Sun (R_{S}) m |

Gravitational Constant (G) × 10^{}N × m2/kg2 |

Mass of the Sun (M_{S}) × 10^{}kg |

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each cosmic velocities calculation, the Cosmic Velocities Calculator will automatically calculate the results and update the Physics formula elements with each element of the cosmic velocities calculation. You can then email or print this cosmic velocities calculation as required for later use.

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v_{1} (cosmic) = √*G × M*_{p}*/**R*_{p}

v_{1} (cosmic) = √*2 × G × M*_{p}*/**R*_{p}

v = √*2 × G × M*_{Sun}*/**R*_{Sun-planet}

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