The escape velocity equation is a mathematical formula that allows us to calculate the escape velocity of an object based on the mass and radius of the celestial body it is escaping from.

To use the escape velocity calculator provided above, simply select the units for mass, distance, and velocity, enter the values for mass and distance, and click the “Calculate” button.

The calculator will use the escape velocity equation to calculate the escape velocity and display it in the chosen velocity units.

It’s important to note that the escape velocity is a theoretical minimum velocity required for an object to escape the gravitational pull of a celestial body.

In reality, other factors such as atmospheric drag, atmospheric density, and gravitational assists can affect the actual escape velocity required for space missions.

## Escape Velocity Equation

The escape velocity equation is given by:

v = √(2GM/r)

Escape Velocity formula **V = √2GM/R**

Where:

V: Escape Velocity, in m/s

M: Planet Mass, in Kg

R: Planet Radius, in m

G: Universal Gravitational Constant, is 6.6726 × 10^{-11}N.m^{2}/kg^{2}

Escape Velocity describes the minimum velocity for an object to escape the gravitational field of a planet.

## How to Calculate Escape Velocity

To calculate the escape velocity of an object, we need to know the mass and radius of the celestial body it is escaping from. We can then use the escape velocity equation to calculate the minimum velocity required for the object to escape the gravitational pull of the celestial body.

Here’s a step-by-step guide on how to calculate escape velocity:

- Determine the mass and radius of the celestial body the object is escaping from.
- Convert the units of mass and radius to kilograms and meters, respectively.
- Plug the values of mass and radius into the escape velocity equation:

v = √(2GM/r)

- Calculate the square root of the result to obtain the escape velocity.
- Convert the escape velocity to the desired units, such as kilometers per second or miles per hour.

## First Cosmic Velocity

The first cosmic velocity is the velocity required for an object to achieve a stable orbit around a celestial body, without falling back to the surface or flying off into space. It is also known as the circular velocity or the orbital velocity.

The first cosmic velocity can be calculated using the following formula:

v = √(GM/r)

Where: v = first cosmic velocity (in meters per second) G = gravitational constant (6.6743 × 10^-11 N m^2/kg^2) M = mass of the planet or celestial object (in kilograms) r = distance from the center of the planet or celestial object to the object in orbit (in meters)

## Typical Values

The escape velocity and first cosmic velocity vary depending on the mass and radius of the celestial body. Here are some typical values for the escape velocity and first cosmic velocity of several celestial bodies in our solar system:

- Mercury: 4.3 km/s (escape velocity), 3.8 km/s (first cosmic velocity)
- Venus: 10.3 km/s (escape velocity), 7.4 km/s (first cosmic velocity)
- Earth: 11.2 km/s (escape velocity), 7.9 km/s (first cosmic velocity)
- Moon: 2.4 km/s (escape velocity), 1.7 km/s (first cosmic velocity)
- Mars: 5.0 km/s (escape velocity), 5.0 km/s (first cosmic velocity)
- Jupiter: 59.6 km/s (escape velocity), 13.1 km/s (first cosmic velocity)
- Saturn: 35.6 km/s (escape velocity), 9.7 km/s (first cosmic velocity)
- Uranus: 21.3 km/s (escape velocity), 6.8 km/s (first cosmic velocity)
- Neptune: 23.8 km/s (escape velocity), 5.4 km/s (first cosmic velocity)

## Planet Escape Velocity Table

Planet | Radius (km) | Escape Velocity (km/s) |
---|---|---|

Mercury | 4878 | 4.25 |

Venus | 12104 | 10.36 |

Earth | 12756 | 11.18 |

Mars | 6787 | 5.02 |

Jupiter | 142800 | 59.54 |

Saturn | 120000 | 35.49 |

Uranus | 51118 | 21.29 |

Neptune | 49528 | 23.71 |