Cosmic Velocities Calculator

The Cosmic Velocities Calculator will calculate:

  1. 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.
  2. 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.
  3. 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.

Cosmic Velocities Calculator
Examples [click to see formula and calculations for each planet within our solar system]
Cosmic Velocities Calculator Results (detailed calculations and formula below)
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
v1 (cosmic) = √G × Mp/Rp
v1 (cosmic) = √ × /
v1 (cosmic) = √/
v1 (cosmic) = √
v1 (cosmic) =
The second cosmic velocity of an object launched from the surface of a planet calculations
v1 (cosmic) = √2 × G × Mp/Rp
v1 (cosmic) = √2 × × /
v1 (cosmic) = √/
v1 (cosmic) = √
v1 (cosmic) =
The third cosmic velocity of an object launched from the surface of a planet calculations
v = √2 × G × MSun/RSun-planet
v = √2 × × /
v = √/
v = √
v =
Input Values
Mass of the planet (Mp) kg
Radius of planet (Rp) m
Distance of the planet from the Sun (RS) m
Gravitational Constant (G) × 10N × m2/kg2
Mass of the Sun (MS) × 10kg

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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Discover Physics with free Physics Revision Notes and Physics Calculator: Cosmic Velocities. This image shows the properties and cosmic velocities formula for the Cosmic Velocities. The Cosmic Velocities Calculator will calculate the first cosmic velocity of an object, the second cosmic velocity of an object and the third cosmic velocity of an object.

Related Physics Sections with Tutorials

Section 3: Kinematics

Section 4: Dynamics

Section 21: Astrophysics

The first cosmic velocity of an object launched from the surface of a planet Formula and Calculation

v1 (cosmic) = √G × Mp/Rp

The second cosmic velocity of an object launched from the surface of a planet Formula and Calculation

v1 (cosmic) = √2 × G × Mp/Rp

The third cosmic velocity of an object launched from the surface of a planet Formula and Calculation

v = √2 × G × MSun/RSun-planet

Gravitation Physics Tutorials associated with the Cosmic Velocities Calculator

The following Physics tutorials are provided within the Gravitation section of our Free Physics Tutorials. Each Gravitation tutorial includes detailed Gravitation formula and example of how to calculate and resolve specific Gravitation questions and problems. At the end of each Gravitation tutorial you will find Gravitation revision questions with a hidden answer that reveals when clicked. This allows you to learn about Gravitation and test your knowledge of Physics by answering the test questions on Gravitation.

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