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Newtonian Escape and Circular-Orbit Speeds

Calculate newtonian escape and circular-orbit speeds with compatible units, known-value inputs and clearly stated model assumptions.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked inputs, Escape velocity (v==e==) is approximately 11.553614 kmps.

vesc = √(2GM/R); vcircular = vesc/√2

Worked example

Enter these known values and leave the other values blank.

Mass (M)
0.167442483506915374568835604969692910485248317203040755500485583202170054586249623254412109 Earths
Radius (R)
0.156961230576047716214095118505729084916025741641814471825459111599434939569926228221629258 R⊕
First cosmic velocity
8.17 km/s
Escape velocity (v==e==)
11.554 km/s

Assumptions and limitations

  • Treat the body as spherical and the launch radius as distance from its center, not altitude above its surface.
  • Ignore atmosphere, rotation, propulsion, other bodies and relativistic effects. Circular-orbit speed is evaluated at the same radius.
  • G = 6.67430 × 10⁻¹¹ in SI has measurement uncertainty; many displayed digits do not make the physical inputs exact.
  • Numerical arithmetic uses 64 significant digits; displayed values are rounded separately. Captured particle-mass and astronomical unit conversions retain their stated approximations.

Common questions

Which inputs and assumptions does this result use?

Treat the body as spherical and the launch radius as distance from its center, not altitude above its surface.

References

Bookify retains the captured physical relationship and inverse controls, while replacing older or rounded constants with the 2022 CODATA values and full-precision π where applicable. Measured constants retain their physical uncertainty.

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