For reference the orbital velocities for a circular orbit and an escape orbit (which has escape velocity) for a test particle (i.e., an object of negligible mass relative to the mass of the primary: the orbited or escaped from astro-body which is assumed to be spherically symmetric) are, respectively:

  1. v_circular = sqrt(GM/R) = (7.9053 km/s) * sqrt[(M/M_⊕)/(R/R_eq_⊕)]
  2. v_escape = sqrt(2GM/R) = (11.180 km/s) * sqrt[(M/M_⊕)/(R/R_eq_⊕)]

where M is the mass of the primary, R is the radius of launch (which is NOT necessarily the radius of the primary), gravitational constant G=6.67408(31)*10**(-11) (MKS units), Earth mass M_⊕ = 5.9722(6)*10**24 kg, Earth equatorial radius R_eq_⊕ = 6378.1370 km, and where the second forms are fiducial-value formulae which use the natural units for Earthlings (i.e., those who live on Earth): the kilometer per second (km/s), M_⊕, and R_eq_⊕.

Note v_circular and v_escape increase (↑) as M increases (M↑) and decrease (↓) as R increases (R ↑).

Note also the formulae are for the ideal cases without air drag and other complicating effects. With those effects probably somewhat higher velocities are needed than those specified by the formulae.

Finally note that the kilometer per second (km/s) is actually a good natural unit for many astrophysical velocities: e.g., order of 1 km/s, a few km/s, tens of km/s, hundreds of km/s, thousands of km/s, and at most for physical velocities (i.e., NOT geometrical velocities) the vacuum light speed c = 2.99792458*10**5 km/s ≅ 3*10**5 km/s. For further examples of the use of the kilometer per second (km/s), see Wikipedia: List of Escape Velocities.

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