Calculate the escape velocity for Mars if its mass=0.12MEarth and the radius=0.55REarth. Show full solving process.

V escape = (2GM/R) ^1/2

M = mass of planet

R = radius of planet

G = gravitational constant (6.67 x 10^-11 x m^3/kg x s^2)

V escape = (0.44 G MEarth/REarth) ^1/2 = 5223.6 m/s

Explanation:

It is given that:

V escape = (2GM/R) ^1/2

where,

M = Mass of Mars = 0.12 MEarth

R = Radius of Mars = 0.55 REarth

G = gravitational constant = 6.67 x 10⁻¹¹ m³/kg s²

Therefore,

V escape = [ (2G) (0.12 MEarth) / (0.55 REarth) ]^1/2

V escape = (0.44 G MEarth/REarth) ^1/2

where,

MEarth = Mass of Earth = 6 x 10²⁴ kg

REarth = Radius of Earth = 6.4 x 10⁶ m

Therefore,

V escape = [ (0.44) (6.67 x 10⁻¹¹ m³/kg. s²) (6 x 10²⁴ kg) / (6.4 x 10⁶ m) ]^1/2

V escape = (27.29 x 10⁶ m²/s²) ^1/2

V escape = 5223.6 m/s