Escape velocity for a planet is calculated as -
Escape Velocity = $\sqrt{\frac{2 \cdot G \cdot M}{R}}$
Where 'G' is Universal Gravitational Constant (= 6.6726*10-11 N-m2/ kg2), M is Mass of the Planet and R is the Radius of the Planet.
Escape Velocity Calculator (Escape Speed Calculator) is an online tool for calculating values of the unknown parameters in the Escape Velocity Formula provided other parameters are known.
Escape Velocity Formula:
Escape Velocity: Ve = Square root of(2GM/R)
Planet Mass: M = (Ve2R)/2G
Planet radius: R = 2GM/(Ve)2
Where,
G = Universal Gravitational Constant = 6.6726*10-11 N-m2/kg2
M = Planet Mass
R = Planet Radius
Step 2 :
State the equation you plan to use and plug in the values.
Calculate the escape velocity on earth with respect to Earth's gravity?
Step 1 :We know that:
Mass of the earth(M) = 5.98x1024kg,
Mass Radius(R) = 6378100 m,
G = 6.6726 x 10-11N-m2/kg2
Escape velocity(ve) = ?
Step 2 :Substitue the given values in the formula:
Escape Velocity: Ve = Square root of(2GM/R)
Ve = Square root of((2×6.6726 x 10-11 ×5.98x1024)/(6378100))
Ve = Square root of((79.73×1013)/(6378100))
Ve = Square root of(125005879.5)
Ve = 11180.06m/s
Answer :Ve = 11185.811m/s
Calculate the mass of the planet Mars, whose escape velocity is 5 × 103?
Step 1 :Given that:
Radius of Mars(R) = 33.97 x 105 kg,
Escape velocity(Ve) = 5 x 103,
Mass of the planet mars(M) = ?
Step 2 :Substitue the given values in the formula:
Mars mass: M = (Ve2R)/2G
M = ((5 x 103)2×(33.97 x 105))/(2×6.6726 x 10-11)
M = 849.25×1022 / 13.3452
M = 6.364×1023 kg
Answer :M = 6.364×1023 kg