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import math

def escape_velocity(mass: float, radius: float) -> float:

"""

Calculates the escape velocity needed to break free from a celestial body's

gravitational field.

The formula used is:

v = sqrt(2 * G * M / R)

where:

v = escape velocity (m/s)

G = gravitational constant (6.67430 * 10^-11 m^3 kg^-1 s^-2)

M = mass of the celestial body (kg)

R = radius from the center of mass (m)

Source:

https://en.wikipedia.org/wiki/Escape_velocity

Args:

mass (float): Mass of the celestial body in kilograms.

radius (float): Radius from the center of mass in meters.

Returns:

float: Escape velocity in meters per second, rounded to 3 decimal places.

Examples:

>>> escape_velocity(mass=5.972e24, radius=6.371e6) # Earth

11185.978

>>> escape_velocity(mass=7.348e22, radius=1.737e6) # Moon

2376.307

>>> escape_velocity(mass=1.898e27, radius=6.9911e7) # Jupiter

60199.545

>>> escape_velocity(mass=0, radius=1.0)

0.0

>>> escape_velocity(mass=1.0, radius=0)

Traceback (most recent call last):

...

ZeroDivisionError: Radius cannot be zero.

"""

gravitational_constant = 6.67430e-11 # m^3 kg^-1 s^-2

if radius == 0:

raise ZeroDivisionError("Radius cannot be zero.")

velocity = math.sqrt(2 * gravitational_constant * mass / radius)

return round(velocity, 3)

if __name__ == "__main__":

import doctest

doctest.testmod()

print("Calculate escape velocity of a celestial body...\n")

try:

mass = float(input("Enter mass of the celestial body (in kgs): ").strip())

radius = float(input("Enter radius from the center of mass (in ms): ").strip())

velocity = escape_velocity(mass=mass, radius=radius)

print(f"Escape velocity is {velocity} m/s")

except ValueError:

print("Invalid input. Please enter valid numeric values.")

except ZeroDivisionError as e:

print(e)

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