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Merged
merged 2 commits into from
May 10, 2025
Merged

[pull] master from TheAlgorithms:master #116

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1317655
Fix error messages for horizontal_projectile_motion.py (#12722)
robohie May 10, 2025
95fb181
Add escape velocity calculator using standard physics formula (#12721)
SajeevSenthil May 10, 2025
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67 changes: 67 additions & 0 deletions physics/escape_velocity.py
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Original file line number Diff line number Diff line change
@@ -0,0 +1,67 @@
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)
18 changes: 9 additions & 9 deletions physics/horizontal_projectile_motion.py
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Original file line number Diff line number Diff line change
Expand Up @@ -17,7 +17,7 @@
"""

# Importing packages
from math import radians as angle_to_radians
from math import radians as deg_to_rad
from math import sin

# Acceleration Constant on Earth (unit m/s^2)
Expand All @@ -31,10 +31,10 @@ def check_args(init_velocity: float, angle: float) -> None:

# Ensure valid instance
if not isinstance(init_velocity, (int, float)):
raise TypeError("Invalid velocity. Should be a positive number.")
raise TypeError("Invalid velocity. Should be an integer or float.")

if not isinstance(angle, (int, float)):
raise TypeError("Invalid angle. Range is 1-90 degrees.")
raise TypeError("Invalid angle. Should be an integer or float.")

# Ensure valid angle
if angle > 90 or angle < 1:
Expand Down Expand Up @@ -71,7 +71,7 @@ def horizontal_distance(init_velocity: float, angle: float) -> float:
ValueError: Invalid angle. Range is 1-90 degrees.
"""
check_args(init_velocity, angle)
radians = angle_to_radians(2 * angle)
radians = deg_to_rad(2 * angle)
return round(init_velocity**2 * sin(radians) / g, 2)


Expand All @@ -94,14 +94,14 @@ def max_height(init_velocity: float, angle: float) -> float:
>>> max_height("a", 20)
Traceback (most recent call last):
...
TypeError: Invalid velocity. Should be a positive number.
TypeError: Invalid velocity. Should be an integer or float.
>>> horizontal_distance(30, "b")
Traceback (most recent call last):
...
TypeError: Invalid angle. Range is 1-90 degrees.
TypeError: Invalid angle. Should be an integer or float.
"""
check_args(init_velocity, angle)
radians = angle_to_radians(angle)
radians = deg_to_rad(angle)
return round(init_velocity**2 * sin(radians) ** 2 / (2 * g), 2)


Expand All @@ -128,10 +128,10 @@ def total_time(init_velocity: float, angle: float) -> float:
>>> total_time(30, "b")
Traceback (most recent call last):
...
TypeError: Invalid angle. Range is 1-90 degrees.
TypeError: Invalid angle. Should be an integer or float.
"""
check_args(init_velocity, angle)
radians = angle_to_radians(angle)
radians = deg_to_rad(angle)
return round(2 * init_velocity * sin(radians) / g, 2)


Expand Down