import numpy as np

def schwarzschild_radius(mass, mass_unit):
    """Computes the Schwarzschild radius of an object.

    Parameters
    ----------
    mass : float
        The mass of the object.
    mass_unit : str
        The unit of the mass. Must be one of "sun masses", "earth masses", or "kg".

    Returns
    -------
    float or None
        The Schwarzschild radius in meters, or None if the input is invalid.
    """
    G = 6.67430e-11  # Gravitational constant (m^3/kg/s^2)
    c = 299_792_458  # Speed of light (m/s)

    if mass_unit == "sun":
        mass_kg = mass * 1.988e30
    elif mass_unit == "earth":
        mass_kg = mass * 5.972e24
    elif mass_unit == "kg":
        mass_kg = mass
    else:
        print("Invalid mass unit. Please use 'sun', 'earth', or 'kg'.")
        return None

    if mass_kg <= 0:
        print("Mass must be positive.")
        return None

    radius = (2 * G * mass_kg) / (c**2)
    return radius

# Example usage
mass_sun = 1  # Solar mass
radius_sun = schwarzschild_radius(mass_sun, "sun")
print(f"Schwarzschild radius of the Sun: {radius_sun} meters")

mass_earth = 1 # Earth mass
radius_earth = schwarzschild_radius(mass_earth, "earth")
print(f"Schwarzschild radius of the Earth: {radius_earth} meters")

mass_kg = 1000 # Kilograms
radius_kg = schwarzschild_radius(mass_kg, "kg")
print(f"Schwarzschild radius of a 1000 kg object: {radius_kg} meters")

import math

def time_dilation(schwarzschild_radius, distance):
  """Calculates the time dilation factor near a black hole.

  Args:
    schwarzschild_radius: Schwarzschild radius of the black hole in meters.
    distance: Distance from the center of the black hole in meters.

  Returns:
    The time dilation factor.
  """
  if distance <= schwarzschild_radius:
    return 0  # Time stops at and inside the event horizon
  else:
    return math.sqrt(1-(schwarzschild_radius / distance))

# Example usage
rs = schwarzschild_radius(100_000_000, "sun")  # Schwarzschild radius for a black hole
distance = 2 * rs  # Distance outside the event horizon
t_0 = time_dilation(rs, distance)
print(f"Time dilation factor: {t_0}")