




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
UpperCamelCase__		=						2_0

# Time between time steps in seconds
UpperCamelCase__		=						INTERVAL / 1_0_0_0


class     __SCREAMING_SNAKE_CASE							:

					def __init__(    self			,	__lowercase			,	__lowercase			,	__lowercase			,	__lowercase			,	__lowercase = 1.0			,	__lowercase = 1.0			,	__lowercase = "blue"			,	):







						'''simple docstring'''




						lowerCamelCase_							:		str							       =							position_x
						lowerCamelCase_							:		Optional[int]							       =							position_y
						lowerCamelCase_							:		Tuple							       =							velocity_x
						lowerCamelCase_							:		Any							       =							velocity_y
						lowerCamelCase_							:		Tuple							       =							mass
						lowerCamelCase_							:		Optional[Any]							       =							size
						lowerCamelCase_							:		int							       =							color

					@property
					def      lowercase_							(    self ):







						'''simple docstring'''




						return self.position_x, self.position_y

					@property
					def      lowercase_							(    self ):







						'''simple docstring'''




						return self.velocity_x, self.velocity_y

					def      lowercase_							(    self			,	__lowercase			,	__lowercase			,	__lowercase ):







						'''simple docstring'''




						self.velocity_x += force_x * delta_time
						self.velocity_y += force_y * delta_time





					def      lowercase_							(    self			,	__lowercase ):







						'''simple docstring'''




						self.position_x += self.velocity_x * delta_time
						self.position_y += self.velocity_y * delta_time


class     __SCREAMING_SNAKE_CASE							:

					def __init__(    self			,	__lowercase			,	__lowercase = 1.0			,	__lowercase = 1.0			,	__lowercase = 0.0			,	):







						'''simple docstring'''




						lowerCamelCase_							:		Optional[Any]							       =							bodies
						lowerCamelCase_							:		Tuple							       =							gravitation_constant
						lowerCamelCase_							:		Any							       =							time_factor
						lowerCamelCase_							:		str							       =							softening_factor

					def __len__(    self ):







						'''simple docstring'''




						return len(self.bodies )





					def      lowercase_							(    self			,	__lowercase ):







						'''simple docstring'''




						for bodya in self.bodies:
							lowerCamelCase_							:		Optional[Any]							       =							0.0
							lowerCamelCase_							:		str							       =							0.0
							for bodya in self.bodies:
								if bodya != bodya:
									lowerCamelCase_							:		Optional[int]							       =							bodya.position_x - bodya.position_x
									lowerCamelCase_							:		Any							       =							bodya.position_y - bodya.position_y

									# Calculation of the distance using Pythagoras's theorem
									# Extra factor due to the softening technique
									lowerCamelCase_							:		Optional[Any]							       =							(dif_x**2 + dif_y**2 + self.softening_factor) ** (
									    1 / 2
									)

									# Newton's law of universal gravitation.
									force_x += (
									    self.gravitation_constant * bodya.mass * dif_x / distance**3
									)
									force_y += (
									    self.gravitation_constant * bodya.mass * dif_y / distance**3
									)

            # Update the body's velocity once all the force components have been added
							bodya.update_velocity(__lowercase			,	__lowercase			,	delta_time * self.time_factor )

						# Update the positions only after all the velocities have been updated
						for body in self.bodies:
							body.update_position(delta_time * self.time_factor )






def  snake_case (							A						,       A						,       A      )							->							None:




	'''simple docstring'''


	body_system.update_system(A      )

	# Update the positions of the patches
	for patch, body in zip(A						,       body_system.bodies      ):
		lowerCamelCase_							:		Union[str, Any]							       =							(body.position_x, body.position_y)






def  snake_case (							A						,       A						,       A = -1						,       A = 1						,       A = -1						,       A = 1						,       )							->							None:




	'''simple docstring'''


	lowerCamelCase_							:		List[Any]							       =							plt.figure()
	fig.canvas.set_window_title(A      )
	lowerCamelCase_							:		Union[str, Any]							       =							plt.axes(
	    xlim=(x_start, x_end)						,       ylim=(y_start, y_end)      )  # Set section to be plotted
	plt.gca().set_aspect('equal'      )  # Fix aspect ratio

	# Each body is drawn as a patch by the plt-function
	lowerCamelCase_							:		Any							       =							[
	    plt.Circle((body.position_x, body.position_y)						,       body.size						,       fc=body.color      )
	    for body in body_system.bodies
	]

	for patch in patches:
		ax.add_patch(A      )

	# Function called at each step of the animation
	def update(A      ) -> list[plt.Circle]:
		update_step(A						,       A						,       A      )
		return patches

	lowerCamelCase_							:		List[str]							       =							animation.FuncAnimation(  # noqa: F841
	    A						,       A						,       interval=A						,       blit=A      )

	plt.show()






def  snake_case (							)							->							BodySystem:




	'''simple docstring'''


	lowerCamelCase_							:		Dict							       =							0.970_0436
	lowerCamelCase_							:		Union[str, Any]							       =							-0.2430_8753
	lowerCamelCase_							:		Dict							       =							0.4_6620_3685
	lowerCamelCase_							:		Dict							       =							0.4323_6573

	lowerCamelCase_							:		Optional[Any]							       =							[
	    Body(A						,       A						,       A						,       A						,       size=0.2						,       color='red'      ),
	    Body(-position_x						,       -position_y						,       A						,       A						,       size=0.2						,       color='green'      ),
	    Body(0						,       0						,       -2 * velocity_x						,       -2 * velocity_y						,       size=0.2						,       color='blue'      ),
	]
	return BodySystem(A						,       time_factor=3      )






def  snake_case (							)							->							BodySystem:




	'''simple docstring'''


	lowerCamelCase_							:		int							       =							7.3476e22
	lowerCamelCase_							:		Optional[int]							       =							5.972e24
	lowerCamelCase_							:		List[str]							       =							1022
	lowerCamelCase_							:		str							       =							384399000
	lowerCamelCase_							:		List[str]							       =							6.674e-11

	# Calculation of the respective velocities so that total impulse is zero,
	# i.e. the two bodies together don't move
	lowerCamelCase_							:		int							       =							earth_mass * velocity_dif / (earth_mass + moon_mass)
	lowerCamelCase_							:		List[str]							       =							moon_velocity - velocity_dif

	lowerCamelCase_							:		Union[str, Any]							       =							Body(-earth_moon_distance						,       0						,       0						,       A						,       A						,       10000000						,       'grey'      )
	lowerCamelCase_							:		Tuple							       =							Body(0						,       0						,       0						,       A						,       A						,       50000000						,       'blue'      )
	return BodySystem([earth, moon]						,       A						,       time_factor=1000000      )






def  snake_case (							)							->							BodySystem:




	'''simple docstring'''


	lowerCamelCase_							:		Optional[Any]							       =							[]
	for _ in range(10      ):
		lowerCamelCase_							:		Optional[Any]							       =							random.uniform(-0.5						,       0.5      )
		lowerCamelCase_							:		Union[str, Any]							       =							random.uniform(-0.5						,       0.5      )

		# Bodies are created pairwise with opposite velocities so that the
		# total impulse remains zero
		bodies.append(
		    Body(
		        random.uniform(-0.5						,       0.5      )						,       random.uniform(-0.5						,       0.5      )						,       A						,       A						,       size=0.05						,       )      )
		bodies.append(
		    Body(
		        random.uniform(-0.5						,       0.5      )						,       random.uniform(-0.5						,       0.5      )						,       -velocity_x						,       -velocity_y						,       size=0.05						,       )      )
	return BodySystem(A						,       0.01						,       10						,       0.1      )


if __name__ == "__main__":
							plot('Figure-8 solution to the 3-body-problem', example_a(), -2, 2, -2, 2)
							plot(
							    'Moon\'s orbit around the earth',
							    example_a(),
							    -4_3_0_0_0_0_0_0_0,
							    4_3_0_0_0_0_0_0_0,
							    -4_3_0_0_0_0_0_0_0,
							    4_3_0_0_0_0_0_0_0,
							)
							plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)






UpperCamelCase__		=						{
    "kilogram": 1,
    "gram": pow(1_0, 3),
    "milligram": pow(1_0, 6),
    "metric-ton": pow(1_0, -3),
    "long-ton": 0.0_009_842_073,
    "short-ton": 0.0_011_023_122,
    "pound": 2.2_046_244_202,
    "stone": 0.1_574_731_728,
    "ounce": 35.273_990_723,
    "carrat": 5_0_0_0,
    "atomic-mass-unit": 6.022136652e26,
}

UpperCamelCase__		=						{
    "kilogram": 1,
    "gram": pow(1_0, -3),
    "milligram": pow(1_0, -6),
    "metric-ton": pow(1_0, 3),
    "long-ton": 1_016.04_608,
    "short-ton": 907.184,
    "pound": 0.453_592,
    "stone": 6.35_029,
    "ounce": 0.0_283_495,
    "carrat": 0.0_002,
    "atomic-mass-unit": 1.660540199e-27,
}






def  snake_case (							A						,       A						,       A      )							->							float:




	'''simple docstring'''


	if to_type not in KILOGRAM_CHART or from_type not in WEIGHT_TYPE_CHART:
		lowerCamelCase_							:		Union[str, Any]							       =							(
		    f"Invalid 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"
		    f"Supported values are: {', '.join(A      )}"
		)
		raise ValueError(A      )
	return value * KILOGRAM_CHART[to_type] * WEIGHT_TYPE_CHART[from_type]


if __name__ == "__main__":
							import doctest

							doctest.testmod()
