# set values of constants

v_0 = 5     # initial velocity
y_0 = 200   # initial y position
g = 9.81    # acceleration due to gravity

# calculate y at time t=3

t = 6.385
y = y_0 - 0.5 * g * t ** 2
x = v_0 * t

print("t (seconds):", t)
print("y (metres):", y)
print("x (metres):", x)

v_0 = 5     # initial velocity
y_0 = 200   # initial y position
g = 9.81    # acceleration due to gravity

t = 6.385

def x_t(t):
    x = v_0 * t
    return x

def y_t(t):
    y = y_0 - 0.5 * g * t ** 2
    return y

print("x_t (metres):", x)
print("y_t (metres):", y)

import numpy as np

# set values of constants

v_0 = 5     # initial velocity
y_0 = 200   # initial y position
g = 9.81    # acceleration due to gravity

# calculate y for integer values of t from 0 to 9

t = np.arange(0, 10)
y = y_0 - 0.5 * g * t ** 2
x = v_0 * t

print("t (seconds):", t)
print("y (metres):", y)
print("x (metres):", x)

import matplotlib.pyplot as plt

plt.figure(figsize=(5,5))
plt.plot(t, y)

plt.figure(figsize=(5,5))
plt.plot(t, x)

plt.figure(figsize=(5,5))
plt.plot(x, y)

from matplotlib import animation
from IPython.display import HTML, display
import random

filename = "animation.gif"
# Number of animation frames equals the length of time array t
frames = len(t)
interval = 100

def ganimate(frame):
    plt.cla()
    plt.scatter(t[frame], y[frame])
    plt.xlim(0, 10)
    plt.ylim(0, 200)
    
fig = plt.figure(figsize=(5, 5))
anim = animation.FuncAnimation(fig, ganimate, frames=frames, interval=interval)
anim.save(filename, writer='imagemagick')
plt.close()

__counter__ = str(random.randint(0,2e9))
display(HTML('<img src="' + filename + '?' + __counter__ + '">'))

from matplotlib import animation
from IPython.display import HTML, display
import random

filename = "animation.gif"
# Number of animation frames equals the length of time array t
frames = len(x)
interval = 100

def ganimate(frame):
    plt.cla()
    plt.scatter(x[frame], y[frame])
    plt.xlim(0, 40)
    plt.ylim(0, 300)
    
fig = plt.figure(figsize=(5, 5))
anim = animation.FuncAnimation(fig, ganimate, frames=frames, interval=interval)
anim.save(filename, writer='imagemagick')
plt.close()

__counter__ = str(random.randint(0,2e9))
display(HTML('<img src="' + filename + '?' + __counter__ + '">'))

t = np.arange(0, 365)
d = 300000000
p = 365

import numpy as np

x = d * np.cos(2 * np.pi * t/p)
y = d * np.sin(2 * np.pi * t/p)

print("Earth")

import matplotlib.pyplot as plt

plt.figure(figsize=(5,5))
plt.plot(x, y)

t = np.arange(0, 88)
d = 70000000
p = 87

import numpy as np

x = d * np.cos(2 * np.pi * t/p)
y = d * np.sin(2 * np.pi * t/p)

print("Mercury")

import matplotlib.pyplot as plt

plt.figure(figsize=(5,5))
plt.plot(x, y)

t = np.arange(0, 225)
d = 108000000
p = 224

import numpy as np

x = d * np.cos(2 * np.pi * t/p)
y = d * np.sin(2 * np.pi * t/p)

print("Venus")

import matplotlib.pyplot as plt

plt.figure(figsize=(5,5))
plt.plot(x, y)