#!/usr/bin/env python
# coding: utf-8

# # <font color="880000">Venus</font>
# 
# OK. Venus is at its maximum angular separation from the Sun when Earth-Venus-Sun [form a right triangle](https://en.wikipedia.org/wiki/Elongation)—which is when the Earth-Venus line-of-sight is tangent to the orbit of Venus... 
# 
# &nbsp;

# In[32]:


get_ipython().run_line_magic('matplotlib', 'inline')

import matplotlib.pyplot as plt
plt.style.use('seaborn-whitegrid')

import numpy as np
import pandas as pd


# In[33]:


theta = []
thetaprime = []
thetadiff = []

b = 0.723
pi = 3.141592653

for i in range(-500,500):
    thetai = pi*i/1000
    y = np.sin(thetai)
    x = np.cos(thetai)
    yprime = y - b
    xprime = x
    thetaprimei = np.arctan(yprime/xprime)
    thetadiffi = thetai - thetaprimei
    theta = theta + [thetai]
    thetaprime = thetaprime + [thetaprimei]
    thetadiff = thetadiff + [thetadiffi]

data = [('theta', theta),('thetaprime', thetaprime), ('thetadiff', thetadiff)]
venus = pd.DataFrame.from_items(data)
venus.plot()


# ## <font color="880000">Venus</font>
# 
# <img src="https://tinyurl.com/20190119a-delong" width="300" style="float:right" />
# 
# ## Catch Our Breath—Further Notes:
# 
# * Questions
# * Comments
# * Readings <https://en.wikipedia.org/wiki/Elongation>
# 
# <br clear="all" />
# 
# ----
# 
# * Weblog Support <https://github.com/braddelong/WS2019/blob/master/2019-02-11-venus.ipynb>
# * nbViewer <https://nbviewer.jupyter.org/github/braddelong/WS2019/blob/master/2019-02-11-venus.ipynb>
# 
# 
# &nbsp;
# 
# ----