import numpy as np
from matplotlib import pyplot as plt
%matplotlib inline

a = 6378.1370
b = 6356.7523

lat = np.linspace(0,90,90)
latr = np.radians(lat)

denom = (a * np.cos(latr))**2. + (b * np.sin(latr))**2.
numer = (a**2. * np.cos(latr))**2. + (b**2. * np.sin(latr))**2.

R = np.sqrt(numer/denom)

plt.plot(lat, R)
plt.show()

mountains = """
Summit, Distance from center, Elevation above sea level, Latitude, Country
Chimborazo, 6384.4, 6268.2, -1.469167, Ecuador
Huascaran, 6384.4, 6748, -9.121389, Peru
Kilimanjaro, 6383, 5895, -3.075833, Tanzania
Everest, 6382.3, 8848, 27.988056, Nepal
"""

m = filter(None, mountains.split('\n'))

# Start the plot.
plt.figure(figsize=(12,12))
ax = plt.subplot(111)
ax.plot(lat[:40], R[:40])

# Iterate over the mountains, skipping the first.
for row in m[1:]:
    
    # Make a list out of each row.
    data = row.split(',')
        
    # Extract data we can use.
    deg = np.abs(np.round(float(data[3]),0))
    ht = float(data[2])/1000.
    
    # Add to the plot.
    ax.axhline(R[deg]+ht, color="lightgray")
    ax.vlines(np.abs(float(data[3])), R[deg], R[deg]+ht)
    ax.text(deg+0.5, R[deg]-1, data[0], fontsize=12, rotation=90, horizontalalignment='right')
    ax.text(deg+0.5, 1.0004*(R[deg]+ht), str(np.round(R[deg]+ht,3))+" km" , fontsize=10, rotation=90, horizontalalignment='right')
    
# Adjust and show the plot.
ax.set_xlim(-5, 45)
ax.set_ylim(6370, 6390)
plt.xlabel('Absolute latitude in degrees')
plt.ylabel("Distance from Earth's centre")
plt.show()