Calculating the radius of earth by latitude in Python - replicating a formula

Question

I am trying to replicate a formula I found on this website, it relates to calculating the radius of the earth at a given latitude.

https://rechneronline.de/earth-radius/ or https://planetcalc.com/7721/

I then use the calculator on the website to determine whether I have replicated the formula correctly.

I have written the following code, but I can't replicate the answer given on the website (except when the latitude is equal to zero). Since the equation is quite complicated, I've even split each part into a seperate variable. However, my results are still not correct.

Example code

import math

def radius (B):
  a = 6378.137  #Radius at sea level at equator
  b = 6356.752  #Radius at poles

  c = (a**2*math.cos(B))**2
  d = (b**2*math.sin(B))**2
  e = (a*math.cos(B))**2
  f = (b*math.sin(B))**2

  R = math.sqrt((c+d)/(e+f))


  return R

For example, using a latitude of 2 (the variable B), the website calculates the radius of the earth as 6378.111km. My answer is 6360.481km.

Any help will be appreciated. Thank you in advance

Answer 1

python math library takes radians as input for trignometric functions,

so make sure you convert the value of B into radians

it can be done by B=math.radians(B)

final code:

import math
def radius (B):
    B=math.radians(B) #converting into radians
    a = 6378.137  #Radius at sea level at equator
    b = 6356.752  #Radius at poles
    c = (a**2*math.cos(B))**2
    d = (b**2*math.sin(B))**2
    e = (a*math.cos(B))**2
    f = (b*math.sin(B))**2
    R = math.sqrt((c+d)/(e+f))
    return R