How to find/extract the semi-major axis from a TLE with Skyfield?

Question

I have a TLE:

1 33591U 09005A 21024.46740879 .00000049 00000-0 52095-4 0 9997
2 33591 99.1927 41.5349 0014084 172.6670 187.4709 14.12449679616592

And I would like to extract the semi-major axis using Skyfield. I also tried manually calculating it, looking at this answer: How to get semi-major axis from TLE?, but seems like I am missing something in my calculations (calculations below).

$$\mu = 398600 \ \ km^3/s^2$$

$$mm = 14.12449679 \ \ day^{-1}$$

$$n = mm \frac{2 \pi}{86400 \ \ sec}$$

$$a = \frac{\mu^{1/3}}{(2 \pi n / 86400)^{2/3}}$$

and in Python (for example):

import math
mu = 398600;
mm = 14.12449679;
n = mm * ((2 * math.pi) / 86400);
a = mu**(1/3) /(2*n*pi/86400)**(2/3);

which yields:

a = 4.1493e+06

Answer 1

Your formulas, constants, and code have mistakes.

Here is the correct code (in Python), using the example n = 15.5918272 from the page you linked to above (How to get semi-major axis from TLE?)

import math
mu = 3.986004418E14
n = 15.5918272
a = mu**(1/3) / (2*n*math.pi/86400)**(2/3) # meters
print(a/1000.0) # kilometers

I get:

6768.158167689445