The differential rotation rate is usually described by the equation:

${\displaystyle \omega =A+B\,\sin ^{2}(\varphi )+C\,\sin ^{4}(\varphi )}$

where ${\displaystyle \omega }$ is the angular velocity in degrees per day, ${\displaystyle \varphi }$ is the solar latitude, A is angular velocity at the equator, and B, C are constants controlling the decrease in velocity with increasing latitude. The values of A, B, and C differ depending on the techniques used to make the measurement, as well as the time period studied.^[1] A current set of accepted average values^[2] is:

A= 14.713 ± 0.0491 °/day

B= −2.396 ± 0.188 °/day

C= −1.787 ± 0.253 °/day

Plotted in python ```python import numpy as np import matplotlib.pyplot as plt

1. Constants

A = 14.713 B = -2.396 C = -1.787

1. Latitude values

latitude = np.linspace(0, 90, 100)

1. Angular velocity equation

omega = A + B * np.sin(np.deg2rad(latitude))**2 + C * np.sin(np.deg2rad(latitude))**4

1. Rotational period (in days)

rotational_period = 360 / omega

1. Plotting

plt.plot(latitude, rotational_period) plt.xlabel('Latitude (degrees)') plt.ylabel('Rotational Period (days)') plt.title('Solar rotation period') plt.grid(True) plt.show()