syms M m rho R V G T v
% for earth:

M = 5.972 * 10^27 % grams
rho = 5.515 % g/cm^3

% M = (10^25) * 1000 % grams
% rho = 3.0 % g/cm^3

G = 6.67408 * 10^-11 % m^3 kg^-1 s^-2
% to find the radius

V = M / rho %cm^3

volume_equ = (4/3)*pi*R^3 == V

sol0 = solve(volume_equ, R);
sol0 = sol0(1);
sol0 = double(sol0) / 100; % in meters

R = sol0
% at the equator we have
% (mv^2)/R = (GMm)/R^2

force_equ = (m*v^2)/R == (G*M*m)/(R^2)

sol1 = solve(force_equ, v);
sol1 = sol1(2);
v = double(sol1) % linear speed in m/s

period_equ = v == (2*pi*R) / T

sol2 = solve(period_equ, T)
T = double(sol2) % in seconds
T_hours = T /(60*60) % in hours