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# Untitled

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1. syms M m rho R V G T v
2. % for earth:
3.
4. M = 5.972 * 10^27 % grams
5. rho = 5.515 % g/cm^3
6.
7. % M = (10^25) * 1000 % grams
8. % rho = 3.0 % g/cm^3
9.
10. G = 6.67408 * 10^-11 % m^3 kg^-1 s^-2
11. % to find the radius
12.
13. V = M / rho %cm^3
14.
15. volume_equ = (4/3)*pi*R^3 == V
16.
17. sol0 = solve(volume_equ, R);
18. sol0 = sol0(1);
19. sol0 = double(sol0) / 100; % in meters
20.
21. R = sol0
22. % at the equator we have
23. % (mv^2)/R = (GMm)/R^2
24.
25. force_equ = (m*v^2)/R == (G*M*m)/(R^2)
26.
27. sol1 = solve(force_equ, v);
28. sol1 = sol1(2);
29. v = double(sol1) % linear speed in m/s
30.
31. period_equ = v == (2*pi*R) / T
32.
33. sol2 = solve(period_equ, T)
34. T = double(sol2) % in seconds
35. T_hours = T /(60*60) % in hours
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