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Well, you "overwrite" the table at every loop... As a result when the for loop is terminated the table has only the t,X,Y columns for theta=75. Try this: columns = [] for theta in range(30, 90, 15): tmax = v * np.sin(theta*np.pi/180)/g #Time to reach maximum height t = np.linspace(0, tmax,600) X = x(theta) #Maximum horizontal ...


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The Kepler laws, or simple insertion of $z(t)=re^{iωt}$, tell that for a circular orbit of radius $r$ in the central field $\ddot z=-\mu\frac{z}{|z|^3}$ the angular speed $\omega$ is given by $$ r^3ω^2=μ. $$ That is how you get the initial velocity $(0,\sqrt{\mu/r})$ at the point $(r,0)$. The period of the orbit is $$ T=\frac{2\pi}{ω}=2π\sqrt{r^3/μ}. $$ ...


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