computational-physics

Mercury’s precession & double pendulum simulation
This Jupyter notebook based project can give one experience in computational physics solving numerically for the dynamics of the systems.
Four formulas describing the Keplerian orbit of a test particle around the Sun will be needed:
i. $$r(\theta) = \frac{a(1-e^2)}{1+e\ cos(\theta-\theta_{E})} $$
where $$r$$ is its radius, $$\theta$$ is its angle, $$a$$ is the semimajor axis, $$e$$ is the eccentricity, and $$\theta_E$$ is the orientation of the ellipse; specifically, it gives the angle of closest approach to the Sun("periapse").
ii. Its energy per unit mass is
$$u = -\frac{GM_{s}}{2a}$$
where $$M_{s}$$ is the Sun's mass.
iii. Its angular momentum per unit mass is
$$h=\sqrt{GM_{S}a(1-e^2)}$$
iv. Its orbital period is
$$T=2\pi (\frac{a^3}{GM_S})^{\frac{1}{2}}$$