[planetary orbit] Simulating a stable planetary orbit in Manim. #manim #astro #physics #updater #newton

20251211_newton.py

class orbit(Scene):
    def construct(self):
        ax = Axes(
            x_range=[-200e9,200e9,50e9],
            y_range=[-200e9,200e9,50e9],
            x_length=8,
            y_length=8,
            tips=False
        )
        G = 6.67e-11
        sun = Dot(point=ax.c2p(0,0),color=YELLOW)
        sun.m = 2e30
        p = Dot()
        p.m = 6e24
        p_blue = p.copy().set_color(BLUE).move_to(ax.c2p(150e9,0,0))
        p_blue.v = np.array([0,30e3])
        p_red  = p.copy().set_color(RED).move_to(ax.c2p(-150e9,0,0))
        p_red.v = np.array([0,-30e3])

        speed_factor = 24*60*60*20# time steps

        def blue_updater(obj,dt):
            dvec = ax.p2c(sun.get_center())-ax.p2c(obj.get_center())
            a = dvec*G*sun.m/(np.linalg.norm(dvec)**3)
            obj.v = obj.v + a*dt*speed_factor
            obj.shift(ax.c2p(*(obj.v*dt*speed_factor)))

        def red_updater(obj,dt):
            dvec = ax.p2c(sun.get_center()) - ax.p2c(obj.get_center())
            a = dvec*G*sun.m/(np.linalg.norm(dvec)**3)
            obj.shift(ax.c2p(*(obj.v*dt*speed_factor)))
            obj.v = obj.v + a*dt*speed_factor

        p_blue.add_updater(blue_updater)
        p_red.add_updater(red_updater)

        bluetrace = TracedPath(p_blue.get_center, stroke_width=1, stroke_color=BLUE)
        redtrace  = TracedPath(p_red.get_center, stroke_width=1, stroke_color=RED)

        self.add(sun,p_blue,p_red,bluetrace,redtrace)
        self.wait(30)

readme.md

Following a video released today by user braintruffle on youtube https://www.youtube.com/watch?v=nCg3aXn5F3M

Showing the difference the update order of motion equations makes in computer simulations for example of planetary orbits. The red planet is simulated by first updating the planet's position and then the velocity, the blue planet is simulated by first updating the speed and then the position.

The blue simulated orbit is much more stable than the red one - the initial values are taken from the Earth-Sun system.

I have been simulating planetary systems for the first time using Turbo Pascal in the middle of the 1990s and observed how planets got sling-shotted out of the system under certain circumstances - if I only had my old code I could check in which order I had made the updates back then, but I remember how critical short time steps were in order to keep the simulations and orbits somewhat stable.