Orbit

A planet on a Kepler orbit around a star at focus: semi_major units, eccentricity, the perihelion to the right of the star, once around every period seconds (Kepler’s equation is solved for each frame). With sweeps, the first orbit shades that many sectors from the star, each swept in the same sweep fraction of the period. The sector near the star is short and wide, the far one long and thin, and their areas are equal. position(t) and eccentric_anomaly(m, e) give the numbers. Gallery scene: Orbit.

Orbit 6 sPlayUnmuteCopy render command

use fframes_kit::prelude::*;

fn figure<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    ui.show(Orbit {
        focus: (2.0, -0.5),
        semi_major: 4.0,
        eccentricity: 0.6,
        period: 5.0,
        sweeps: 3,
        sweep: 0.12,
        ..ui.defaults()
    })
}

API

Components are plain structs. Set the fields you need and fill the rest with ..ui.defaults(): the defaults below come from the current theme (theme. values are fields of Theme).

Orbit

Field	Type	Default	Description
focus	(f64, f64)	(1.5, 0.0)	Where the star sits, one focus of the ellipse, in units of ui.space.
semi_major	f64	3.5	Half the long axis of the ellipse in units of ui.space.
eccentricity	f64	0.6	How stretched the ellipse is: 0 is a circle, close to 1 a thin ellipse.
period	f64	5.0	Seconds the planet takes for one orbit.
start	f64	0.0	Where the planet is when its clock starts, as a fraction of the period after the closest point to the star.
delay	f32	0.0	Seconds after the container’s start before the planet starts to move.
time_scale	f32	1.0	Speed of the motion over local time; 2 runs twice as fast, 1 is real time.
sweeps	usize	3	Number of shaded sectors, swept at even times around the first orbit; 0 for none.
sweep	f64	0.1	Fraction of the period each sector takes to sweep, so each covers the same area.
star_radius	f32	24.0	Radius of the star in pixels.
planet_radius	f32	13.0	Radius of the planet in pixels.
orbit_color	Color	theme.colors.muted	Colour of the dashed orbit ellipse.
star_color	Color	theme.colors.highlight	Colour of the star.
planet_color	Color	theme.colors.accent	Colour of the planet.
sweep_color	Color	theme.colors.accent	Colour of the shaded sectors.
stroke_width	f32	theme.stroke.thin	Width of the orbit ellipse in pixels.
enter	Option<EnterAnim>	None	How the orbit and the star draw in; None shows them from the start.
exit	Option<ExitAnim>	None	How the orbit and the star leave at the end of the container; None stays.
parts_enter	Option<FadeIn>	None	How the planet and the sectors fade in; None for none.
parts_exit	Option<FadeOut>	None	How the planet and the sectors fade out before the end; None for none.

Methods:

• fn semi_minor(&self) -> f64: The semi-minor axis, a √(1 - e²).
• fn position(&self, t: f64) -> (f64, f64): The planet’s offset from the star in units after t seconds of its clock.
• fn sweep_start(&self, i: usize) -> f64: Seconds of the planet’s clock when sector i of Orbit::sweeps starts.

Feature physics · Source