About

Mars has two small, irregularly shaped moons: Phobos (mean radius 11.267 km) and Deimos (mean radius 6.2 km). Phobos orbits at a semi-major axis of 9,376 km with a period of 7.66 hours. It orbits faster than Mars rotates, meaning it rises in the west and sets in the east. Deimos sits at 23,463 km with a period of 30.31 hours. Both orbits have low eccentricity (e ≈ 0.0151 for Phobos, 0.00033 for Deimos) and low inclination relative to Mars's equator. This tool solves Kepler's equation at each frame to compute true anomaly and radial distance, then projects the orbital ellipse onto a 2D canvas. It does not interpolate or fake positions. Phobos is tidally decelerating and will impact Mars or break apart in roughly 50 million years. Deimos is slowly spiraling outward.

Formulas

Moon positions are computed by solving Kepler's equation at each animation frame. Given mean anomaly M advancing linearly with time, the eccentric anomaly E is found iteratively:

M = E − e ⋅ sin(E)

Newton-Raphson iteration: E_n+1 = E_n − E_n − e ⋅ sin(E_n) − M1 − e ⋅ cos(E_n)

True anomaly ν is then:

ν = 2 ⋅ atan2(√1 + e ⋅ sin(E2), √1 − e ⋅ cos(E2))

Radial distance from Mars center:

r = a ⋅ (1 − e ⋅ cos(E))

Where M = mean anomaly (radians), E = eccentric anomaly, e = orbital eccentricity, ν = true anomaly, a = semi-major axis, r = radial distance. Mean anomaly advances as M(t) = 2πT ⋅ t, where T is the orbital period.

Reference Data

Property	Phobos	Deimos	Unit
Semi-major axis (a)	9,376	23,463	km
Orbital period (T)	7.6562	30.312	hours
Eccentricity (e)	0.0151	0.00033	-
Inclination (i)	1.093	0.93	°
Mean radius	11.267	6.2	km
Mass	1.0659 × 10¹⁶	1.4762 × 10¹⁵	kg
Surface gravity	0.0057	0.003	m/s²
Escape velocity	11.39	5.556	m/s
Geometric albedo	0.071	0.068	-
Dimensions (tri-axial)	26.8 × 22.4 × 18.4	15 × 12.2 × 10.4	km
Orbital velocity (mean)	2.138	1.3513	km/s
Discovery year	1877	1877	-
Discoverer	Asaph Hall	Asaph Hall	-
Synchronous orbit?	Below (spiraling in)	Above (spiraling out)	-
Mars equatorial radius	3,396.2		km
Mars rotation period	24.6229		hours

Frequently Asked Questions

Phobos orbits at a semi-major axis of 9,376 km, well below Mars's synchronous orbit radius of approximately 20,428 km. Any moon below synchronous altitude must have a shorter orbital period than the planet's rotation period. Phobos completes one orbit in 7.66 hours versus Mars's 24.62-hour rotation. This means Phobos rises in the west and sets in the east as seen from Mars's surface. Tidal forces are gradually decelerating Phobos and shrinking its orbit by about 1.8 cm per year.

The Newton-Raphson iteration converges to a tolerance of 1×10⁻⁸ radians, typically in 3-5 iterations for the low eccentricities of Phobos (e = 0.0151) and Deimos (e = 0.00033). For these near-circular orbits, even a first-order approximation E ≈ M would produce sub-pixel positional error at typical zoom levels. The full solver is implemented for correctness.

At true scale, Phobos (11.267 km radius) orbiting at 9,376 km would subtend roughly 0.07° - less than one pixel on any reasonable display. The animation uses a configurable scale factor for moon radii (default ~200×) while keeping orbital distances proportional. Mars radius is also scaled but less aggressively to maintain visual hierarchy. The orbital ellipse geometry remains accurate.

Increasing Phobos's eccentricity would make its orbit noticeably elliptical, causing significant radial velocity variation. At e = 0.3, periapsis would drop to about 6,563 km (within Mars's Roche limit of ~5,100 km for a rigid body), likely causing tidal disruption. The animation's speed slider lets you observe how eccentricity affects the non-uniform angular velocity predicted by Kepler's second law (equal areas in equal times).

No. The animation uses the restricted two-body Keplerian model, treating each moon independently under Mars's gravity. Mutual gravitational interaction between Phobos and Deimos is negligible - Phobos's mass is approximately 1.066×10¹⁶ kg, producing a gravitational acceleration on Deimos of order 10⁻¹² m/s² at closest approach. Solar and Jovian perturbations, also omitted, are orders of magnitude larger but still minor over short timescales.

At 1× speed, one real second equals one simulated hour. At this rate, Phobos completes one orbit in about 7.66 seconds and Deimos in about 30.3 seconds. The speed slider ranges from 0.1× to 100×. The displayed elapsed time is shown in Martian sols (1 sol = 24.6229 hours). All timing uses requestAnimationFrame delta-time accumulation, so the simulation stays consistent regardless of frame rate drops.