Sun-Synchronous Orbit Designer

Inputs

Calculation method

Altitude

Results

Inclination 98.188deg

Altitude 700km

Semi-major axis 7,078km

Orbital period 98.8 min

Orbital velocity 7.504km/s

Highest latitude 81.81deg

Revolutions per day 14.58

Ground-track shift per orbit 2,749km

Nodal precession rate +0.9856deg/day

Method

A circular Earth orbit whose plane precesses under J2 at exactly the Sun's mean rate, solved for the inclination at a given altitude or the altitude at a given inclination.

Ω̇ = −(3/2)·J₂·n·(R/a)²·cos i = Ω̇_☉ The oblate Earth swings the orbit plane around at the Sun’s rate, so the orbit keeps the same local time over the ground all year.

Derivation

Set the rate to match The mean Sun moves east along the equator once per tropical year. A sun-synchronous orbit’s ascending node has to move east at the same rate, so the angle between the orbit plane and the Sun never changes. Ω̇_☉ = 360° / 365.2422 d = +0.9856°/day

Solve for the inclination Earth’s equatorial bulge drags the node around at a rate set by the orbit radius and the cosine of the inclination. Eastward precession needs a negative cosine, which is why every Earth sun-synchronous orbit is retrograde. a = R + h, cos i = −Ω̇_☉ / ((3/2)·J₂·n·(R/a)²)

…or for the altitude Run the same condition the other way. Precession weakens as a^(−7/2), so an inclination near 90° needs an orbit below the surface (the tool refuses anything under about 95.7°), and 180° is the highest orbit that works, at about 5,974 km. a = ((3/2)·J₂·R²·√μ·(−cos i) / Ω̇_☉)^2/7

Size the orbit With the radius fixed, the period and speed follow from the circular two-body orbit. Putting the solved orbit back into the precession equation reproduces +0.9856°/day, the check shown in the results. T = 2π·√(a³/μ), v = √(μ/a)

Read off the coverage The ground track reaches latitude 180° − i and misses the caps beyond it. Earth turns 360.99° a sidereal day while the plane follows the Sun 0.99° east, so under the orbit the ground slips west by exactly one full turn per solar day, split across however many orbits fit into it. φ_max = 180° − i, Δλ = 360°·T / 1 solar day

Symbols

Input	Description	Unit
h	Orbit altitude above the equatorial radius (altitude method)	km
i	Orbit inclination (inclination method)	deg
μ	Earth’s gravitational parameter	km³/s²
R	Earth’s equatorial radius	km
J₂	Earth’s oblateness coefficient
Ω̇_☉	Mean motion of the Sun: the rate to match	°/day

Derived	Description	Unit
a	Orbit radius: R + h	km
n	Mean motion: √(μ/a³)	rad/s
Ω̇	Nodal precession rate, positive east	°/day
T	Orbital period: 2π/n	s
v	Circular orbital velocity	km/s
φ_max	Highest latitude overflown: 180° − i	deg
Δλ	Westward ground-track shift per orbit	deg

Reference values

First-order figures for sanity-checking inputs.

Altitude km	Inclination deg	Period
400	97.03	92.6 min
500	97.40	94.6 min
600	97.79	96.7 min
700	98.19	98.8 min
800	98.60	100.9 min
1,000	99.48	105.1 min
1,500	101.96	116.0 min

Constant	Symbol	Value
Gravitational parameter	μ	398,614 km³/s²
Equatorial radius	R	6,378.137 km
Oblateness (EGM2008)	J₂	1.08263 × 10⁻³
Mean Sun motion	Ω̇☉	0.985647 °/day

This is the secular J2 condition for a circular Earth orbit: no eccentricity, no higher gravity harmonics, no drag and no solar or lunar perturbations. Operational sun-synchronous missions fly slightly eccentric frozen orbits and trim their inclination through the mission, so a published inclination can differ from these figures in the second decimal place. Below about 300 km drag decays the orbit faster than the plane can be maintained. The tool does not compute local time of the ascending node, eclipse, or a repeating ground track. Treat these results as first-pass sizing, not a mission analysis.