Inclination from the J2 nodal rate
The first-order nodal precession of an Earth orbit is Ω̇ = −(3/2) n J2 (R_eq / a)² cos i / (1−e²)², with n = √(μ / a³). Setting Ω̇ to the mean apparent solar rate, 360° / 365.24219 days ≈ 0.985647 °/day, and solving for i gives a retrograde inclination (cos i is negative). At 800 km, circular, with J2 = 1.08263×10⁻³ and R_eq = 6,378.137 km, that inclination is about 98.60°, and the period is about 101 minutes. Higher altitudes need a slightly shallower (closer to 90°) inclination because n and (R/a)² both fall off.
Higher-order gravity, drag, and lunisolar perturbations all move a real SSO off this first-order i. Use an official ephemeris or a mission-design tool for a frozen or repeating ground-track orbit. Geostationary radius, circular speed, and vis-viva are on the orbital velocity and period page; a nadir footprint is on satellite FOV.
Sources
- Vallado, Fundamentals of Astrodynamics and Applications (J2 nodal precession and sun-synchronous inclination).
- Wertz and Larson, Space Mission Analysis and Design.
- IERS / WGS-84 Earth constants (μ, R_eq, J2 ≈ 1.08263×10⁻³).
Frequently asked questions
Why is the inclination more than 90°?
J2 regresses the nodes of a prograde orbit (i < 90°). A sun-synchronous orbit needs the nodes to advance with the mean Sun, so the orbit is slightly retrograde.
Can I use this for Mars or the Moon?
Not with the default constants. The formula is general, but this page is wired to Earth’s μ, J2, and equatorial radius.
Is this the same as a geostationary orbit?
No. A geostationary orbit is equatorial and has a one-day period. Sun-synchronous orbits are usually low, polar, and retrograde. Geostationary radius is on the orbital-velocity page.