J2 Orbit Precession & SSO Calculator
Astrodynamics & Earth observation: Compute Right Ascension of the Ascending Node (RAAN) precession rate, apsidal drift, and exact Sun-Synchronous Orbit inclination from Earth’s $J_2$ gravitational potential.
Orbit Altitude & Geometry
Standard SSO ~500–800 km
Near-circular e ~0.001 for frozen SSO
Earth J₂ Geopotential Constant
Earth's equatorial bulge ($J_2 = 1.08263 \times 10^{-3}$) exerts a torque that precesses the orbital plane (RAAN) at rate:
$$\dot{\Omega} = -\frac{3}{2} J_2 \left(\frac{R_E}{p}\right)^2 \bar{n} \cos(i)$$
To match Earth's annual rotation around the Sun, $\dot{\Omega}$ must equal $+0.9856^\circ/\text{day}$ ($360^\circ / 365.25\text{ days}$).
Precession & SSO Alignment
Orbit Inclination (i)
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RAAN Precession (dΩ/dt)
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Apsidal Precession (Argument of Perigee)
Apsidal Drift (dω/dt)
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Perigee rotation rate
Critical Inclination Status
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dω/dt = 0 at 63.4° / 116.6°
Orbital Geometry Metrics
Orbital Period (T):
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Orbits Per Day:
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Sun-Synchronous Viability:
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