How do I install the Sun Synchronous Inclination skill?

Run npx skillmds@latest add ashfordeou/sun-synchronous-inclination in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

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Is Sun Synchronous Inclination free to use?

Yes. Installing skills from SkillMD is free. This skill is licensed under Apache-2.

Who published Sun Synchronous Inclination?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Sun Synchronous Inclination by ashfordeou

Name: Sun Synchronous Inclination
Author: ashfordeOU

Sun Synchronous Inclination

Use when you must compute the sun-synchronous orbital inclination from altitude for a circular Earth orbit: determine the orbital mean motion from the semimajor axis, evaluate the J2 nodal regression rate, solve the sun-synchronous condition cos(i) = -omega_dot_desired / (1.5 n J2 (Re/a)^2), and produce the inclination in radians and degrees. Produces the altitude, semimajor axis, mean motion, and inclination that gate dawn-dusk and local-time-of-ascending-node orbit selection. Trigger: sun-synchronous orbit, inclination, nodal regression, ascending node, local solar time, dawn-dusk, j2.

ashfordeOU Updated Sep 17, 2026

File contents

Sun-Synchronous Inclination (space-systems/orbit-mechanics/sun-synchronous-inclination)

Use when the task is sun-synchronous orbit design: compute the mean motion, the J2 nodal regression rate, and the inclination that makes the ascending node precess with the sun, keeping the local solar time fixed.

Domain quick reference

Units: altitude in km in, meters internally, mean motion in rad/s, inclination in RADIANS out, degrees for display.
Semimajor axis: a = Re + altitude_km * 1000 m (altitude in km converted to m), with Re = 6371000 m and mu = 3.986004418e14 m^3/s^2.
Mean motion: n = sqrt(mu / a^3) rad/s.
Nodal regression: om_dot = -1.5 * n * J2 * (Re / a)^2 * cos(i) rad/s, with J2 = 1.08262668e-3.
Sun-synchronous condition: cos(i) = -omega_dot_desired / (1.5 * n * J2 * (Re / a)^2), omega_dot_desired = 2 pi / 365.2421897 / 86400 rad/s, one revolution per tropical year.
At 500 km altitude the solution is 97.39 deg: sun-synchronous orbits are always retrograde.
Above roughly 6000 km no sun-synchronous inclination exists: the required cos(i) leaves [-1, 1] and the solver raises ValueError.

Workflow

Take the circular orbit altitude in km.
Compute the semimajor axis and mean motion with orbital_mean_motion.
Solve the inclination with sun_synchronous_inclination (radians).
Check the regression rate with nodal_regression_rate.
Pack the full solution with sun_synchronous_properties.
Gate the orbit selection on the 97-99 deg retrograde band for LEO.

Pitfalls

Feeding degrees into radian-based functions.
Negative altitude or an inclination outside [0, pi] raising ValueError.
Forgetting that high altitudes have no solution: the solver raises instead of returning a nonsense angle.
Misreading the sign: the regression rate is negative for prograde orbits, and the sun-synchronous inclination is always above 90 degrees.

Behavior contract (gate 3)

The mean motion, nodal regression, and inclination logic is exercised by the gate 3 contract test: scripts/test_sun_synchronous.py against scripts/sun_synchronous_logic.py (stdlib unittest, offline). Run: python3 scripts/test_sun_synchronous.py

Compliance

Standards referenced, not reproduced: ECSS series text is copyright ESA; the J2 nodal regression and sun-synchronous condition are common astrodynamics, summary-only per standards-map.yaml (ecss is a free ESA download).
compliance: STANDARDS-REF, gated: false.

---name: sun-synchronous-inclinationdescription: Use when you must compute the sun-synchronous orbital inclination from altitude for a circular Earth orbit: determine the orbital mean motion from the semimajor axis, evaluate the J2 nodal regression rate, solve the sun-synchronous condition cos(i) = -omega_dot_desired / (1.5 n J2 (Re/a)^2), and produce the inclination in radians and degrees. Produces the altitude, semimajor axis, mean motion, and inclination that gate dawn-dusk and local-time-of-ascending-node orbit selection. Trigger: sun-synchronous orbit, inclination, nodal regression, ascending node, local solar time, dawn-dusk, j2.license: Apache-2.0---# Sun-Synchronous Inclination (space-systems/orbit-mechanics/sun-synchronous-inclination)Use when the task is sun-synchronous orbit design: compute themean motion, the J2 nodal regression rate, and the inclination thatmakes the ascending node precess with the sun, keeping the localsolar time fixed.## Domain quick reference- Units: altitude in km in, meters internally, mean motion in rad/s, inclination in RADIANS out, degrees for display.- Semimajor axis: a = Re + altitude_km * 1000 m (altitude in km converted to m), with Re = 6371000 m and mu = 3.986004418e14 m^3/s^2.- Mean motion: n = sqrt(mu / a^3) rad/s.- Nodal regression: om_dot = -1.5 * n * J2 * (Re / a)^2 * cos(i) rad/s, with J2 = 1.08262668e-3.- Sun-synchronous condition: cos(i) = -omega_dot_desired / (1.5 * n * J2 * (Re / a)^2), omega_dot_desired = 2 pi / 365.2421897 / 86400 rad/s, one revolution per tropical year.- At 500 km altitude the solution is 97.39 deg: sun-synchronous orbits are always retrograde.- Above roughly 6000 km no sun-synchronous inclination exists: the required cos(i) leaves [-1, 1] and the solver raises ValueError.## Workflow1. Take the circular orbit altitude in km.2. Compute the semimajor axis and mean motion with orbital_mean_motion.3. Solve the inclination with sun_synchronous_inclination (radians).4. Check the regression rate with nodal_regression_rate.5. Pack the full solution with sun_synchronous_properties.6. Gate the orbit selection on the 97-99 deg retrograde band for LEO.## Pitfalls- Feeding degrees into radian-based functions.- Negative altitude or an inclination outside [0, pi] raising ValueError.- Forgetting that high altitudes have no solution: the solver raises instead of returning a nonsense angle.- Misreading the sign: the regression rate is negative for prograde orbits, and the sun-synchronous inclination is always above 90 degrees.## Behavior contract (gate 3)The mean motion, nodal regression, and inclination logic isexercised by the gate 3 contract test:scripts/test_sun_synchronous.py againstscripts/sun_synchronous_logic.py (stdlib unittest, offline). Run:python3 scripts/test_sun_synchronous.py## Compliance- Standards referenced, not reproduced: ECSS series text is copyright ESA; the J2 nodal regression and sun-synchronous condition are common astrodynamics, summary-only per standards-map.yaml (ecss is a free ESA download).- compliance: STANDARDS-REF, gated: false.

Frequently asked questions