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Sun-Synchronous Orbit Designer

Inputs

Select the input parameter to use for the calculation.

km

Orbital altitude above Earth's equatorial radius.

Outputs

Prograde inclination
81.812 deg
Retrograde inclination
98.188 deg
Orbit altitude
700 km
Semi-major axis
7078.137 km
Orbital period
98.773 min
Nodal precession rate
-0.985645 deg/day

Methodology

Sun-Synchronous Orbit Condition

A sun-synchronous orbit requires that the nodal precession rate matches Earth's orbital angular velocity around the Sun. The J2-induced RAAN precession is given by:

Ω ˙ = − 3 2 · J 2 · n · R e 2 a 2 · cos ( i )

where Ω̇ is the nodal precession rate, J₂ is Earth's second zonal harmonic coefficient, n is the mean motion, Rₑ is Earth's radius, a is the semi-major axis, and i is the inclination.

Inclination Calculation

To achieve sun-synchronicity, the precession rate must equal Earth's orbital angular velocity (approximately -360° per year). Solving for inclination:

cos ( i ) = Ω ˙ sun sync − 3 2 · J 2 · n · R e 2 a 2

The inclination is then calculated as i = arccos(cos(i)), which typically results in inclinations greater than 90° (retrograde orbits).

Orbital Period

The orbital period for a circular orbit is calculated using Kepler's third law:

T = 2 π a 3 μ

where T is the orbital period, a is the semi-major axis, and μ is Earth's standard gravitational parameter (3.986004418 × 10¹⁴ m³/s²).

Instructions

Inputs

Input instructions are shown below.

  1. Altitude: Enter the desired orbital altitude in kilometers above Earth's equatorial radius. Typical sun-synchronous orbits range from 500 km to 1000 km.

Outputs

The tool calculates the following sun-synchronous orbit properties:

  1. Required inclination: The orbital inclination (in degrees) required to achieve sun-synchronous precession at the specified altitude.
  2. Orbit altitude: Echo of the input altitude for reference.
  3. Semi-major axis: The distance from Earth's center to the spacecraft in a circular sun-synchronous orbit.
  4. Orbital period: The time required for one complete orbit around Earth.
  5. Nodal precession rate: The rate at which the orbital plane rotates to maintain sun-synchronicity (approximately -360° per year).

Notes

Items to consider during calculation:

  1. Sun-synchronous orbits are designed to maintain a constant angle between the orbital plane and the Sun, ensuring consistent lighting conditions.
  2. The required inclination increases with altitude. For altitudes around 700 km, the inclination is typically around 98 degrees.
  3. This calculation assumes a circular orbit and uses Earth's J2 gravitational perturbation to achieve sun-synchronicity.
  4. The nodal precession rate is fixed at approximately -360° per year to match Earth's orbital motion around the Sun.