Repeat Ground Track Orbit

Author: Tianjiang Shuo
Website: https://cislunarspace.cn

Definition

A repeat ground track orbit is an orbit in which the satellite's subsatellite track repeats with a fixed period. In $D$ sidereal days, the satellite completes $N$ revolutions before the subsatellite track begins to repeat, satisfying $24/T = N/D$ , where $T$ is the orbital period in sidereal time. If $D=1$ , the track repeats within 1 sidereal day and the orbit is called a repeat ground track orbit; if $D>1$ and $N$ and $D$ are coprime, it is called a quasi-repeat ground track orbit.

Core Elements

Repeat Criterion

\frac{24}{T} = \frac{N}{D}

where $N$ and $D$ are the minimum number of revolutions and sidereal days required for the subsatellite track to repeat.

Repeat Ground Track Orbit Characteristics

Characteristic	Description
Repeat period	$D=1$ sidereal day
Inter-revolution spacing	$L = 360°/N = 15°T$
Revolution number sequence	Westward order: 0-1-2-...-(N-1)
Longitude span	Shifts westward by $15°T$ per revolution, equal to the inter-revolution spacing

Quasi-Repeat Ground Track Orbit Characteristics

The subsatellite track of a quasi-repeat ground track orbit does not repeat daily but repeats after $D$ sidereal days. The revolution numbers are no longer in sequential order and must be determined by solving a linear Diophantine equation for adjacent revolution numbers:

D \cdot n_W - N \cdot d_W = 1 \quad (\text{westward neighbor})

D \cdot n_E - N \cdot d_E = -1 \quad (\text{eastward neighbor})

Combination with Sun-Synchronous Orbits

When a repeat/quasi-repeat ground track orbit simultaneously satisfies the sun-synchronous constraint $\dot{\Omega} = \omega_S$ , it is called a sun-synchronous (quasi-) repeat ground track orbit. In this case, the nodal day equals the mean solar day:

T = \frac{D^* \text{ mean solar days}}{N}

Application Value

Repeat ground track orbits enable satellites to periodically re-observe the same ground areas, which is significant for Earth resource observation, weather monitoring, and reconnaissance missions. Quasi-repeat ground track orbits achieve a balance between coverage period and coverage uniformity through proper design of the $N$ and $D$ ratio. Sun-synchronous quasi-repeat ground track orbits are currently the most commonly used orbit type for Earth observation satellites.

References

Zheng W, An X Y, Zhou X, He R Z. Aerospace Flight Mechanics[M]. National University of Defense Technology, 2026.
Jia P R, Chen K J, et al. Long-Range Rocket Ballistics[M]. National University of Defense Technology Press.