Continuous Coverage

Author: Tianjiang Says

Website: https://cislunarspace.cn

Definition

Continuous Coverage (CP) is a metric measuring the coverage performance of a single satellite observing a target orbit, defined as the ratio of covered arc length to the total orbit length.

Calculation

CP=1−SaveCP = 1 - S_{ave}

where SaveS_{ave} is the average obscuration ratio caused by the Moon over one orbital period:

Save=∑i=1,2...Ls,iLnS_{ave} = \frac{\sum_{i=1,2...} \frac{L_{s,i}}{L}}{n}

  • Ls,iL_{s,i}: obscured arc length when observing the target orbit from observation point ii
  • LL: total orbit length of the target orbit over one period
  • nn: total number of discrete observation points

The obscuration angle θ\theta is calculated as:

θ=2⋅arcsin⁡(rmoonl1)\theta = 2 \cdot \arcsin\left(\frac{r_{moon}}{l_1}\right)

where l1l_1 is the distance from the observation satellite to the Moon's center, and rmoonr_{moon} is the Moon's radius.

Simulation Results

For DRO orbits designed for situational awareness missions:

Observing DRO-M:

  • CR3BP model: maximum CP = 99.1%, minimum CP = 98.1%
  • Ephemeris model: maximum CP = 99.1%, minimum CP = 98.1%

Observing South/North family NRHO:

  • Maximum CP = 100%, minimum CP = 98.5%

References

  • Chen Yuju. DRO Orbit Design and Control Research for Cislunar Space Situation Awareness[D]. 2024.