Satellite Ring

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A satellite ring is a spatial configuration formed by placing multiple satellites at equal intervals along the same circular orbit. Satellite rings are the fundamental building blocks of satellite constellations, and multiple satellite rings can be combined to form a complete constellation system.

Core Elements

Satellite Ring Parameters

Given kk satellites uniformly distributed on a circular orbit at altitude hh, the subsatellite point angular separation between adjacent satellites is:

l=360°kl = \frac{360°}{k}

Continuous Coverage Condition

The condition for overlap between adjacent satellite coverage areas is:

d>l2=180°kd > \frac{l}{2} = \frac{180°}{k}

where dd is the coverage angle of a single satellite.

Satellite Ring Coverage Band Width

cos⁡dr=cos⁡dcos⁡(180°/k)\cos d_r = \frac{\cos d}{\cos(180°/k)}

where drd_r is the equivalent coverage angle of the satellite ring. The coverage band width is greater than that of a single satellite.

Blind Spot Analysis

The region outside the satellite ring coverage band is called the blind spot. The declination range of the left blind spot:

δLmax⁡=180°−(i+dr),δLmin⁡=dr−i\delta_{L\max} = 180° - (i + d_r), \quad \delta_{L\min} = d_r - i

The half-width of the blind spot in the right ascension direction:

sin⁡αr=cos⁡drsin⁡i\sin\alpha_r = \frac{\cos d_r}{\sin i}

Blind Spot Elimination Conditions

A constellation composed of multiple satellite rings can achieve global coverage when blind spots do not overlap:

  • Latitude direction: 90°−dr≤i≤dr90° - d_r \leq i \leq d_r
  • Longitude direction: arcsin⁡(cos⁡drsin⁡i)<180°P\arcsin\left(\frac{\cos d_r}{\sin i}\right) < \frac{180°}{P}

where PP is the number of satellite rings.

Application Value

Satellite rings are the fundamental building blocks of constellation design. By analyzing the coverage characteristics and blind spot distribution of a single satellite ring, one can determine the minimum number of orbital planes and satellites per plane required for a constellation. Three equally spaced satellites in geostationary orbit forming a satellite ring above the equator can achieve global communication coverage except for polar regions -- this is a classic example of satellite ring application.

References

  • 郑伟, 安雪滢, 周祥, 何睿智. 空天飞行力学[M]. 国防科技大学, 2026.
  • 贾沛然, 陈克俊, 等. 远程火箭弹道学[M]. 国防科技大学出版社.