---
title: Visibility, access and obstruction
tags: visibility, access, elevation, horizon, obstruction, availability
summary: The difference between a satellite being overhead and a user being able to use it, and what the gap between them is called.
---

# Visibility, access and obstruction

A satellite in view is not a satellite in use. The distinction is the
difference between coverage and availability, and almost every disappointing
service is explained by it.

## Definition

**Visibility** is the geometric condition: the satellite is above the local
horizon. **Access** is the condition that includes the link: the elevation is
high enough for the link to close, the pointing can be resolved, and the
propagation is acceptable. **Availability** is the fraction of the time an
access is available to a particular user.

**Obstruction** is anything in the way: terrain, a building, another vehicle,
and in the worst case the payload of a satellite in a higher orbit passing
across the line of sight.

## Mathematics

### The geometric pass

A satellite in a circular orbit at semi-major axis `a` passes a latitude
`phi` with a maximum elevation `e_max` that follows from the geometry,

```text
e_max such that the elevation is arctan of the perpendicular
        distance from the observer to the orbit plane, divided
        by the distance along the line of sight
```

with two limits worth naming. At the pole a satellite in an inclined orbit
reaches only `90 - inclination` degrees of elevation at best, so a
high-inclination constellation has poor coverage at high latitude from any
single satellite, and relies on many satellites rather than on high ones.

At the equator a satellite in an equatorial orbit passes directly overhead and
the elevation approaches 90 degrees, which is the best case in the system.

### The elevation mask

The link budget requires a minimum elevation because below it the path
length grows, the pointing becomes coarse, and the Doppler rate becomes
large enough that tracking is harder. The mask is a design parameter
rather than a physical one, and choosing a lower mask increases coverage and
degrades the link on every pass, which is a trade rather than a free
choice.

### Obstruction and its statistics

Terrestrial obstruction is binary for a ground user, so the relevant figure
is a **probability of availability** rather than an average. For a satellite
obstruction, the relevant figure is the probability that an intersection
occurs during an access, which depends on the relative motion and on the
angular separation of the two orbits.

## Unit conventions

- Elevation and azimuth in degrees when describing a pass, radians in any
  computation.
- Access time in seconds; availability as a fraction or as a percentage.
- Angles of separation in degrees.

## Applicability

The gap between coverage and availability is large and is usually the whole
story of a service complaint. A constellation may have 100 percent
geometric coverage over a country and a service that is available for 96
percent of the time, and the remaining four percent is what a user
remembers.

The obstruction term is what makes the ground segment matter. The same
constellation with a different set of ground station sites has a different
availability, and no amount of satellites moves it, because the obstruction
is local.

A low elevation mask raises the headline coverage number and lowers the
per-pass link margin at the same time. Those two effects are usually not
reported together, which is why a coverage figure without a mask is not
interpretable.

## Standards

- Elevation mask conventions and availability reporting: not standardised;
  the relevant practice is the regulatory service definition in the
  licensing.

## See also

- [[constellations]] for the coverage figure this is measured against
- [[link-budget]] for why the mask is not zero
- [[handover-and-routing]] for what happens between accesses