Sensor Geometry: how a satellite actually sees the ground
Delta-V Academy / Learn / Lesson 6
A satellite's view shrinks as it climbs and stretches as it tilts. The geometry sets what's possible.
Every satellite sensor has a finite field of view (FOV). That FOV maps to a finite footprint on Earth. The exact size of that footprint depends on the sensor's look angle, the satellite's altitude, and the geometry of intersecting that FOV cone with a curved Earth. Understanding this geometry is the difference between a satellite that covers New York and one that covers the entire eastern seaboard. It's also why every reconnaissance and communications satellite design starts with sensor geometry, not the sensor itself.
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What you'll learn
- How to compute a satellite's horizon limit from any altitude
- Why higher orbits see more ground per second but with less detail
- The difference between field of view (FOV) and field of regard (FOR)
- How nadir-pointing vs slewing sensors trade off coverage area for revisit rate
- Slant range math: distance from satellite to a point on the ground
The horizon limit
From any altitude h above a sphere of radius R, the horizon is at a distance d = √(2Rh + h²). For Earth (R = 6,378 km) at h = 400 km (ISS altitude), the horizon is 2,294 km away. At h = 35,786 km (GEO), the horizon is 41,679 km. The maximum slant range a satellite can see is set by this geometry. Anything beyond the horizon is below the satellite's line of sight and physically invisible.
Field of view vs field of regard
Field of view (FOV) is the angle the sensor sees at any instant. A 10° FOV imaging sensor sees a circle on the ground sized by (FOV/2) × altitude × 2 ≈ 70 km from a 400 km LEO. Field of regard (FOR) is the total angle the sensor can be slewed through. A satellite with a 10° FOV but a 60° FOR can image any point within a much larger swath by pointing the sensor toward it. FOV sets instantaneous coverage; FOR sets accessible coverage. Both matter for design.
Slant range and look angle
When a satellite looks at a point on Earth not directly below it, the line of sight is called the slant range. At nadir (straight down) the slant range equals the altitude. As you tilt off-nadir, slant range grows and the angle between the sensor and the ground (look angle) decreases. Once look angle reaches zero, you're at the horizon and can't see further. The math: slant_range = √(altitude² + ground_distance² + 2 × altitude × R × (1 − cos(central_angle))).
Frequently asked questions
What is a satellite's field of view?
The angular extent of what the sensor can observe at any instant. A wide FOV means a larger footprint on the ground but lower spatial resolution per pixel. A narrow FOV means smaller footprint but higher resolution.
How far can a satellite at the ISS altitude see?
About 2,294 km to the horizon, assuming an unobstructed view. The visible footprint depends on the sensor FOV; a narrow sensor sees only directly below, a wide sensor sees out to the horizon.
What is the difference between FOV and FOR?
Field of view (FOV) is the instantaneous angular coverage. Field of regard (FOR) is the total angle a sensor can be slewed across. A satellite with a small FOV but large FOR can image many different points by pointing the sensor at each, but only one at a time.
Why do higher orbits cover more area?
Because the horizon distance grows roughly as the square root of altitude. At 400 km, horizon is 2,294 km. At 20,200 km (GPS), horizon is 17,580 km. The footprint a sensor with the same FOV draws on Earth grows proportionally.
What is nadir pointing?
Pointing the sensor straight down, toward the point on Earth directly below the satellite. Nadir is the simplest pointing mode and gives the shortest slant range, highest resolution, and least atmospheric distortion. Most Earth-imaging satellites operate nadir-pointed by default.
Related lessons
- Lesson 7: Orbital Regimes — Four altitude bands. Four totally different design philosophies.
- Lesson 9: Sensor Archetypes — Where the sensor looks defines what the satellite can do.
- Lesson 10: Space Domain Awareness — Radars, telescopes, and tracking algorithms. The architecture that keeps orbital traffic safe.
Open it in the simulator
Delta-V Academy is a free interactive orbital mechanics simulator that runs entirely in your browser. The 10-lesson curriculum covers everything from these basics through space domain awareness, with three difficulty levels (novice, intermediate, advanced) plus a kid-friendly mode. Launch the simulator and try Lesson 6 interactively.
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